Gmsh

Gmsh Reference Manual

The documentation for Gmsh 4.11.1
A finite element mesh generator with built-in pre- and post-processing facilities

21 December 2022

Christophe Geuzaine
Jean-François Remacle
Copyright
c 1997-2022 Christophe Geuzaine, Jean-François Remacle

Permission is granted to make and distribute verbatim copies of this manual provided the copy-
right notice and this permission notice are preserved on all copies.
 i

Short Contents
Obtaining Gmsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Copying conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Reporting a bug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1 Overview of Gmsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Gmsh tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Gmsh graphical user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 Gmsh command-line interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5 Gmsh scripting language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Gmsh application programming interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7 Gmsh options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8 Gmsh mesh size fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
9 Gmsh plugins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
10 Gmsh file formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
A Compiling the source code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
B Information for developers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
C Frequently asked questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
D Version history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
E Copyright and credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
F License . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
Concept index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
Syntax index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
 iii

Table of Contents

Obtaining Gmsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Copying conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Reporting a bug . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1 Overview of Gmsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1 Geometry module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Mesh module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Choosing the right unstructured algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Specifying mesh element sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 Elementary entities vs. physical groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Solver module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Post-processing module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 What Gmsh is pretty good at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 . . . and what Gmsh is not so good at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 Installing and running Gmsh on your computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Gmsh tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 t1: Geometry basics, elementary entities, physical groups . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 t2: Transformations, extruded geometries, volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 t3: Extruded meshes, ONELAB parameters, options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 t4: Built-in functions, holes in surfaces, annotations, entity colors . . . . . . . . . . . . . . . . . 23
2.5 t5: Mesh sizes, macros, loops, holes in volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 t6: Transfinite meshes, deleting entities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.7 t7: Background meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.8 t8: Post-processing, image export and animations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.9 t9: Plugins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.10 t10: Mesh size fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.11 t11: Unstructured quadrangular meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.12 t12: Cross-patch meshing with compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.13 t13: Remeshing an STL file without an underlying CAD model . . . . . . . . . . . . . . . . . . 43
2.14 t14: Homology and cohomology computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.15 t15: Embedded points, lines and surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.16 t16: Constructive Solid Geometry, OpenCASCADE geometry kernel . . . . . . . . . . . . . 48
2.17 t17: Anisotropic background mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.18 t18: Periodic meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.19 t19: Thrusections, fillets, pipes, mesh size from curvature . . . . . . . . . . . . . . . . . . . . . . . . 53
2.20 t20: STEP import and manipulation, geometry partitioning . . . . . . . . . . . . . . . . . . . . . 55
2.21 t21: Mesh partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.22 x1: Geometry and mesh data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.23 x2: Mesh import, discrete entities, hybrid models, terrain meshing . . . . . . . . . . . . . . . 61
2.24 x3: Post-processing data import: list-based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.25 x4: Post-processing data import: model-based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.26 x5: Additional geometrical data: parametrizations, normals, curvatures . . . . . . . . . . 70
2.27 x6: Additional mesh data: integration points, Jacobians and basis functions . . . . . . 72
2.28 x7: Additional mesh data: internal edges and faces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
iv Gmsh 4.11.1

3 Gmsh graphical user interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.1 Mouse actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2 Keyboard shortcuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4 Gmsh command-line interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Gmsh scripting language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.1 General scripting commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.1 Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.2 Floating point expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.3 String expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.1.4 Color expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1.5 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1.6 Built-in functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1.7 User-defined macros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.1.8 Loops and conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.1.9 Other general commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2 Geometry scripting commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.1 Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.2 Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.3 Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2.4 Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.5 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2.6 Boolean operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2.7 Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2.8 Other geometry commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.3 Mesh scripting commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.3.1 Mesh element sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.3.2 Structured grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.3.3 Other mesh commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.4 Post-processing scripting commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6 Gmsh application programming interface . . . . . . . . . . . . . . . . . 123

6.1 Namespace gmsh: top-level functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.2 Namespace gmsh/option: option handling functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.3 Namespace gmsh/model: model functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.4 Namespace gmsh/model/mesh: mesh functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.5 Namespace gmsh/model/mesh/field: mesh size field functions . . . . . . . . . . . . . . . . . . . 167
6.6 Namespace gmsh/model/geo: built-in CAD kernel functions . . . . . . . . . . . . . . . . . . . . . 170
6.7 Namespace gmsh/model/geo/mesh: built-in CAD kernel meshing constraints . . . . . 179
6.8 Namespace gmsh/model/occ: OpenCASCADE CAD kernel functions . . . . . . . . . . . . 182
6.9 Namespace gmsh/model/occ/mesh: OpenCASCADE CAD kernel meshing constraints
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.10 Namespace gmsh/view: post-processing view functions . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.11 Namespace gmsh/view/option: view option handling functions . . . . . . . . . . . . . . . . . 206
6.12 Namespace gmsh/plugin: plugin functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
6.13 Namespace gmsh/graphics: graphics functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
6.14 Namespace gmsh/fltk: FLTK graphical user interface functions . . . . . . . . . . . . . . . . 209
6.15 Namespace gmsh/parser: parser functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
6.16 Namespace gmsh/onelab: ONELAB server functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.17 Namespace gmsh/logger: information logging functions . . . . . . . . . . . . . . . . . . . . . . . . 217
 v

7 Gmsh options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

7.1 General options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.2 Print options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
7.3 Geometry options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
7.4 Mesh options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
7.5 Solver options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
7.6 Post-processing options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
7.7 Post-processing view options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

8 Gmsh mesh size fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

9 Gmsh plugins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

10 Gmsh file formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

10.1 MSH file format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
10.2 Node ordering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
10.2.1 Low order elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
10.2.2 High-order elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
10.3 Legacy formats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
10.3.1 MSH file format version 2 (Legacy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
10.3.2 MSH file format version 1 (Legacy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
10.3.3 POS ASCII file format (Legacy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
10.3.4 POS binary file format (Legacy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

Appendix A Compiling the source code . . . . . . . . . . . . . . . . . . . . 369

Appendix B Information for developers . . . . . . . . . . . . . . . . . . . . 373

B.1 Source code structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
B.2 Coding style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
B.3 Adding a new option. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

Appendix C Frequently asked questions . . . . . . . . . . . . . . . . . . . . 375

C.1 The basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
C.2 Installation problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
C.3 General questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
C.4 Geometry module. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
C.5 Mesh module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
C.6 Solver module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
C.7 Post-processing module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

Appendix D Version history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383

Appendix E Copyright and credits. . . . . . . . . . . . . . . . . . . . . . . . . . 405

Appendix F License . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

Concept index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

Syntax index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419

Obtaining Gmsh 1

Obtaining Gmsh
The source code and pre-compiled binary versions of Gmsh (for Windows, macOS and Linux)
can be downloaded from https://gmsh.info. Gmsh packages are also directly available in
various Linux and BSD distributions (Debian, Ubuntu, FreeBSD, ...).
If you use Gmsh, we would appreciate that you mention it in your work by citing the follow-
ing paper: C. Geuzaine and J.-F. Remacle, Gmsh: a three-dimensional finite element mesh
generator with built-in pre- and post-processing facilities. International Journal for Numerical
Methods in Engineering, Volume 79, Issue 11, pages 1309-1331, 2009. A preprint of that pa-
per as well as other references and the latest news about Gmsh development are available on
https://gmsh.info.
Copying conditions 3

Copying conditions
Gmsh is free software; this means that everyone is free to use it and to redistribute it on a
free basis. Gmsh is not in the public domain; it is copyrighted and there are restrictions on its
distribution, but these restrictions are designed to permit everything that a good cooperating
citizen would want to do. What is not allowed is to try to prevent others from further sharing
any version of Gmsh that they might get from you.
Specifically, we want to make sure that you have the right to give away copies of Gmsh, that
you receive source code or else can get it if you want it, that you can change Gmsh or use pieces
of Gmsh in new free programs, and that you know you can do these things.
To make sure that everyone has such rights, we have to forbid you to deprive anyone else of
these rights. For example, if you distribute copies of Gmsh, you must give the recipients all the
rights that you have. You must make sure that they, too, receive or can get the source code.
And you must tell them their rights.
Also, for our own protection, we must make certain that everyone finds out that there is no
warranty for Gmsh. If Gmsh is modified by someone else and passed on, we want their recipients
to know that what they have is not what we distributed, so that any problems introduced by
others will not reflect on our reputation.
The precise conditions of the license for Gmsh are found in the General Public
License that accompanies the source code (see Appendix F [License], page 409).
Further information about this license is available from the GNU Project webpage
https://www.gnu.org/copyleft/gpl-faq.html. Detailed copyright information can be found
in Appendix E [Copyright and credits], page 405.
If you want to integrate parts of Gmsh into a closed-source software, or want to sell a modified
closed-source version of Gmsh, you will need to obtain a different license. Please contact us
directly for more information.
Reporting a bug 5

Reporting a bug
If, after reading this reference manual, you think you have found a bug in Gmsh, please file an
issue on https://gitlab.onelab.info/gmsh/gmsh/issues. Provide as precise a description
of the problem as you can, including sample input files that produce the bug. Don’t forget to
mention both the version of Gmsh and your operation system.
See Appendix C [Frequently asked questions], page 375, and the bug tracking system to see
which problems we already know about.
Chapter 1: Overview of Gmsh 7

1 Overview of Gmsh
Gmsh is a three-dimensional finite element mesh generator with a build-in CAD engine and
post-processor. Its design goal is to provide a fast, light and user-friendly meshing tool with
parametric input and flexible visualization capabilities.
Gmsh is built around four modules (geometry, mesh, solver and post-processing), which can be
controlled with the graphical user interface (GUI; see Chapter 3 [Gmsh graphical user interface],
page 77), from the command line (see Chapter 4 [Gmsh command-line interface], page 83), using
text files written in Gmsh’s own scripting language (‘.geo’ files; see Chapter 5 [Gmsh scripting
language], page 89), or through the C++, C, Python, Julia and Fortran application programming
interface (API; see Chapter 6 [Gmsh application programming interface], page 123).
A brief description of the four modules is given hereafter, before an overview of what Gmsh does
best (... and what it is not so good at), and some practical information on how to install and
run Gmsh on your computer.

1.1 Geometry module

A model in Gmsh is defined using its Boundary Representation (BRep): a volume is bounded
by a set of surfaces, a surface is bounded by a series of curves, and a curve is bounded by two
end points. Model entities are topological entities, i.e., they only deal with adjacencies in the
model, and are implemented as a set of abstract topological classes. This BRep is extended by
the definition of embedded, or internal, model entities: internal points, curves and surfaces can
be embedded in volumes; and internal points and curves can be embedded in surfaces.
The geometry of model entities can be provided by different CAD kernels. The two default
kernels interfaced by Gmsh are the built-in kernel and the OpenCASCADE kernel. Gmsh does
not translate the geometrical representation from one kernel to another, or from these kernels
to some neutral representation. Instead, Gmsh directly queries the native data for each CAD
kernel, which avoids data loss and is crucial for complex models where translations invariably
introduce issues linked to slightly different representations. Selecting the CAD kernel in ‘.geo’
scripts is done with the SetFactory command (see Section 5.2 [Geometry scripting commands],
page 102), while in the Gmsh API the kernel appears explicitly in all the relevant functions
from the gmsh/model namespace, with geo or occ prefixes for the built-in and OpenCASCADE
kernel, respectively (see Section 6.3 [Namespace gmsh/model], page 128).
Entities can either be built in a bottom-up manner (first points, then curves, surfaces and
volumes) with the built-in and OpenCASCADE kernels, or in a top-down constructive solid
geometry fashion (solids on which boolean operations are performed) with the OpenCASCADE
kernel. Both methodologies can also be combined. Finally, groups of model entities (called
“physical groups”) can be defined, based on the elementary geometric entities. (See Section 1.2.3
[Elementary entities vs physical groups], page 11, for more information about how physical
groups affect the way meshes are saved.)
Both model entities (also referred to as “elementary entities”) and physical groups are uniquely
defined by a pair of integers: their dimension (0 for points, 1 for curves, 2 for surfaces, 3 for
volumes) and their tag, a strictly positive global identification number. Entity and group tags
are unique per dimension:
1. each point must possess a unique tag;
2. each curve must possess a unique tag;
3. each surface must possess a unique tag;
4. each volume must possess a unique tag.
Zero or negative tags are reserved by Gmsh for internal use.
 8 Gmsh 4.11.1

Model entities can be manipulated and transformed in a variety of ways within the geometry
module, but operations are always performed directly within their respective CAD kernels. As
explained above, there is no common internal geometrical representation: rather, Gmsh directly
performs the operations (translation, rotation, intersection, union, fragments, ...) on the native
geometrical representation using each CAD kernel’s own API. In the same philosophy, models
can be imported in the geometry module through each CAD kernel’s own import mechanisms.
For example, by default Gmsh imports STEP and IGES files through OpenCASCADE, which
will lead to the creation of model entities with an internal OpenCASCADE representation.
The Chapter 2 [Gmsh tutorial], page 15, starting with Section 2.1 [t1], page 15, is the best place
to learn how to use the geometry module: it contains examples of increasing complexity based
on both the built-in and the OpenCASCADE kernel. Note that many features of the geometry
module can be used interactively in the GUI (see Chapter 3 [Gmsh graphical user interface],
page 77), which is also a good way to learn about both Gmsh’s scripting language and the API,
as actions in the geometry module automatically append the related command in the input
script file, and can optionally also generate input for the languages supported by the API (see
the General.ScriptingLanguages option; this is still work-in-progress as of Gmsh 4.11.)
In addition to CAD-type geometrical entities, whose geometry is provided by a CAD kernel,
Gmsh also supports discrete model entities, which are defined by a mesh (e.g. STL). Gmsh does
not perform geometrical operations on such discrete entities, but they can be equipped with a
geometry through a so-called “reparametrization” procedure1 . The parametrization is then used
for meshing, in exactly the same way as for CAD entities. See Section 2.13 [t13], page 43 for an
example.

1.2 Mesh module

A finite element mesh of a model is a tessellation of its geometry by simple geometrical elements
of various shapes (in Gmsh: lines, triangles, quadrangles, tetrahedra, prisms, hexahedra and
pyramids), arranged in such a way that if two of them intersect, they do so along a face, an
edge or a node, and never otherwise. This defines a so-called conformal mesh. The mesh mod-
ule implements several algorithms to generate such meshes automatically. By default, meshes
produced by Gmsh are considered as unstructured, even if they were generated in a structured
way (e.g., by extrusion). This implies that the mesh elements are completely defined simply by
an ordered list of their nodes, and that no predefined ordering relation is assumed between any
two elements.
In order to guarantee the conformity of the mesh, mesh generation is performed in a bottom-up
flow: curves are discretized first; the mesh of the curves is then used to mesh the surfaces;
then the mesh of the surfaces is used to mesh the volumes. In this process, the mesh of an
entity is only constrained by the mesh of its boundary, unless entities of lower dimensions are
explicitly embedded in entities of higher dimension. For example, in three dimensions, the
triangles discretizing a surface will be forced to be faces of tetrahedra in the final 3D mesh only
if the surface is part of the boundary of a volume, or if that surface has been explicitly embedded
in the volume. This automatically ensures the conformity of the mesh when, for example, two
volumes share a common surface. Every meshing step is constrained by a mesh size field, which
prescribes the desired size of the elements in the mesh. This size field can be uniform, specified by
values associated with points in the geometry, or defined by general mesh size fields (for example
related to the distance to some boundary, to a arbitrary scalar field defined on another mesh,
etc.): see Chapter 8 [Gmsh mesh size fields], page 299. For each meshing step, all structured
mesh directives are executed first, and serve as additional constraints for the unstructured parts.
(The generation and handling of conformal meshes has important consequences on how meshes
1
P. A. Beaufort, C. Geuzaine, J.-F. Remacle Automatic surface mesh generation for discrete modelsA complete
and automatic pipeline based on reparametrization. Journal of Computational Physics, 417, 109575, 2020.
 Chapter 1: Overview of Gmsh 9

are stored internally in Gmsh, and how they are accessed through the API: see Chapter 6 [Gmsh
application programming interface], page 123.)
Gmsh’s mesh module regroups several 1D, 2D and 3D meshing algorithms:
• The 2D unstructured algorithms generate triangles and/or quadrangles (when recombina-
tion commands or options are used). The 3D unstructured algorithms generate tetrahedra,
or tetrahedra and pyramids (when the boundary mesh contains quadrangles).
• The 2D structured algorithms (transfinite and extrusion) generate triangles by default, but
quadrangles can be obtained by using the recombination commands or options. The 3D
structured algorithms generate tetrahedra, hexahedra, prisms and pyramids, depending on
the type of the surface meshes they are based on.
All meshes can be subdivided to generate fully quadrangular or fully hexahedral meshes with
the Mesh.SubdivisionAlgorithm option (see Section 7.4 [Mesh options], page 255).

1.2.1 Choosing the right unstructured algorithm

Gmsh provides a choice between several 2D and 3D unstructured algorithms. Each algorithm
has its own advantages and disadvantages.
For all 2D unstructured algorithms a Delaunay mesh that contains all the points of the 1D mesh
is initially constructed using a divide-and-conquer algorithm2 . Missing edges are recovered using
edge swaps3 . After this initial step several algorithms can be applied to generate the final mesh:
• The “MeshAdapt” algorithm4 is based on local mesh modifications. This technique makes
use of edge swaps, splits, and collapses: long edges are split, short edges are collapsed, and
edges are swapped if a better geometrical configuration is obtained.
• The “Delaunay” algorithm is inspired by the work of the GAMMA team at INRIA5 . New
points are inserted sequentially at the circumcenter of the element that has the largest
adimensional circumradius. The mesh is then reconnected using an anisotropic Delaunay
criterion.
• The “Frontal-Delaunay” algorithm is inspired by the work of S. Rebay6 .
• Other experimental algorithms with specific features are also available. In particular,
“Frontal-Delaunay for Quads”7 is a variant of the “Frontal-Delaunay” algorithm aiming
at generating right-angle triangles suitable for recombination; and “BAMG”8 allows to
generate anisotropic triangulations.
For very complex curved surfaces the “MeshAdapt” algorithm is the most robust. When high
element quality is important, the “Frontal-Delaunay” algorithm should be tried. For very large
meshes of plane surfaces the “Delaunay” algorithm is the fastest; it usually also handles com-
plex mesh size fields better than the “Frontal-Delaunay”. When the “Delaunay” or “Frontal-
2
R. A. Dwyer, A simple divide-and-conquer algorithm for computing Delaunay triangulations in O(n log n) expected
time, In Proceedings of the second annual symposium on computational geometry, Yorktown Heights, 2–4 June
1986.
3
N. P. Weatherill, The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation, Commun.
Appl. Numer. Methods 6(2), pp. 101–109, 1990.
4
C. Geuzaine and J.-F. Remacle, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and
post-processing facilities, International Journal for Numerical Methods in Engineering 79(11), pp. 1309–1331,
2009.
5
P.-L. George and P. Frey, Mesh generation, Hermes, Lyon, 2000.
6
S. Rebay, Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algo-
rithm, J. Comput. Phys. 106, pp. 25–138, 1993.
7
J.-F. Remacle, F. Henrotte, T. Carrier-Baudouin, E. Bchet, E. Marchandise, C. Geuzaine and T. Mouton, A
frontal Delaunay quad mesh generator using the Linf norm, International Journal for Numerical Methods in
Engineering, 94(5), pp. 494-512, 2013.
8
F. Hecht, BAMG: bidimensional anisotropic mesh generator, User Guide, INRIA, Rocquencourt, 1998.
 10 Gmsh 4.11.1

Delaunay” algorithms fail, “MeshAdapt” is automatically triggered. The “Automatic” algorithm

uses “Delaunay” for plane surfaces and “MeshAdapt” for all other surfaces.
Several 3D unstructured algorithms are also available:
• The “Delaunay” algorithm is split into three separate steps. First, an initial mesh of the
union of all the volumes in the model is performed, without inserting points in the volume.
The surface mesh is then recovered using H. Si’s boundary recovery algorithm Tetgen/BR.
Then a three-dimensional version of the 2D Delaunay algorithm described above is applied
to insert points in the volume to respect the mesh size constraints.
• The “Frontal” algorithm uses J. Schoeberl’s Netgen algorithm9 .
• The “HXT” algorithm10 is a new efficient and parallel reimplementaton of the Delaunay
algorithm.
• Other experimental algorithms with specific features are also available. In particular,
“MMG3D”11 allows to generate anisotropic tetrahedralizations.
The “Delaunay” algorithm is currently the most robust and is the only one that supports the
automatic generation of hybrid meshes with pyramids. Embedded model entities and general
mesh size fields (see Section 1.2.2 [Specifying mesh element sizes], page 10) are currently only
supported by the “Delaunay” and “HXT” algorithms.
When Gmsh is configured with OpenMP support (see Appendix A [Compiling the source code],
page 369), most of the meshing steps can be performed in parallel:
• 1D and 2D meshing is parallelized using a coarse-grained approach, i.e. curves (resp. sur-
faces) are each meshed sequentially, but several curves (resp. surfaces) can be meshed at
the same time.
• 3D meshing using HXT is parallelized using a fine-grained approach, i.e. the actual meshing
procedure for a single volume is done is parallel.
The number of threads can be controlled with the -nt flag on the command line (see
Chapter 4 [Gmsh command-line interface], page 83), or with the General.NumThreads,
Mesh.MaxNumThreads1D, Mesh.MaxNumThreads2D and Mesh.MaxNumThreads3D options (see
Section 7.1 [General options], page 219 and Section 7.4 [Mesh options], page 255).

1.2.2 Specifying mesh element sizes

There are several ways to specify the size of the mesh elements for a given geometry:
1. First, if the options Mesh.MeshSizeFromPoints and Mesh.MeshSizeExtendFromBoundary
are set (they are by default; see Section 7.4 [Mesh options], page 255), you can simply
specify desired mesh element sizes at the geometrical points of the model. The size of the
mesh elements will then be computed by interpolating these values inside the domain during
mesh generation. This might sometimes lead to over-refinement in some areas, so that you
may have to add “dummy” geometrical entities in the model in order to get the desired
element sizes or use more advanced methods explained below.
2. Second, if Mesh.MeshSizeFromCurvature is set to a positive value (it is set to 0 by default),
the mesh will be adapted with respect to the curvature of the model entities, the value giving
the target number of elements per 2 Pi radians.
3. Next, you can specify a general target mesh size, expressed as a combination of mesh size
fields (see Chapter 8 [Gmsh mesh size fields], page 299):
9
J. Schoeberl, Netgen, an advancing front 2d/3d-mesh generator based on abstract rules, Comput. Visual. Sci., 1,
pp. 41–52, 1997.
10
C. Marot, J. Pellerin and J.F. Remacle, One machine, one minute, three billion tetrahedra, International Journal
for Numerical Methods in Engineering 117.9, pp 967-990, 2019.
11
C. Dobrzynski, MMG3D: user guide, INRIA, 2012.
Chapter 1: Overview of Gmsh 11

• The Box field specifies the size of the elements inside and outside of a parallelepipedic
region.
• The Distance field specifies the size of the mesh according to the distance to some
model entities.
• The MathEval field specifies the size of the mesh using an explicit mathematical func-
tion.
• The PostView field specifies an explicit background mesh in the form of a scalar post-
processing view (see Section 1.4 [Post-processing module], page 12, and Chapter 10
[Gmsh file formats], page 345) in which the nodal values are the target element sizes.
This method is very general but it requires a first (usually rough) mesh and a way to
compute the target sizes on this mesh (usually through an error estimation procedure,
e.g. in an iterative process of mesh adaptation).
• The Min field specifies the size as the minimum of the sizes computed using other fields.
• ...
4. Mesh sizes are also constrained by structured meshing constraints (e.g. transfinite or ex-
truded meshes) as well as by any discrete model entity that is not equipped with a geometry,
and which will thus preserve it mesh during mesh generation.
5. Boundary mesh sizes are interpolated inside surfaces and/or volumes depending on the
value of Mesh.MeshSizeExtendFromBoundary.
To determine the actual mesh size at any given point in the model, Gmsh evaluates all the above
mesh size constraints and selects the smallest value. Using the Gmsh API, this value can then
be further modified using a C++, C, Python, Julia or Fortran mesh size callback function pro-
vided via gmsh/model/mesh/setSizeCallback (see Section 6.4 [Namespace gmsh/model/mesh],
page 140).
The resulting value is further constrained in the interval [ Mesh.MeshSizeMin,
Mesh.MeshSizeMax ] (which can also be provided on the command line with -clmin and
-clmax). The resulting value is then finally multiplied by Mesh.MeshSizeFactor (-clscale on
the command line).
Note that when the element size is fully specified by a mesh size field, it is thus often desirable
to set
Mesh.MeshSizeFromPoints = 0;
Mesh.MeshSizeFromCurvature = 0;
Mesh.MeshSizeExtendFromBoundary = 0;
to prevent over-refinement inside an entity due to small mesh sizes on its boundary.

1.2.3 Elementary entities vs. physical groups

It is usually convenient to combine elementary geometrical entities into more meaningful groups,
e.g. to define some mathematical (“domain”, “boundary with Neumann condition”), functional
(“left wing”, “fuselage”) or material (“steel”, “carbon”) properties. Such grouping is done in
Gmsh’s geometry module (see Section 1.1 [Geometry module], page 7) through the definition of
“physical groups”.
By default in the native Gmsh MSH mesh file format (see Chapter 10 [Gmsh file formats],
page 345), as well as in most other mesh formats, if physical groups are defined, the output
mesh only contains those elements that belong to at least one physical group. (Different mesh
file formats treat physical groups in slightly different ways, depending on their capability to
define groups.) To save all mesh elements whether or not physical groups are defined, use the
Mesh.SaveAll option (see Section 7.4 [Mesh options], page 255) or specify -save_all on the
command line. In some formats (e.g. MSH2), setting Mesh.SaveAll will however discard all
physical group definitions.
12 Gmsh 4.11.1

1.3 Solver module

Gmsh implements a ONELAB (http://onelab.info) server to exchange data with external
solvers or other codes (called “clients”). The ONELAB interface allows to call such clients and
have them share parameters and modeling information.
The implementation is based on a client-server model, with a server-side database and local
or remote clients communicating in-memory or through TCP/IP sockets. Contrary to most
solver interfaces, the ONELAB server has no a priori knowledge about any specifics (input file
format, syntax, ...) of the clients. This is made possible by having any simulation preceded
by an analysis phase, during which the clients are asked to upload their parameter set to the
server. The issues of completeness and consistency of the parameter sets are completely dealt
with on the client side: the role of ONELAB is limited to data centralization, modification and
re-dispatching.
Using the Gmsh API, you can directly embed Gmsh in your C++, C, Python, Julia or Fortran
solver, use ONELAB for interactive parameter definition and modification, and to create post-
processing data on the fly. See prepro.py, custom gui.py and custom gui.cpp for examples.
If you prefer to keep codes separate, you can also communicate with Gmsh through a socket by
providing the solver name (Solver.Name0, Solver.Name1, etc.) and the path to the executable
(Solver.Executable0, Solver.Executable1, etc.). Parameters can then be exchanged using
the ONELAB protocol: see the utils/solvers directory for examples. A full-featured solver
interfaced in this manner is GetDP (https://getdp.info), a general finite element solver using
mixed finite elements.

1.4 Post-processing module

The post-processing module can handle multiple scalar, vector or tensor datasets along with
the geometry and the mesh. The datasets can be given in several formats: in human-readable
“parsed” format (these are just part of a standard input script, but are usually put in separate
files with a ‘.pos’ extension – see Section 5.4 [Post-processing scripting commands], page 117),
in native MSH files (ASCII or binary files with ‘.msh’ extensions: see Chapter 10 [Gmsh file
formats], page 345), or in standard third-party formats such as CGNS or MED. Datasets can also
be directly imported using the Gmsh API (see Section 6.10 [Namespace gmsh/view], page 201).
Once loaded into Gmsh, scalar fields can be displayed as iso-curves, iso-surfaces or color maps,
whereas vector fields can be represented either by three-dimensional arrows or by displacement
maps. Tensor fields can be displayed as Von-Mises effective stresses, min/max eigenvalues,
eigenvectors, ellipses or ellipsoids. (To display other combinations of components, you can use
the View.ForceNumComponents option – see Section 7.6 [Post-processing options], page 280.)
Each dataset, along with the visualization options, is called a “post-processing view”, or simply
a “view”. Each view is given a name, and can be manipulated either individually (each view has
its own button in the GUI and can be referred to by its index or its unique tag in a script or in the
API) or globally (see the PostProcessing.Link option in Section 7.6 [Post-processing options],
page 280). Possible operations on post-processing views include section computation, offset,
elevation, boundary and component extraction, color map and range modification, animation,
vector graphic output, etc. These operations are either carried out nondestructively through
the modification of post-processing options, or can lead to the actual modification of the view
data or the creation of new views when done using post-processing plugins (see Chapter 9
[Gmsh plugins], page 317). Both can be fully automated in scripts or through the API (see e.g.,
Section 2.8 [t8], page 33, and Section 2.9 [t9], page 36).
By default, Gmsh treats all post-processing views as three-dimensional plots, i.e., draws the
scalar, vector and tensor primitives (points, curves, triangles, tetrahedra, etc.) in 3D space. But
Gmsh can also represent each post-processing view containing scalar points as two-dimensional
(“X-Y”) plots, either space- or time-oriented:
Chapter 1: Overview of Gmsh 13

• in a ‘2D space’ plot, the scalar points are taken in the same order as they are defined in the
post-processing view: the abscissa of the 2D graph is the curvilinear abscissa of the curve
defined by the point series, and only one curve is drawn using the values associated with
the points. If several time steps are available, each time step generates a new curve;
• in a ‘2D time’ plot, one curve is drawn for each scalar point in the view and the abscissa is
the time step.

1.5 What Gmsh is pretty good at . . .

Here is a tentative list of what Gmsh does best:
• quickly describe simple and/or “repetitive” geometries with the built-in scripting language,
thanks to user-defined macros, loops, conditionals and includes (see Section 5.1.7 [User-
defined macros], page 96, Section 5.1.8 [Loops and conditionals], page 96, and Section 5.1.9
[Other general commands], page 97). For more advanced geometries, using the Gmsh API
(see Chapter 6 [Gmsh application programming interface], page 123) in the language of
your choice (C++, C, Python, Julia or Fortran) brings even greater flexibility, the only
downside being that you need to either compile your code (for C++, C and Fortran) or
to configure and install an interpreter (Python or Julia) in addition to Gmsh. A binary
Software Development Kit (SDK) is distributed on the Gmsh web site to make the process
easier (see Section 1.7 [Installing and running Gmsh on your computer], page 14);
• parametrize these geometries. Gmsh’s scripting language or the Gmsh API enable all com-
mands and command arguments to depend on previous calculations. Using the OpenCAS-
CADE geometry kernel, Gmsh gives access to all the usual constructive solid geometry
operations (see e.g. Section 2.16 [t16], page 48);
• import geometries from other CAD software in standard exchange formats. Gmsh uses
OpenCASCADE to import such files, including label and color information from STEP and
IGES files (see e.g. Section 2.20 [t20], page 55);
• generate unstructured 1D, 2D and 3D simplicial (i.e., using line segments, triangles and
tetrahedra) finite element meshes (see Section 1.2 [Mesh module], page 8), with fine control
over the element size (see Section 1.2.2 [Specifying mesh element sizes], page 10);
• create simple extruded geometries and meshes, and allow to automatically couple such
structured meshes with unstructured ones (using a layer of pyramids in 3D);
• generate high-order (curved) meshes that conform to the CAD model geometry. High-order
mesh optimization tools allow to guarantee the validity of such curved meshes;
• interact with external solvers by defining ONELAB parameters, shared between Gmsh and
the solvers and easily modifiable in the GUI (see Section 1.3 [Solver module], page 12);
• visualize and export computational results in a great variety of ways. Gmsh can dis-
play scalar, vector and tensor datasets, perform various operations on the resulting post-
processing views (see Section 1.4 [Post-processing module], page 12), can export plots in
many different formats, and can generate complex animations (see e.g. Section 2.8 [t8],
page 33);
• run on low end machines and/or machines with no graphical interface. Gmsh can be
compiled with or without the GUI (see Appendix A [Compiling the source code], page 369),
and all versions can be used either interactively or directly from the command line;
• configure your preferred options. Gmsh has a large number of configuration options that
can be set interactively using the GUI, scattered inside script files, changed through the
API, set in per-user configuration files and specified on the command line (see Chapter 7
[Gmsh options], page 219);
• and do all the above on various platforms (Windows, macOS and Linux), for free (see
[Copying conditions], page 3)!
14 Gmsh 4.11.1

1.6 . . . and what Gmsh is not so good at

Here are some known weaknesses of Gmsh:
• Gmsh is not a multi-bloc mesh generator: all meshes produced by Gmsh are conforming in
the sense of finite element meshes;
• Gmsh’s graphical user interface is only exposing a limited number of the available features,
and many aspects of the interface could be enhanced (especially manipulators).
• Your complaints about Gmsh here :-)
If you have the skills and some free time, feel free to join the project: we gladly accept any code
contributions (see Appendix B [Information for developers], page 373) to remedy the aforemen-
tioned (and all other) shortcomings!

1.7 Installing and running Gmsh on your computer

Gmsh can be used either as a standalone application, or as a library.
As a standalone application, Gmsh can be controlled with the GUI (see Chapter 3 [Gmsh
graphical user interface], page 77), through the command line (see Chapter 4 [Gmsh command-
line interface], page 83) and through ‘.geo’ script files (see Chapter 5 [Gmsh scripting lan-
guage], page 89). In addition, the ONELAB interface (see Section 1.3 [Solver module],
page 12) allows to interact with the Gmsh application through Unix or TCP/IP sockets. Bi-
nary versions of the Gmsh app for Windows, Linux and macOS can be downloaded from
https://gmsh.info/#Download. Several Linux distributions also ship the Gmsh app. See
Appendix A [Compiling the source code], page 369 for instructions on how to compile the Gmsh
app from source.
As a library, Gmsh can still be used in the same way as the standalone Gmsh app, but in addition
it can also be embedded in external codes using the Gmsh API (see Chapter 6 [Gmsh application
programming interface], page 123). The API is available in C++, C, Python, Julia and Fortran.
A binary Software Development Kit (SDK) for Windows, Linux and macOS, that contains the
dynamic Gmsh library and the associated header and module files, can be downloaded from
https://gmsh.info/#Download. Python users can use
pip install --upgrade gmsh
which will download the binary SDK and install the files in the appropriate system directories.
Several Linux distributions also ship the Gmsh SDK. See Appendix A [Compiling the source
code], page 369 for instructions on how to compile the dynamic Gmsh library from source.
Chapter 2: Gmsh tutorial 15

2 Gmsh tutorial
The following tutorials introduce new features gradually, starting with the first tutorial t1 (see
Section 2.1 [t1], page 15). The corresponding files are available in the tutorials directory of the
Gmsh distribution.
The ‘.geo’ files (e.g. ‘t1.geo’) are written in Gmsh’s built-in scripting language (see Chapter 5
[Gmsh scripting language], page 89). You can open them directly with the Gmsh app: in the
GUI (see Chapter 3 [Gmsh graphical user interface], page 77), use the ‘File->Open’ menu and
select e.g. ‘t1.geo’. Or on the command line, run
> gmsh t1.geo
which will launch the GUI, or run
> gmsh t1.geo -2
to perform 2D meshing in batch mode (see Chapter 4 [Gmsh command-line interface], page 83).
The ‘c++’, ‘c’, ‘python’, ‘julia’ and ‘fortran’ subdirectories of the tutorials directory contain
the C++, C, Python, Julia and Fortran versions of the tutorials, written using the Gmsh API
(see Chapter 6 [Gmsh application programming interface], page 123). You will need the Gmsh
dynamic library and the associated header files (for C++ and C) or modules (for Python, Julia
and Fortran) to run them (see Section 1.7 [Installing and running Gmsh on your computer],
page 14). Each subdirectory contains additional information on how to run the tutorials for
each supported language.
All the tutorials starting with the letter ‘t’ are available both using the scripting language
and the API. Extended tutorials, starting with the letter ‘x’, introduce features that are only
available through the API.
Note that besides these tutorials, the Gmsh distribution contains many other examples written
using both the built-in scripting language and the API: see examples and benchmarks.

2.1 t1: Geometry basics, elementary entities, physical groups

See t1.geo. Also available in C++ (t1.cpp), C (t1.c), Python (t1.py), Julia (t1.jl) and Fortran
(t1.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 1
//
// Geometry basics, elementary entities, physical groups
//
// -----------------------------------------------------------------------------

// The simplest construction in Gmsh’s scripting language is the

16 Gmsh 4.11.1

// ‘affectation’. The following command defines a new variable ‘lc’:

lc = 1e-2;

// This variable can then be used in the definition of Gmsh’s simplest

// ‘elementary entity’, a ‘Point’. A Point is uniquely identified by a tag (a
// strictly positive integer; here ‘1’) and defined by a list of four numbers:
// three coordinates (X, Y and Z) and the target mesh size (lc) close to the
// point:

Point(1) = {0, 0, 0, lc};

// The distribution of the mesh element sizes will then be obtained by

// interpolation of these mesh sizes throughout the geometry. Another method to
// specify mesh sizes is to use general mesh size Fields (see ‘t10.geo’). A
// particular case is the use of a background mesh (see ‘t7.geo’).

// If no target mesh size of provided, a default uniform coarse size will be

// used for the model, based on the overall model size.

// We can then define some additional points. All points should have different
// tags:

Point(2) = {.1, 0, 0, lc};

Point(3) = {.1, .3, 0, lc};
Point(4) = {0, .3, 0, lc};

// Curves are Gmsh’s second type of elementary entities, and, amongst curves,
// straight lines are the simplest. A straight line is identified by a tag and
// is defined by a list of two point tags. In the commands below, for example,
// the line 1 starts at point 1 and ends at point 2.
//
// Note that curve tags are separate from point tags - hence we can reuse tag
// ‘1’ for our first curve. And as a general rule, elementary entity tags in
// Gmsh have to be unique per geometrical dimension.

Line(1) = {1, 2};

Line(2) = {3, 2};
Line(3) = {3, 4};
Line(4) = {4, 1};

// The third elementary entity is the surface. In order to define a simple

// rectangular surface from the four curves defined above, a curve loop has
// first to be defined. A curve loop is also identified by a tag (unique amongst
// curve loops) and defined by an ordered list of connected curves, a sign being
// associated with each curve (depending on the orientation of the curve to form
// a loop):

Curve Loop(1) = {4, 1, -2, 3};

// We can then define the surface as a list of curve loops (only one here,
// representing the external contour, since there are no holes--see ‘t4.geo’ for
Chapter 2: Gmsh tutorial 17

// an example of a surface with a hole):

Plane Surface(1) = {1};

// At this level, Gmsh knows everything to display the rectangular surface 1 and
// to mesh it. An optional step is needed if we want to group elementary
// geometrical entities into more meaningful groups, e.g. to define some
// mathematical ("domain", "boundary"), functional ("left wing", "fuselage") or
// material ("steel", "carbon") properties.
//
// Such groups are called "Physical Groups" in Gmsh. By default, if physical
// groups are defined, Gmsh will export in output files only mesh elements that
// belong to at least one physical group. (To force Gmsh to save all elements,
// whether they belong to physical groups or not, set ‘Mesh.SaveAll=1;’, or
// specify ‘-save_all’ on the command line.) Physical groups are also identified
// by tags, i.e. strictly positive integers, that should be unique per dimension
// (0D, 1D, 2D or 3D). Physical groups can also be given names.
//
// Here we define a physical curve that groups the left, bottom and right curves
// in a single group (with prescribed tag 5); and a physical surface with name
// "My surface" (with an automatic tag) containing the geometrical surface 1:

Physical Curve(5) = {1, 2, 4};

Physical Surface("My surface") = {1};

// Now that the geometry is complete, you can

// - either open this file with Gmsh and select ‘2D’ in the ‘Mesh’ module to
// create a mesh; then select ‘Save’ to save it to disk in the default format
// (or use ‘File->Export’ to export in other formats);
// - or run ‘gmsh t1.geo -2‘ to mesh in batch mode on the command line.

// You could also uncomment the following lines in this script:

//
// Mesh 2;
// Save "t1.msh";
//
// which would lead Gmsh to mesh and save the mesh every time the file is
// parsed. (To simply parse the file from the command line, you can use ‘gmsh
// t1.geo -’)

// By default, Gmsh saves meshes in the latest version of the Gmsh mesh file
// format (the ‘MSH’ format). You can save meshes in other mesh formats by
// specifying a filename with a different extension in the GUI, on the command
// line or in scripts. For example
//
// Save "t1.unv";
//
// will save the mesh in the UNV format. You can also save the mesh in older
// versions of the MSH format:
//
// - In the GUI: open ‘File->Export’, enter your ‘filename.msh’ and then pick
// the version in the dropdown menu.
18 Gmsh 4.11.1

// - On the command line: use the ‘-format’ option (e.g. ‘gmsh file.geo -format
// msh2 -2’).
// - In a ‘.geo’ script: add ‘Mesh.MshFileVersion = x.y;’ for any version
// number ‘x.y’.
// - As an alternative method, you can also not specify the format explicitly,
// and just choose a filename with the ‘.msh2’ or ‘.msh4’ extension.

// Note that starting with Gmsh 3.0, models can be built using other geometry
// kernels than the default built-in kernel. By specifying
//
// SetFactory("OpenCASCADE");
//
// any subsequent command in the ‘.geo’ file would be handled by the OpenCASCADE
// geometry kernel instead of the built-in kernel. Different geometry kernels
// have different features. With OpenCASCADE, instead of defining the surface by
// successively defining 4 points, 4 curves and 1 curve loop, one can define the
// rectangular surface directly with
//
// Rectangle(2) = {.2, 0, 0, .1, .3};
//
// The underlying curves and points could be accessed with the ‘Boundary’ or
// ‘CombinedBoundary’ operators.
//
// See e.g. ‘t16.geo’, ‘t18.geo’, ‘t19.geo’ or ‘t20.geo’ for complete examples
// based on OpenCASCADE, and ‘examples/boolean’ for more.

2.2 t2: Transformations, extruded geometries, volumes

See t2.geo. Also available in C++ (t2.cpp), C (t2.c), Python (t2.py), Julia (t2.jl) and Fortran
(t2.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 2
//
// Transformations, extruded geometries, volumes
//
// -----------------------------------------------------------------------------

// We first include the previous tutorial file, in order to use it as a basis

// for this one. Including a file is equivalent to copy-pasting its contents:
Chapter 2: Gmsh tutorial 19

Include "t1.geo";

// We can then add new points and curves in the same way as we did in ‘t1.geo’:

Point(5) = {0, .4, 0, lc};

Line(5) = {4, 5};

// Gmsh also provides tools to transform (translate, rotate, etc.)

// elementary entities or copies of elementary entities. For example, point
// 5 can be moved by 0.02 to the left with:

Translate {-0.02, 0, 0} { Point{5}; }

// And it can be further rotated by -Pi/4 around (0, 0.3, 0) (with the rotation
// along the z axis) with:

Rotate {{0,0,1}, {0,0.3,0}, -Pi/4} { Point{5}; }

// Note that there are no units in Gmsh: coordinates are just numbers - it’s up
// to the user to associate a meaning to them.

// Point 3 can be duplicated and translated by 0.05 along the y axis:

Translate {0, 0.05, 0} { Duplicata{ Point{3}; } }

// This command created a new point with an automatically assigned tag. This tag
// can be obtained using the graphical user interface by hovering the mouse over
// the point: in this case, the new point has tag ‘6’.

Line(7) = {3, 6};

Line(8) = {6, 5};
Curve Loop(10) = {5,-8,-7,3};
Plane Surface(11) = {10};

// To automate the workflow, instead of using the graphical user interface to

// obtain the tags of newly created entities, one can use the return value of
// the transformation commands directly. For example, the ‘Translate’ command
// returns a list containing the tags of the translated entities. Let’s
// translate copies of the two surfaces 1 and 11 to the right with the following
// command:

my_new_surfs[] = Translate {0.12, 0, 0} { Duplicata{ Surface{1, 11}; } };

// my_new_surfs[] (note the square brackets, and the ‘;’ at the end of the
// command) denotes a list, which contains the tags of the two new surfaces
// (check ‘Tools->Message console’ to see the message):

Printf("New surfaces ’%g’ and ’%g’", my_new_surfs[0], my_new_surfs[1]);

// In Gmsh lists use square brackets for their definition (mylist[] = {1, 2,
// 3};) as well as to access their elements (myotherlist[] = {mylist[0],
// mylist[2]}; mythirdlist[] = myotherlist[];), with list indexing starting at
20 Gmsh 4.11.1

// 0. To get the size of a list, use the hash (pound): len = #mylist[].
//
// Note that parentheses can also be used instead of square brackets, so that we
// could also write ‘myfourthlist() = {mylist(0), mylist(1)};’.

// Volumes are the fourth type of elementary entities in Gmsh. In the same way
// one defines curve loops to build surfaces, one has to define surface loops
// (i.e. ‘shells’) to build volumes. The following volume does not have holes
// and thus consists of a single surface loop:

Point(100) = {0., 0.3, 0.12, lc}; Point(101) = {0.1, 0.3, 0.12, lc};
Point(102) = {0.1, 0.35, 0.12, lc};

xyz[] = Point{5}; // Get coordinates of point 5

Point(103) = {xyz[0], xyz[1], 0.12, lc};

Line(110) = {4, 100}; Line(111) = {3, 101};

Line(112) = {6, 102}; Line(113) = {5, 103};
Line(114) = {103, 100}; Line(115) = {100, 101};
Line(116) = {101, 102}; Line(117) = {102, 103};

Curve Loop(118) = {115, -111, 3, 110}; Plane Surface(119) = {118};

Curve Loop(120) = {111, 116, -112, -7}; Plane Surface(121) = {120};
Curve Loop(122) = {112, 117, -113, -8}; Plane Surface(123) = {122};
Curve Loop(124) = {114, -110, 5, 113}; Plane Surface(125) = {124};
Curve Loop(126) = {115, 116, 117, 114}; Plane Surface(127) = {126};

Surface Loop(128) = {127, 119, 121, 123, 125, 11};

Volume(129) = {128};

// When a volume can be extruded from a surface, it is usually easier to use the
// ‘Extrude’ command directly instead of creating all the points, curves and
// surfaces by hand. For example, the following command extrudes the surface 11
// along the z axis and automatically creates a new volume (as well as all the
// needed points, curves and surfaces):

Extrude {0, 0, 0.12} { Surface{my_new_surfs[1]}; }

// The following command permits to manually assign a mesh size to some of the
// new points:

MeshSize {103, 105, 109, 102, 28, 24, 6, 5} = lc * 3;

// We finally group volumes 129 and 130 in a single physical group with tag ‘1’
// and name "The volume":

Physical Volume("The volume", 1) = {129,130};

// Note that, if the transformation tools are handy to create complex

// geometries, it is also sometimes useful to generate the ‘flat’ geometry, with
// an explicit representation of all the elementary entities.
//
Chapter 2: Gmsh tutorial 21

// With the built-in geometry kernel, this can be achieved with ‘File->Export’ by
// selecting the ‘Gmsh Unrolled GEO’ format, or by adding
//
// Save "file.geo_unrolled";
//
// in the script. It can also be achieved with ‘gmsh t2.geo -0’ on the command
// line.
//
// With the OpenCASCADE geometry kernel, unrolling the geometry can be achieved
// with ‘File->Export’ by selecting the ‘OpenCASCADE BRep’ format, or by adding
//
// Save "file.brep";
//
// in the script. (OpenCASCADE geometries can also be exported to STEP.)

// It is important to note that Gmsh never translates geometry data into a

// common representation: all the operations on a geometrical entity are
// performed natively with the associated geometry kernel. Consequently, one
// cannot export a geometry constructed with the built-in kernel as an
// OpenCASCADE BRep file; or export an OpenCASCADE model as an Unrolled GEO
// file.

2.3 t3: Extruded meshes, ONELAB parameters, options

See t3.geo. Also available in C++ (t3.cpp), Python (t3.py), Julia (t3.jl) and Fortran (t3.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 3
//
// Extruded meshes, ONELAB parameters, options
//
// -----------------------------------------------------------------------------

// Again, we start by including the first tutorial:

Include "t1.geo";

// As in ‘t2.geo’, we plan to perform an extrusion along the z axis. But here,

// instead of only extruding the geometry, we also want to extrude the 2D
// mesh. This is done with the same ‘Extrude’ command, but by specifying element
// ’Layers’ (2 layers in this case, the first one with 8 subdivisions and the
22 Gmsh 4.11.1

// second one with 2 subdivisions, both with a height of h/2):

h = 0.1;

Extrude {0,0,h} {
Surface{1}; Layers{ {8,2}, {0.5,1} };
}

// The extrusion can also be performed with a rotation instead of a translation,

// and the resulting mesh can be recombined into prisms (we use only one layer
// here, with 7 subdivisions). All rotations are specified by an axis direction
// ({0,1,0}), an axis point ({-0.1,0,0.1}) and a rotation angle (-Pi/2):

Extrude { {0,1,0} , {-0.1,0,0.1} , -Pi/2 } {

Surface{28}; Layers{7}; Recombine;
}

// Using the built-in geometry kernel, only rotations with angles < Pi are
// supported. To do a full turn, you will thus need to apply at least 3
// rotations. The OpenCASCADE geometry kernel does not have this limitation.

// Note that a translation ({-2*h,0,0}) and a rotation ({1,0,0}, {0,0.15,0.25},

// Pi/2) can also be combined to form a "twist". Here the angle is specified as
// a ONELAB parameter, using the ‘DefineConstant’ syntax. ONELAB parameters can
// be modified interactively in the GUI, and can be exchanged with other codes
// connected to the same ONELAB database:

DefineConstant[ angle = {90, Min 0, Max 120, Step 1,

Name "Parameters/Twisting angle"} ];

// In more details, ‘DefineConstant’ allows you to assign the value of the

// ONELAB parameter "Parameters/Twisting angle" to the variable ‘angle’. If the
// ONELAB parameter does not exist in the database, ‘DefineConstant’ will create
// it and assign the default value ‘90’. Moreover, if the variable ‘angle’ was
// defined before the call to ‘DefineConstant’, the ‘DefineConstant’ call would
// simply be skipped. This allows to build generic parametric models, whose
// parameters can be frozen from the outside - the parameters ceasing to be
// "parameters".
//
// An interesting use of this feature is in conjunction with the ‘-setnumber
// name value’ command line switch, which defines a variable ‘name’ with value
// ‘value’. Calling ‘gmsh t2.geo -setnumber angle 30’ would define ‘angle’
// before the ‘DefineConstant’, making ‘t2.geo’ non-parametric
// ("Parameters/Twisting angle" will not be created in the ONELAB database and
// will not be available for modification in the graphical user interface).

out[] = Extrude { {-2*h,0,0}, {1,0,0} , {0,0.15,0.25} , angle * Pi / 180 } {

Surface{50}; Layers{10}; Recombine;
};

// In this last extrusion command we retrieved the volume number

// programmatically by using the return value (a list) of the ‘Extrude’
Chapter 2: Gmsh tutorial 23

// command. This list contains the "top" of the extruded surface (in ‘out[0]’),
// the newly created volume (in ‘out[1]’) and the tags of the lateral surfaces
// (in ‘out[2]’, ‘out[3]’, ...).

// We can then define a new physical volume (with tag 101) to group all the
// elementary volumes:

Physical Volume(101) = {1, 2, out[1]};

// Let us now change some options... Since all interactive options are
// accessible in Gmsh’s scripting language, we can for example make point tags
// visible or redefine some colors directly in the input file:

Geometry.PointNumbers = 1;
Geometry.Color.Points = Orange;
General.Color.Text = White;
Mesh.Color.Points = {255, 0, 0};

// Note that all colors can be defined literally or numerically, i.e.

// ‘Mesh.Color.Points = Red’ is equivalent to ‘Mesh.Color.Points = {255,0,0}’;
// and also note that, as with user-defined variables, the options can be used
// either as right or left hand sides, so that the following command will set
// the surface color to the same color as the points:

Geometry.Color.Surfaces = Geometry.Color.Points;

// You can use the ‘Help->Current Options and Workspace’ menu to see the current
// values of all options. To save all the options in a file, use
// ‘File->Export->Gmsh Options’. To associate the current options with the
// current file use ‘File->Save Model Options’. To save the current options for
// all future Gmsh sessions use ‘File->Save Options As Default’.

2.4 t4: Built-in functions, holes in surfaces, annotations, entity

colors
See t4.geo. Also available in C++ (t4.cpp), Python (t4.py), Julia (t4.jl) and Fortran (t4.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 4
//
// Built-in functions, holes in surfaces, annotations, entity colors
24 Gmsh 4.11.1

//
// -----------------------------------------------------------------------------

// As usual, we start by defining some variables:

cm = 1e-02;
e1 = 4.5 * cm; e2 = 6 * cm / 2; e3 = 5 * cm / 2;
h1 = 5 * cm; h2 = 10 * cm; h3 = 5 * cm; h4 = 2 * cm; h5 = 4.5 * cm;
R1 = 1 * cm; R2 = 1.5 * cm; r = 1 * cm;
Lc1 = 0.01;
Lc2 = 0.003;

// We can use all the usual mathematical functions (note the capitalized first
// letters), plus some useful functions like Hypot(a, b) := Sqrt(a^2 + b^2):

ccos = (-h5*R1 + e2 * Hypot(h5, Hypot(e2, R1))) / (h5^2 + e2^2);

ssin = Sqrt(1 - ccos^2);

// Then we define some points and some lines using these variables:

Point(1) = {-e1-e2, 0 , 0, Lc1}; Point(2) = {-e1-e2, h1 , 0, Lc1};

Point(3) = {-e3-r , h1 , 0, Lc2}; Point(4) = {-e3-r , h1+r , 0, Lc2};
Point(5) = {-e3 , h1+r , 0, Lc2}; Point(6) = {-e3 , h1+h2, 0, Lc1};
Point(7) = { e3 , h1+h2, 0, Lc1}; Point(8) = { e3 , h1+r , 0, Lc2};
Point(9) = { e3+r , h1+r , 0, Lc2}; Point(10)= { e3+r , h1 , 0, Lc2};
Point(11)= { e1+e2, h1 , 0, Lc1}; Point(12)= { e1+e2, 0 , 0, Lc1};
Point(13)= { e2 , 0 , 0, Lc1};

Point(14)= { R1 / ssin, h5+R1*ccos, 0, Lc2};

Point(15)= { 0 , h5 , 0, Lc2};
Point(16)= {-R1 / ssin, h5+R1*ccos, 0, Lc2};
Point(17)= {-e2 , 0.0 , 0, Lc1};

Point(18)= {-R2 , h1+h3 , 0, Lc2}; Point(19)= {-R2 , h1+h3+h4, 0, Lc2};

Point(20)= { 0 , h1+h3+h4, 0, Lc2}; Point(21)= { R2 , h1+h3+h4, 0, Lc2};
Point(22)= { R2 , h1+h3 , 0, Lc2}; Point(23)= { 0 , h1+h3 , 0, Lc2};

Point(24)= { 0, h1+h3+h4+R2, 0, Lc2}; Point(25)= { 0, h1+h3-R2, 0, Lc2};

Line(1) = {1 , 17};
Line(2) = {17, 16};

// Gmsh provides other curve primitives than straight lines: splines, B-splines,
// circle arcs, ellipse arcs, etc. Here we define a new circle arc, starting at
// point 14 and ending at point 16, with the circle’s center being the point 15:

Circle(3) = {14,15,16};

// Note that, in Gmsh, circle arcs should always be smaller than Pi. The
// OpenCASCADE geometry kernel does not have this limitation.

// We can then define additional lines and circles, as well as a new surface:
Chapter 2: Gmsh tutorial 25

Line(4) = {14, 13}; Line(5) = {13, 12}; Line(6) = {12, 11};

Line(7) = {11, 10}; Circle(8) = {8, 9, 10}; Line(9) = {8, 7};
Line(10) = {7, 6}; Line(11) = {6, 5}; Circle(12) = {3, 4, 5};
Line(13) = {3, 2}; Line(14) = {2, 1}; Line(15) = {18, 19};
Circle(16) = {21, 20, 24}; Circle(17) = {24, 20, 19};
Circle(18) = {18, 23, 25}; Circle(19) = {25, 23, 22};
Line(20) = {21,22};

Curve Loop(21) = {17, -15, 18, 19, -20, 16};

Plane Surface(22) = {21};

// But we still need to define the exterior surface. Since this surface has a
// hole, its definition now requires two curves loops:

Curve Loop(23) = {11, -12, 13, 14, 1, 2, -3, 4, 5, 6, 7, -8, 9, 10};

Plane Surface(24) = {23, 21};

// As a general rule, if a surface has N holes, it is defined by N+1 curve loops:

// the first loop defines the exterior boundary; the other loops define the
// boundaries of the holes.

// Finally, we can add some comments by embedding a post-processing view

// containing some strings:

View "comments" {
// Add a text string in window coordinates, 10 pixels from the left and 10
// pixels from the bottom, using the ‘StrCat’ function to concatenate strings:
T2(10, -10, 0){ StrCat("Created on ", Today, " with Gmsh") };

// Add a text string in model coordinates centered at (X,Y,Z) = (0, 0.11, 0):
T3(0, 0.11, 0, TextAttributes("Align", "Center", "Font", "Helvetica")){
"Hole"
};

// If a string starts with ‘file://’, the rest is interpreted as an image

// file. For 3D annotations, the size in model coordinates can be specified
// after a ‘@’ symbol in the form ‘widthxheight’ (if one of ‘width’ or
// ‘height’ is zero, natural scaling is used; if both are zero, original image
// dimensions in pixels are used):
T3(0, 0.09, 0, TextAttributes("Align", "Center")){
"file://t4_image.png@0.01x0"
};

// The 3D orientation of the image can be specified by proving the direction

// of the bottom and left edge of the image in model space:
T3(-0.01, 0.09, 0, 0){ "file://t4_image.png@0.01x0,0,0,1,0,1,0" };

// The image can also be drawn in "billboard" mode, i.e. always parallel to
// the camera, by using the ‘#’ symbol:
T3(0, 0.12, 0, TextAttributes("Align", "Center")){
"file://t4_image.png@0.01x0#"
26 Gmsh 4.11.1

};

// The size of 2D annotations is given directly in pixels:

T2(350, -7, 0){ "file://t4_image.png@20x0" };
};

// This post-processing view is in the "parsed" format, i.e. it is interpreted

// using the same parser as the ‘.geo’ file. For large post-processing datasets,
// that contain actual field values defined on a mesh, you should use the MSH
// file format instead, which allows to efficiently store continuous or
// discontinuous scalar, vector and tensor fields, or arbitrary polynomial
// order.

// Views and geometrical entities can be made to respond to double-click events,

// here to print some messages to the console:

View[0].DoubleClickedCommand = "Printf(’View[0] has been double-clicked!’);";

Geometry.DoubleClickedCurveCommand = "Printf(’Curve %g has been double-clicked!’,
Geometry.DoubleClickedEntityTag);";

// We can also change the color of some entities:

Color Grey50{ Surface{ 22 }; }

Color Purple{ Surface{ 24 }; }
Color Red{ Curve{ 1:14 }; }
Color Yellow{ Curve{ 15:20 }; }

2.5 t5: Mesh sizes, macros, loops, holes in volumes

See t5.geo. Also available in C++ (t5.cpp), Python (t5.py), Julia (t5.jl) and Fortran (t5.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 5
//
// Mesh sizes, macros, loops, holes in volumes
//
// -----------------------------------------------------------------------------

// We start by defining some target mesh sizes:

lcar1 = .1;
Chapter 2: Gmsh tutorial 27

lcar2 = .0005;
lcar3 = .055;

// If we wanted to change these mesh sizes globally (without changing the above
// definitions), we could give a global scaling factor for all mesh sizes on the
// command line with the ‘-clscale’ option (or with ‘Mesh.MeshSizeFactor’ in an
// option file). For example, with:
//
// > gmsh t5.geo -clscale 1
//
// this input file produces a mesh of approximately 3000 nodes and 14,000
// tetrahedra. With
//
// > gmsh t5.geo -clscale 0.2
//
// the mesh counts approximately 231,000 nodes and 1,360,000 tetrahedra. You can
// check mesh statistics in the graphical user interface with the
// ‘Tools->Statistics’ menu.
//
// See ‘t10.geo’ for more information about mesh sizes.

// We proceed by defining some elementary entities describing a truncated cube:

Point(1) = {0.5,0.5,0.5,lcar2}; Point(2) = {0.5,0.5,0,lcar1};

Point(3) = {0,0.5,0.5,lcar1}; Point(4) = {0,0,0.5,lcar1};
Point(5) = {0.5,0,0.5,lcar1}; Point(6) = {0.5,0,0,lcar1};
Point(7) = {0,0.5,0,lcar1}; Point(8) = {0,1,0,lcar1};
Point(9) = {1,1,0,lcar1}; Point(10) = {0,0,1,lcar1};
Point(11) = {0,1,1,lcar1}; Point(12) = {1,1,1,lcar1};
Point(13) = {1,0,1,lcar1}; Point(14) = {1,0,0,lcar1};

Line(1) = {8,9}; Line(2) = {9,12}; Line(3) = {12,11};

Line(4) = {11,8}; Line(5) = {9,14}; Line(6) = {14,13};
Line(7) = {13,12}; Line(8) = {11,10}; Line(9) = {10,13};
Line(10) = {10,4}; Line(11) = {4,5}; Line(12) = {5,6};
Line(13) = {6,2}; Line(14) = {2,1}; Line(15) = {1,3};
Line(16) = {3,7}; Line(17) = {7,2}; Line(18) = {3,4};
Line(19) = {5,1}; Line(20) = {7,8}; Line(21) = {6,14};

Curve Loop(22) = {-11,-19,-15,-18}; Plane Surface(23) = {22};

Curve Loop(24) = {16,17,14,15}; Plane Surface(25) = {24};
Curve Loop(26) = {-17,20,1,5,-21,13}; Plane Surface(27) = {26};
Curve Loop(28) = {-4,-1,-2,-3}; Plane Surface(29) = {28};
Curve Loop(30) = {-7,2,-5,-6}; Plane Surface(31) = {30};
Curve Loop(32) = {6,-9,10,11,12,21}; Plane Surface(33) = {32};
Curve Loop(34) = {7,3,8,9}; Plane Surface(35) = {34};
Curve Loop(36) = {-10,18,-16,-20,4,-8}; Plane Surface(37) = {36};
Curve Loop(38) = {-14,-13,-12,19}; Plane Surface(39) = {38};

// Instead of using included files, we now use a user-defined macro in order

// to carve some holes in the cube:
28 Gmsh 4.11.1

Macro CheeseHole

// In the following commands we use the reserved variable name ‘newp’, which
// automatically selects a new point tag. Analogously to ‘newp’, the special
// variables ‘newc’, ‘newcl, ‘news’, ‘newsl’ and ‘newv’ select new curve,
// curve loop, surface, surface loop and volume tags.
//
// If ‘Geometry.OldNewReg’ is set to 0, the new tags are chosen as the highest
// current tag for each category (points, curves, curve loops, ...), plus
// one. By default, for backward compatibility, ‘Geometry.OldNewReg’ is set
// to 1, and only two categories are used: one for points and one for the
// rest.

p1 = newp; Point(p1) = {x, y, z, lcar3};

p2 = newp; Point(p2) = {x+r,y, z, lcar3};
p3 = newp; Point(p3) = {x, y+r,z, lcar3};
p4 = newp; Point(p4) = {x, y, z+r,lcar3};
p5 = newp; Point(p5) = {x-r,y, z, lcar3};
p6 = newp; Point(p6) = {x, y-r,z, lcar3};
p7 = newp; Point(p7) = {x, y, z-r,lcar3};

c1 = newc; Circle(c1) = {p2,p1,p7}; c2 = newc; Circle(c2) = {p7,p1,p5};

c3 = newc; Circle(c3) = {p5,p1,p4}; c4 = newc; Circle(c4) = {p4,p1,p2};
c5 = newc; Circle(c5) = {p2,p1,p3}; c6 = newc; Circle(c6) = {p3,p1,p5};
c7 = newc; Circle(c7) = {p5,p1,p6}; c8 = newc; Circle(c8) = {p6,p1,p2};
c9 = newc; Circle(c9) = {p7,p1,p3}; c10 = newc; Circle(c10) = {p3,p1,p4};
c11 = newc; Circle(c11) = {p4,p1,p6}; c12 = newc; Circle(c12) = {p6,p1,p7};

// We need non-plane surfaces to define the spherical holes. Here we use

// ‘Surface’, which can be used for surfaces with 3 or 4 curves on their
// boundary. With the he built-in kernel, if the curves are circle arcs, ruled
// surfaces are created; otherwise transfinite interpolation is used.
//
// With the OpenCASCADE kernel, ‘Surface’ uses a much more general generic
// surface filling algorithm, creating a BSpline surface passing through an
// arbitrary number of boundary curves; and ‘ThruSections’ allows to create
// ruled surfaces (see ‘t19.geo’).

l1 = newcl; Curve Loop(l1) = {c5,c10,c4};

l2 = newcl; Curve Loop(l2) = {c9,-c5,c1};
l3 = newcl; Curve Loop(l3) = {c12,-c8,-c1};
l4 = newcl; Curve Loop(l4) = {c8,-c4,c11};
l5 = newcl; Curve Loop(l5) = {-c10,c6,c3};
l6 = newcl; Curve Loop(l6) = {-c11,-c3,c7};
l7 = newcl; Curve Loop(l7) = {-c2,-c7,-c12};
l8 = newcl; Curve Loop(l8) = {-c6,-c9,c2};

s1 = news; Surface(s1) = {l1};

s2 = news; Surface(s2) = {l2};
s3 = news; Surface(s3) = {l3};
s4 = news; Surface(s4) = {l4};
s5 = news; Surface(s5) = {l5};
Chapter 2: Gmsh tutorial 29

s6 = news; Surface(s6) = {l6};

s7 = news; Surface(s7) = {l7};
s8 = news; Surface(s8) = {l8};

// We then store the surface loops tags in a list for later reference (we will
// need these to define the final volume):

theloops[t] = newsl;
Surface Loop(theloops[t]) = {s1, s2, s3, s4, s5, s6, s7, s8};

thehole = newv;
Volume(thehole) = theloops[t];

Return

// We can use a ‘For’ loop to generate five holes in the cube:

x = 0; y = 0.75; z = 0; r = 0.09;

For t In {1:5}

x += 0.166;
z += 0.166;

// We call the ‘CheeseHole’ macro:

Call CheeseHole;

// We define a physical volume for each hole:

Physical Volume (t) = thehole;

// We also print some variables on the terminal (note that, since all
// variables in ‘.geo’ files are treated internally as floating point numbers,
// the format string should only contain valid floating point format
// specifiers like ‘%g’, ‘%f’, ’%e’, etc.):

Printf("Hole %g (center = {%g,%g,%g}, radius = %g) has number %g!",

t, x, y, z, r, thehole);

EndFor

// We can then define the surface loop for the exterior surface of the cube:

theloops[0] = newreg;
Surface Loop(theloops[0]) = {23:39:2};

// The volume of the cube, without the 5 holes, is now defined by 6 surface
// loops: the first surface loop defines the exterior surface; the surface loops
// other than the first one define holes. (Again, to reference an array of
// variables, its identifier is followed by square brackets):
30 Gmsh 4.11.1

Volume(186) = {theloops[]};

// Note that using solid modelling with the OpenCASCADE geometry kernel, the
// same geometry could be built quite differently: see ‘t16.geo’.

// We finally define a physical volume for the elements discretizing the cube,
// without the holes (for which physical groups were already created in the
// ‘For’ loop):

Physical Volume (10) = 186;

// We could make only part of the model visible to only mesh this subset:
//
// Hide {:}
// Recursive Show { Volume{129}; }
// Mesh.MeshOnlyVisible=1;

// Meshing algorithms can changed globally using options:

Mesh.Algorithm = 6; // Frontal-Delaunay for 2D meshes

// They can also be set for individual surfaces, e.g.

MeshAlgorithm Surface {31, 35} = 1; // MeshAdapt on surfaces 31 and 35

// To generate a curvilinear mesh and optimize it to produce provably valid

// curved elements (see A. Johnen, J.-F. Remacle and C. Geuzaine. Geometric
// validity of curvilinear finite elements. Journal of Computational Physics
// 233, pp. 359-372, 2013; and T. Toulorge, C. Geuzaine, J.-F. Remacle,
// J. Lambrechts. Robust untangling of curvilinear meshes. Journal of
// Computational Physics 254, pp. 8-26, 2013), you can uncomment the following
// lines:
//
// Mesh.ElementOrder = 2;
// Mesh.HighOrderOptimize = 2;

2.6 t6: Transfinite meshes, deleting entities

See t6.geo. Also available in C++ (t6.cpp), C (t6.c), Python (t6.py) and Fortran (t6.f90).

// -----------------------------------------------------------------------------
//
Chapter 2: Gmsh tutorial 31

// Gmsh GEO tutorial 6

//
// Transfinite meshes, deleting entities
//
// -----------------------------------------------------------------------------

// Let’s use the geometry from the first tutorial as a basis for this one:
lc = 1e-2;
Point(1) = {0, 0, 0, lc};
Point(2) = {.1, 0, 0, lc};
Point(3) = {.1, .3, 0, lc};
Point(4) = {0, .3, 0, lc};
Line(1) = {1, 2};
Line(2) = {3, 2};
Line(3) = {3, 4};
Line(4) = {4, 1};
Curve Loop(1) = {4, 1, -2, 3};
Plane Surface(1) = {1};

// Delete the surface and the left line, and replace the line with 3 new ones:
Delete{ Surface{1}; Curve{4}; }

p1 = newp; Point(p1) = {-0.05, 0.05, 0, lc};

p2 = newp; Point(p2) = {-0.05, 0.1, 0, lc};

l1 = newc; Line(l1) = {1, p1};

l2 = newc; Line(l2) = {p1, p2};
l3 = newc; Line(l3) = {p2, 4};

// Create a surface:
Curve Loop(2) = {2, -1, l1, l2, l3, -3};
Plane Surface(1) = {-2};

// The ‘Transfinite Curve’ meshing constraints explicitly specifies the location

// of the nodes on the curve. For example, the following command forces 20
// uniformly placed nodes on curve 2 (including the nodes on the two end
// points):
Transfinite Curve{2} = 20;

// Let’s put 20 points total on combination of curves ‘l1’, ‘l2’ and ‘l3’
// (beware that the points ‘p1’ and ‘p2’ are shared by the curves, so we do not
// create 6 + 6 + 10 = 22 nodes, but 20!)
Transfinite Curve{l1} = 6;
Transfinite Curve{l2} = 6;
Transfinite Curve{l3} = 10;

// Finally, we put 30 nodes following a geometric progression on curve 1

// (reversed) and on curve 3:
Transfinite Curve{-1, 3} = 30 Using Progression 1.2;

// The ‘Transfinite Surface’ meshing constraint uses a transfinite interpolation

// algorithm in the parametric plane of the surface to connect the nodes on the
32 Gmsh 4.11.1

// boundary using a structured grid. If the surface has more than 4 corner
// points, the corners of the transfinite interpolation have to be specified by
// hand:
Transfinite Surface{1} = {1, 2, 3, 4};

// To create quadrangles instead of triangles, one can use the ‘Recombine’

// command:
Recombine Surface{1};

// When the surface has only 3 or 4 points on its boundary the list of corners
// can be omitted in the ‘Transfinite Surface’ constraint:
Point(7) = {0.2, 0.2, 0, 1.0};
Point(8) = {0.2, 0.1, 0, 1.0};
Point(9) = {-0, 0.3, 0, 1.0};
Point(10) = {0.25, 0.2, 0, 1.0};
Point(11) = {0.3, 0.1, 0, 1.0};
Line(10) = {8, 11};
Line(11) = {11, 10};
Line(12) = {10, 7};
Line(13) = {7, 8};
Curve Loop(14) = {13, 10, 11, 12};
Plane Surface(15) = {14};
Transfinite Curve {10:13} = 10;
Transfinite Surface{15};

// The way triangles are generated can be controlled by appending "Left",

// "Right" or "Alternate" after the ‘Transfinite Surface’ command. Try e.g.
//
// Transfinite Surface{15} Alternate;

// Finally we apply an elliptic smoother to the grid to have a more regular

// mesh:
Mesh.Smoothing = 100;

2.7 t7: Background meshes

See t7.geo. Also available in C++ (t7.cpp), Python (t7.py) and Fortran (t7.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 7
//
Chapter 2: Gmsh tutorial 33

// Background meshes
//
// -----------------------------------------------------------------------------

// Mesh sizes can be specified very accurately by providing a background mesh,

// i.e., a post-processing view that contains the target mesh sizes.

// Merge a list-based post-processing view containing the target mesh sizes:

Merge "t7_bgmesh.pos";

// If the post-processing view was model-based instead of list-based (i.e. if it

// was based on an actual mesh), we would need to create a new model to contain
// the geometry so that meshing it does not destroy the background mesh. It’s
// not necessary here since the view is list-based, but it does no harm:
NewModel;

// Merge the first tutorial geometry:

Merge "t1.geo";

// Apply the view as the current background mesh size field:

Background Mesh View[0];

// In order to compute the mesh sizes from the background mesh only, and
// disregard any other size constraints, one can set:
Mesh.MeshSizeExtendFromBoundary = 0;
Mesh.MeshSizeFromPoints = 0;
Mesh.MeshSizeFromCurvature = 0;

// See ‘t10.geo’ for additional information: background meshes are actually a

// particular case of general "mesh size fields".

2.8 t8: Post-processing, image export and animations

See t8.geo. Also available in C++ (t8.cpp), Python (t8.py) and Fortran (t8.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 8
//
// Post-processing, image export and animations
//
// -----------------------------------------------------------------------------
34 Gmsh 4.11.1

// In addition to creating geometries and meshes, GEO scripts can also be used
// to manipulate post-processing datasets (called "views" in Gmsh).

// We first include ‘t1.geo’ as well as some post-processing views:

Include "t1.geo";
Include "view1.pos";
Include "view1.pos";
Include "view4.pos";

// Gmsh can read post-processing views in various formats. Here the ‘view1.pos’
// and ‘view4.pos’ files are in the Gmsh "parsed" format, which is interpreted
// directly by the GEO script parser. The parsed format should only be used for
// relatively small datasets of course: for larger datasets using e.g. MSH files
// is much more efficient.

// We then set some general options:

General.Trackball = 0;
General.RotationX = 0; General.RotationY = 0; General.RotationZ = 0;
General.Color.Background = White; General.Color.Foreground = Black;
General.Color.Text = Black;
General.Orthographic = 0;
General.Axes = 0; General.SmallAxes = 0;

// We also set some options for each post-processing view:

v0 = PostProcessing.NbViews-4;
v1 = v0+1; v2 = v0+2; v3 = v0+3;

View[v0].IntervalsType = 2;
View[v0].OffsetZ = 0.05;
View[v0].RaiseZ = 0;
View[v0].Light = 1;
View[v0].ShowScale = 0;
View[v0].SmoothNormals = 1;

View[v1].IntervalsType = 1;
View[v1].ColorTable = { Green, Blue };
View[v1].NbIso = 10;
View[v1].ShowScale = 0;

View[v2].Name = "Test...";
View[v2].Axes = 1;
View[v2].Color.Axes = Black;
View[v2].IntervalsType = 2;
View[v2].Type = 2;
View[v2].IntervalsType = 2;
View[v2].AutoPosition = 0;
View[v2].PositionX = 85;
View[v2].PositionY = 50;
Chapter 2: Gmsh tutorial 35

View[v2].Width = 200;
View[v2].Height = 130;

View[v3].Visible = 0;

// You can save an MPEG movie directly by selecting ‘File->Export’ in the

// GUI. Several predefined animations are setup, for looping on all the time
// steps in views, or for looping between views.

// But a script can be used to build much more complex animations, by changing
// options at run-time and re-rendering the graphics. Each frame can then be
// saved to disk as an image, and multiple frames can be encoded to form a
// movie. Below is an example of such a custom animation.

t = 0; // Initial step

// Loop on num from 1 to 3

For num In {1:3}

View[v0].TimeStep = t; // Set time step

View[v1].TimeStep = t;
View[v2].TimeStep = t;
View[v3].TimeStep = t;

t = (View[v0].TimeStep < View[v0].NbTimeStep-1) ? t+1 : 0; // Increment

View[v0].RaiseZ += 0.01/View[v0].Max * t; // Raise view v0

If (num == 3)
// Resize the graphics when num == 3, to create 640x480 frames
General.GraphicsWidth = General.MenuWidth + 640;
General.GraphicsHeight = 480;
EndIf

frames = 50;

// Loop on num2 from 1 to frames

For num2 In {1:frames}

// Incrementally rotate the scene

General.RotationX += 10;
General.RotationY = General.RotationX / 3;
General.RotationZ += 0.1;

// Sleep for 0.01 second

Sleep 0.01;

// Draw the scene (one could use ‘DrawForceChanged’ instead to force the
// reconstruction of the vertex arrays, e.g. if changing element clipping)
Draw;

If (num == 3)
36 Gmsh 4.11.1

// Uncomment the following lines to save each frame to an image file (the
// ‘Print’ command saves the graphical window; the ‘Sprintf’ function
// permits to create the file names on the fly):

// Print Sprintf("t8-%g.gif", num2);

// Print Sprintf("t8-%g.ppm", num2);
// Print Sprintf("t8-%g.jpg", num2);
EndIf

EndFor

If(num == 3)
// Here we could make a system call to generate a movie. For example, with
// ffmpeg:

// System "ffmpeg -i t8-%d.jpg t8.mpg"

EndIf

EndFor

2.9 t9: Plugins

See t9.geo. Also available in C++ (t9.cpp), Python (t9.py) and Fortran (t9.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 9
//
// Plugins
//
// -----------------------------------------------------------------------------

// Plugins can be added to Gmsh in order to extend its capabilities. For

// example, post-processing plugins can modify views, or create new views based
// on previously loaded views. Several default plugins are statically linked
// with Gmsh, e.g. Isosurface, CutPlane, CutSphere, Skin, Transform or Smooth.
//
// Plugins can be controlled in the same way as other options: either from the
// graphical interface (right click on the view button, then ‘Plugins’), or from
// the command file.

// Let us for example include a three-dimensional scalar view:

Chapter 2: Gmsh tutorial 37

Include "view3.pos" ;

// We then set some options for the ‘Isosurface’ plugin (which extracts an
// isosurface from a 3D scalar view), and run it:

Plugin(Isosurface).Value = 0.67 ; // Iso-value level

Plugin(Isosurface).View = 0 ; // Source view is View[0]
Plugin(Isosurface).Run ; // Run the plugin!

// We also set some options for the ‘CutPlane’ plugin (which computes a section
// of a 3D view using the plane A*x+B*y+C*z+D=0), and then run it:

Plugin(CutPlane).A = 0 ;
Plugin(CutPlane).B = 0.2 ;
Plugin(CutPlane).C = 1 ;
Plugin(CutPlane).D = 0 ;
Plugin(CutPlane).View = 0 ;
Plugin(CutPlane).Run ;

// Add a title (By convention, for window coordinates a value greater than 99999
// represents the center. We could also use ‘General.GraphicsWidth / 2’, but
// that would only center the string for the current window size.):

Plugin(Annotate).Text = "A nice title" ;

Plugin(Annotate).X = 1.e5;
Plugin(Annotate).Y = 50 ;
Plugin(Annotate).Font = "Times-BoldItalic" ;
Plugin(Annotate).FontSize = 28 ;
Plugin(Annotate).Align = "Center" ;
Plugin(Annotate).View = 0 ;
Plugin(Annotate).Run ;

Plugin(Annotate).Text = "(and a small subtitle)" ;

Plugin(Annotate).Y = 70 ;
Plugin(Annotate).Font = "Times-Roman" ;
Plugin(Annotate).FontSize = 12 ;
Plugin(Annotate).Run ;

// We finish by setting some options:

View[0].Light = 1;
View[0].IntervalsType = 1;
View[0].NbIso = 6;
View[0].SmoothNormals = 1;
View[1].IntervalsType = 2;
View[2].IntervalsType = 2;

2.10 t10: Mesh size fields

See t10.geo. Also available in C++ (t10.cpp), Python (t10.py), Julia (t10.jl) and Fortran
(t10.f90).
38 Gmsh 4.11.1

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 10
//
// Mesh size fields
//
// -----------------------------------------------------------------------------

// In addition to specifying target mesh sizes at the points of the geometry

// (see ‘t1.geo’) or using a background mesh (see ‘t7.geo’), you can use general
// mesh size "Fields".

// Let’s create a simple rectangular geometry

lc = .15;
Point(1) = {0.0,0.0,0,lc}; Point(2) = {1,0.0,0,lc};
Point(3) = {1,1,0,lc}; Point(4) = {0,1,0,lc};
Point(5) = {0.2,.5,0,lc};

Line(1) = {1,2}; Line(2) = {2,3}; Line(3) = {3,4}; Line(4) = {4,1};

Curve Loop(5) = {1,2,3,4}; Plane Surface(6) = {5};

// Say we would like to obtain mesh elements with size lc/30 near curve 2 and
// point 5, and size lc elsewhere. To achieve this, we can use two fields:
// "Distance", and "Threshold". We first define a Distance field (‘Field[1]’) on
// points 5 and on curve 2. This field returns the distance to point 5 and to
// (100 equidistant points on) curve 2.
Field[1] = Distance;
Field[1].PointsList = {5};
Field[1].CurvesList = {2};
Field[1].Sampling = 100;

// We then define a ‘Threshold’ field, which uses the return value of the
// ‘Distance’ field 1 in order to define a simple change in element size
// depending on the computed distances
//
// SizeMax - /------------------
// /
// /
// /
// SizeMin -o----------------/
// | | |
Chapter 2: Gmsh tutorial 39

// Point DistMin DistMax

Field[2] = Threshold;
Field[2].InField = 1;
Field[2].SizeMin = lc / 30;
Field[2].SizeMax = lc;
Field[2].DistMin = 0.15;
Field[2].DistMax = 0.5;

// Say we want to modulate the mesh element sizes using a mathematical function
// of the spatial coordinates. We can do this with the MathEval field:
Field[3] = MathEval;
Field[3].F = "Cos(4*3.14*x) * Sin(4*3.14*y) / 10 + 0.101";

// We could also combine MathEval with values coming from other fields. For
// example, let’s define a ‘Distance’ field around point 1
Field[4] = Distance;
Field[4].PointsList = {1};

// We can then create a ‘MathEval’ field with a function that depends on the
// return value of the ‘Distance’ field 4, i.e., depending on the distance to
// point 1 (here using a cubic law, with minimum element size = lc / 100)
Field[5] = MathEval;
Field[5].F = Sprintf("F4^3 + %g", lc / 100);

// We could also use a ‘Box’ field to impose a step change in element sizes
// inside a box
Field[6] = Box;
Field[6].VIn = lc / 15;
Field[6].VOut = lc;
Field[6].XMin = 0.3;
Field[6].XMax = 0.6;
Field[6].YMin = 0.3;
Field[6].YMax = 0.6;
Field[6].Thickness = 0.3;

// Many other types of fields are available: see the reference manual for a
// complete list. You can also create fields directly in the graphical user
// interface by selecting ‘Define->Size fields’ in the ‘Mesh’ module.

// Let’s use the minimum of all the fields as the background mesh size field
Field[7] = Min;
Field[7].FieldsList = {2, 3, 5, 6};
Background Field = 7;

// To determine the size of mesh elements, Gmsh locally computes the minimum of
//
// 1) the size of the model bounding box;
// 2) if ‘Mesh.MeshSizeFromPoints’ is set, the mesh size specified at
// geometrical points;
// 3) if ‘Mesh.MeshSizeFromCurvature’ is positive, the mesh size based on
// curvature (the value specifying the number of elements per 2 * pi rad);
// 4) the background mesh size field;
40 Gmsh 4.11.1

// 5) any per-entity mesh size constraint.

//
// This value is then constrained in the interval [‘Mesh.MeshSizeMin’,
// ‘Mesh.MeshSizeMax’] and multiplied by ‘Mesh.MeshSizeFactor’. In addition,
// boundary mesh sizes are interpolated inside surfaces and/or volumes depending
// on the value of ‘Mesh.MeshSizeExtendFromBoundary’ (which is set by default).
//
// When the element size is fully specified by a mesh size field (as it is in
// this example), it is thus often desirable to set

Mesh.MeshSizeExtendFromBoundary = 0;
Mesh.MeshSizeFromPoints = 0;
Mesh.MeshSizeFromCurvature = 0;

// This will prevent over-refinement due to small mesh sizes on the boundary.

// Finally, while the default "Frontal-Delaunay" 2D meshing algorithm

// (Mesh.Algorithm = 6) usually leads to the highest quality meshes, the
// "Delaunay" algorithm (Mesh.Algorithm = 5) will handle complex mesh size
// fields better - in particular size fields with large element size gradients:

Mesh.Algorithm = 5;

2.11 t11: Unstructured quadrangular meshes

See t11.geo. Also available in C++ (t11.cpp), Python (t11.py) and Fortran (t11.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 11
//
// Unstructured quadrangular meshes
//
// -----------------------------------------------------------------------------

// We have seen in tutorials ‘t3.geo’ and ‘t6.geo’ that extruded and transfinite
// meshes can be "recombined" into quads, prisms or hexahedra by using the
// "Recombine" keyword. Unstructured meshes can be recombined in the same
// way. Let’s define a simple geometry with an analytical mesh size field:

Point(1) = {-1.25, -.5, 0}; Point(2) = {1.25, -.5, 0};

Point(3) = {1.25, 1.25, 0}; Point(4) = {-1.25, 1.25, 0};
Chapter 2: Gmsh tutorial 41

Line(1) = {1, 2}; Line(2) = {2, 3};

Line(3) = {3, 4}; Line(4) = {4, 1};

Curve Loop(4) = {1, 2, 3, 4}; Plane Surface(100) = {4};

Field[1] = MathEval;
Field[1].F = "0.01*(1.0+30.*(y-x*x)*(y-x*x) + (1-x)*(1-x))";
Background Field = 1;

// To generate quadrangles instead of triangles, we can simply add

Recombine Surface{100};

// If we’d had several surfaces, we could have used ‘Recombine Surface {:};’.
// Yet another way would be to specify the global option "Mesh.RecombineAll =
// 1;".

// The default recombination algorithm is called "Blossom": it uses a minimum

// cost perfect matching algorithm to generate fully quadrilateral meshes from
// triangulations. More details about the algorithm can be found in the
// following paper: J.-F. Remacle, J. Lambrechts, B. Seny, E. Marchandise,
// A. Johnen and C. Geuzaine, "Blossom-Quad: a non-uniform quadrilateral mesh
// generator using a minimum cost perfect matching algorithm", International
// Journal for Numerical Methods in Engineering 89, pp. 1102-1119, 2012.

// For even better 2D (planar) quadrilateral meshes, you can try the
// experimental "Frontal-Delaunay for quads" meshing algorithm, which is a
// triangulation algorithm that enables to create right triangles almost
// everywhere: J.-F. Remacle, F. Henrotte, T. Carrier-Baudouin, E. Bechet,
// E. Marchandise, C. Geuzaine and T. Mouton. A frontal Delaunay quad mesh
// generator using the L^inf norm. International Journal for Numerical Methods
// in Engineering, 94, pp. 494-512, 2013. Uncomment the following line to try
// the Frontal-Delaunay algorithms for quads:
//
// Mesh.Algorithm = 8;

// The default recombination algorithm might leave some triangles in the mesh,
// if recombining all the triangles leads to badly shaped quads. In such cases,
// to generate full-quad meshes, you can either subdivide the resulting hybrid
// mesh (with Mesh.SubdivisionAlgorithm = 1), or use the full-quad recombination
// algorithm, which will automatically perform a coarser mesh followed by
// recombination, smoothing and subdivision. Uncomment the following line to try
// the full-quad algorithm:
//
// Mesh.RecombinationAlgorithm = 2; // or 3

// Note that you could also apply the recombination algorithm and/or the
// subdivision step explicitly after meshing, as follows:
//
// Mesh 2;
// RecombineMesh;
42 Gmsh 4.11.1

// Mesh.SubdivisionAlgorithm = 1;
// RefineMesh;

2.12 t12: Cross-patch meshing with compounds

See t12.geo/ Also available in C++ (t12.cpp), Python (t12.py) and Fortran (t12.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 12
//
// Cross-patch meshing with compounds
//
// -----------------------------------------------------------------------------

// "Compound" meshing constraints allow to generate meshes across surface

// boundaries, which can be useful e.g. for imported CAD models (e.g. STEP) with
// undesired small features.

// When a ‘Compound Curve’ or ‘Compound Surface’ meshing constraint is given,

// at mesh generation time Gmsh
// 1. meshes the underlying elementary geometrical entities, individually
// 2. creates a discrete entity that combines all the individual meshes
// 3. computes a discrete parametrization (i.e. a piece-wise linear mapping)
// on this discrete entity
// 4. meshes the discrete entity using this discrete parametrization instead
// of the underlying geometrical description of the underlying elementary
// entities making up the compound
// 5. optionally, reclassifies the mesh elements and nodes on the original
// entities

// Step 3. above can only be performed if the mesh resulting from the
// combination of the individual meshes can be reparametrized, i.e. if the shape
// is "simple enough". If the shape is not amenable to reparametrization, you
// should create a full mesh of the geometry and first re-classify it to
// generate patches amenable to reparametrization (see ‘t13.geo’).

// The mesh of the individual entities performed in Step 1. should usually be

// finer than the desired final mesh; this can be controlled with the
// ‘Mesh.CompoundMeshSizeFactor’ option.

// The optional reclassification on the underlying elementary entities in Step

Chapter 2: Gmsh tutorial 43

// 5. is governed by the ‘Mesh.CompoundClassify’ option.

lc = 0.1;

Point(1) = {0, 0, 0, lc}; Point(2) = {1, 0, 0, lc};

Point(3) = {1, 1, 0.5, lc}; Point(4) = {0, 1, 0.4, lc};
Point(5) = {0.3, 0.2, 0, lc}; Point(6) = {0, 0.01, 0.01, lc};
Point(7) = {0, 0.02, 0.02, lc}; Point(8) = {1, 0.05, 0.02, lc};
Point(9) = {1, 0.32, 0.02, lc};

Line(1) = {1, 2}; Line(2) = {2, 8}; Line(3) = {8, 9};

Line(4) = {9, 3}; Line(5) = {3, 4}; Line(6) = {4, 7};
Line(7) = {7, 6}; Line(8) = {6, 1}; Spline(9) = {7, 5, 9};
Line(10) = {6, 8};

Curve Loop(11) = {5, 6, 9, 4}; Surface(1) = {11};

Curve Loop(13) = {-9, 3, 10, 7}; Surface(5) = {13};
Curve Loop(15) = {-10, 2, 1, 8}; Surface(10) = {15};

// Treat curves 2, 3 and 4 as a single curve when meshing (i.e. mesh across
// points 6 and 7)
Compound Curve{2, 3, 4};

// Idem with curves 6, 7 and 8

Compound Curve{6, 7, 8};

// Treat surfaces 1, 5 and 10 as a single surface when meshing (i.e. mesh across
// curves 9 and 10)
Compound Surface{1, 5, 10};

2.13 t13: Remeshing an STL file without an underlying CAD

model
See t13.geo. Also available in C++ (t13.cpp), Python (t13.py) and Fortran (t13.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 13
//
// Remeshing an STL file without an underlying CAD model
//
// -----------------------------------------------------------------------------
44 Gmsh 4.11.1

// Let’s merge an STL mesh that we would like to remesh.

Merge "t13_data.stl";

// We first classify ("color") the surfaces by splitting the original surface

// along sharp geometrical features. This will create new discrete surfaces,
// curves and points.

DefineConstant[
// Angle between two triangles above which an edge is considered as sharp
angle = {40, Min 20, Max 120, Step 1,
Name "Parameters/Angle for surface detection"},
// For complex geometries, patches can be too complex, too elongated or too
// large to be parametrized; setting the following option will force the
// creation of patches that are amenable to reparametrization:
forceParametrizablePatches = {0, Choices{0,1},
Name "Parameters/Create surfaces guaranteed to be parametrizable"},
// For open surfaces include the boundary edges in the classification process:
includeBoundary = 1,
// Force curves to be split on given angle:
curveAngle = 180
];
ClassifySurfaces{angle * Pi/180, includeBoundary, forceParametrizablePatches,
curveAngle * Pi / 180};

// Create a geometry for all the discrete curves and surfaces in the mesh, by
// computing a parametrization for each one
CreateGeometry;

// In batch mode the two steps above can be performed with ‘gmsh t13.stl
// -reparam 40’, which will save ‘t13.msh’ containing the parametrizations, and
// which can thus subsequently be remeshed.

// Note that if a CAD model (e.g. as a STEP file, see ‘t20.geo’) is available
// instead of an STL mesh, it is usually better to use that CAD model instead of
// the geometry created by reparametrizing the mesh. Indeed, CAD geometries will
// in general be more accurate, with smoother parametrizations, and will lead to
// more efficient and higher quality meshing. Discrete surface remeshing in Gmsh
// is optimized to handle dense STL meshes coming from e.g. imaging systems
// where no CAD is available; it is less well suited for the poor quality STL
// triangulations (optimized for size, with e.g. very elongated triangles) that
// are usually generated by CAD tools for e.g. 3D printing.

// Create a volume as usual

Surface Loop(1) = Surface{:};
Volume(1) = {1};

// We specify element sizes imposed by a size field, just because we can :-)
funny = DefineNumber[0, Choices{0,1},
Name "Parameters/Apply funny mesh size field?" ];

Field[1] = MathEval;
Chapter 2: Gmsh tutorial 45

If(funny)
Field[1].F = "2*Sin((x+y)/5) + 3";
Else
Field[1].F = "4";
EndIf
Background Field = 1;

2.14 t14: Homology and cohomology computation

See t14.geo. Also available in C++ (t14.cpp), Python (t14.py) and Fortran (t14.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 14
//
// Homology and cohomology computation
//
// -----------------------------------------------------------------------------

// Homology computation in Gmsh finds representative chains of (relative)

// (co)homology space bases using a mesh of a model. The representative basis
// chains are stored in the mesh as physical groups of Gmsh, one for each chain.

// Create an example geometry

m = 0.5; // mesh size

h = 2; // height in the z-direction

Point(1) = {0, 0, 0, m}; Point(2) = {10, 0, 0, m};

Point(3) = {10, 10, 0, m}; Point(4) = {0, 10, 0, m};
Point(5) = {4, 4, 0, m}; Point(6) = {6, 4, 0, m};
Point(7) = {6, 6, 0, m}; Point(8) = {4, 6, 0, m};

Point(9) = {2, 0, 0, m}; Point(10) = {8, 0, 0, m};

Point(11) = {2, 10, 0, m}; Point(12) = {8, 10, 0, m};

Line(1) = {1, 9}; Line(2) = {9, 10}; Line(3) = {10, 2};

Line(4) = {2, 3}; Line(5) = {3, 12}; Line(6) = {12, 11};
Line(7) = {11, 4}; Line(8) = {4, 1}; Line(9) = {5, 6};
Line(10) = {6, 7}; Line(11) = {7, 8}; Line(12) = {8, 5};

Curve Loop(13) = {6, 7, 8, 1, 2, 3, 4, 5};

46 Gmsh 4.11.1

Curve Loop(14) = {11, 12, 9, 10};

Plane Surface(15) = {13, 14};

e() = Extrude {0, 0, h}{ Surface{15}; };

// Create physical groups, which are used to define the domain of the
// (co)homology computation and the subdomain of the relative (co)homology
// computation.

// Whole domain
Physical Volume(1) = {e(1)};

// Four "terminals" of the model

Physical Surface(70) = {e(3)};
Physical Surface(71) = {e(5)};
Physical Surface(72) = {e(7)};
Physical Surface(73) = {e(9)};

// Whole domain surface

bnd() = Boundary{ Volume{e(1)}; };
Physical Surface(80) = bnd();

// Complement of the domain surface with respect to the four terminals

bnd() -= {e(3), e(5), e(7), e(9)};
Physical Surface(75) = bnd();

// Find bases for relative homology spaces of the domain modulo the four
// terminals.
Homology {{1}, {70, 71, 72, 73}};

// Find homology space bases isomorphic to the previous bases: homology spaces
// modulo the non-terminal domain surface, a.k.a the thin cuts.
Homology {{1}, {75}};

// Find cohomology space bases isomorphic to the previous bases: cohomology

// spaces of the domain modulo the four terminals, a.k.a the thick cuts.
Cohomology {{1}, {70, 71, 72, 73}};

// More examples:
// Homology {1};
// Homology;
// Homology {{1}, {80}};
// Homology {{}, {80}};

// For more information, see M. Pellikka, S. Suuriniemi, L. Kettunen and

// C. Geuzaine. Homology and cohomology computation in finite element
// modeling. SIAM Journal on Scientific Computing 35(5), pp. 1195-1214, 2013.

2.15 t15: Embedded points, lines and surfaces

See t15.geo. Also available in C++ (t15.cpp), Python (t15.py) and Fortran (t15.f90).
Chapter 2: Gmsh tutorial 47

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 15
//
// Embedded points, lines and surfaces
//
// -----------------------------------------------------------------------------

// By default, across geometrical dimensions meshes generated by Gmsh are only

// conformal if lower dimensional entities are on the boundary of higher
// dimensional ones (i.e. if points, curves or surfaces are part of the boundary
// of volumes).

// Embedding constraints allow to force a mesh to be conformal to other lower

// dimensional entities.

// We start one again by including the first tutorial:

Include "t1.geo";

// We change the mesh size to generate coarser mesh

lc = lc * 4;
MeshSize {1:4} = lc;

// We define a new point

Point(5) = {0.02, 0.02, 0, lc};

// One can force this point to be included ("embedded") in the 2D mesh, using
// the ‘Point In Surface’ command:
Point{5} In Surface{1};

// In the same way, one can force a curve to be embedded in the 2D mesh using
// the ‘Curve in Surface’ command:
Point(6) = {0.02, 0.12, 0, lc};
Point(7) = {0.04, 0.18, 0, lc};
Line(5) = {6, 7};
Curve{5} In Surface{1};

// One can also embed points and curves in a volume using the ‘Curve/Point In
// Volume’ commands:
Extrude {0, 0, 0.1}{ Surface {1}; }

p = newp;
Point(p) = {0.07, 0.15, 0.025, lc};
48 Gmsh 4.11.1

Point{p} In Volume {1};

l = newc;
Point(p+1) = {0.025, 0.15, 0.025, lc};
Line(l) = {7, p+1};
Curve{l} In Volume {1};

// Finally, one can also embed a surface in a volume using the ‘Surface In
// Volume’ command:
Point(p+2) = {0.02, 0.12, 0.05, lc};
Point(p+3) = {0.04, 0.12, 0.05, lc};
Point(p+4) = {0.04, 0.18, 0.05, lc};
Point(p+5) = {0.02, 0.18, 0.05, lc};
Line(l+1) = {p+2, p+3};
Line(l+2) = {p+3, p+4};
Line(l+3) = {p+4, p+5};
Line(l+4) = {p+5, p+2};
ll = newcl;
Curve Loop(ll) = {l+1:l+4};
s = news;
Plane Surface(s) = {ll};
Surface{s} In Volume {1};

// Note that with the OpenCASCADE kernel (see ‘t16.geo’), when the
// ‘BooleanFragments’ command is applied to entities of different dimensions,
// the lower dimensional entities will be autmatically embedded in the higher
// dimensional entities if necessary.

Physical Point("Embedded point") = {p};

Physical Curve("Embdded curve") = {l};
Physical Surface("Embedded surface") = {s};
Physical Volume("Volume") = {1};

2.16 t16: Constructive Solid Geometry, OpenCASCADE

geometry kernel
See t16.geo. Also available in C++ (t16.cpp), C (t16.c), Python (t16.py), Julia (t16.jl) and
Fortran (t16.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 16
Chapter 2: Gmsh tutorial 49

//
// Constructive Solid Geometry, OpenCASCADE geometry kernel
//
// -----------------------------------------------------------------------------

// Instead of constructing a model in a bottom-up fashion with Gmsh’s built-in

// geometry kernel, starting with version 3 Gmsh allows you to directly use
// alternative geometry kernels. Here we use the OpenCASCADE kernel:

SetFactory("OpenCASCADE");

// Let’s build the same model as in ‘t5.geo’, but using constructive solid
// geometry.

// We first create two cubes:

Box(1) = {0,0,0, 1,1,1};
Box(2) = {0,0,0, 0.5,0.5,0.5};

// We apply a boolean difference to create the "cube minus one eigth" shape:
BooleanDifference(3) = { Volume{1}; Delete; }{ Volume{2}; Delete; };

// Boolean operations with OpenCASCADE always create new entities. Adding

// ‘Delete’ in the arguments allows to automatically delete the original
// entities.

// We then create the five spheres:

x = 0 ; y = 0.75 ; z = 0 ; r = 0.09 ;
For t In {1:5}
x += 0.166 ;
z += 0.166 ;
Sphere(3 + t) = {x,y,z,r};
Physical Volume(t) = {3 + t};
EndFor

// If we had wanted five empty holes we would have used ‘BooleanDifference’

// again. Here we want five spherical inclusions, whose mesh should be conformal
// with the mesh of the cube: we thus use ‘BooleanFragments’, which intersects
// all volumes in a conformal manner (without creating duplicate interfaces):
v() = BooleanFragments{ Volume{3}; Delete; }{ Volume{3 + 1 : 3 + 5}; Delete; };

// When the boolean operation leads to simple modifications of entities, and if

// one deletes the original entities with ‘Delete’, Gmsh tries to assign the
// same tag to the new entities. (This behavior is governed by the
// ‘Geometry.OCCBooleanPreserveNumbering’ option.)

// Here the ‘Physical Volume’ definitions made above will thus still work, as
// the five spheres (volumes 4, 5, 6, 7 and 8), which will be deleted by the
// fragment operations, will be recreated identically (albeit with new surfaces)
// with the same tags.

// The tag of the cube will change though, so we need to access it

// programmatically:
50 Gmsh 4.11.1

Physical Volume(10) = v(#v()-1);

// Creating entities using constructive solid geometry is very powerful, but can
// lead to practical issues for e.g. setting mesh sizes at points, or
// identifying boundaries.

// To identify points or other bounding entities you can take advantage of the
// ‘PointfsOf’ (a special case of the more general ‘Boundary’ command) and the
// ‘In BoundingBox’ commands.
lcar1 = .1;
lcar2 = .0005;
lcar3 = .055;
eps = 1e-3;

// Assign a mesh size to all the points of all the volumes:

MeshSize{ PointsOf{ Volume{:}; } } = lcar1;

// Override this constraint on the points of the five spheres:

MeshSize{ PointsOf{ Volume{3 + 1 : 3 + 5}; } } = lcar3;

// Select the corner point by searching for it geometrically:

p() = Point In BoundingBox{0.5-eps, 0.5-eps, 0.5-eps,
0.5+eps, 0.5+eps, 0.5+eps};
MeshSize{ p() } = lcar2;

// Additional examples created with the OpenCASCADE geometry kernel are

// available in ‘t18.geo’, ‘t19.geo’ and ‘t20.geo’, as well as in the
// ‘examples/boolean’ directory.

2.17 t17: Anisotropic background mesh

See t17.geo. Also available in C++ (t17.cpp), Python (t17.py) and Fortran (t17.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 17
//
// Anisotropic background mesh
//
// -----------------------------------------------------------------------------

// As seen in ‘t7.geo’, mesh sizes can be specified very accurately by providing

Chapter 2: Gmsh tutorial 51

// a background mesh, i.e., a post-processing view that contains the target mesh
// sizes.

// Here, the background mesh is represented as a metric tensor field defined on

// a square. One should use bamg as 2d mesh generator to enable anisotropic
// meshes in 2D.

SetFactory("OpenCASCADE");

// Create a square
Rectangle(1) = {-2, -2, 0, 4, 4};

// Merge a post-processing view containing the target anisotropic mesh sizes

Merge "t17_bgmesh.pos";

// Apply the view as the current background mesh

Background Mesh View[0];

// Use bamg
Mesh.SmoothRatio = 3;
Mesh.AnisoMax = 1000;
Mesh.Algorithm = 7;

2.18 t18: Periodic meshes

See t18.geo. Also available in C++ (t18.cpp), Python (t18.py) and Fortran (t18.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 18
//
// Periodic meshes
//
// -----------------------------------------------------------------------------

// Periodic meshing constraints can be imposed on surfaces and curves.

// Let’s use the OpenCASCADE geometry kernel to build two geometries.

SetFactory("OpenCASCADE");

// The first geometry is very simple: a unit cube with a non-uniform mesh size
52 Gmsh 4.11.1

// constraint (set on purpose to be able to verify visually that the periodicity

// constraint works!):

Box(1) = {0, 0, 0, 1, 1, 1};

MeshSize {:} = 0.1;
MeshSize {1} = 0.02;

// To impose that the mesh on surface 2 (the right side of the cube) should
// match the mesh from surface 1 (the left side), the following periodicity
// constraint is set:
Periodic Surface {2} = {1} Translate {1, 0, 0};

// During mesh generation, the mesh on surface 2 will be created by copying the
// mesh from surface 1. Periodicity constraints can be specified with a
// ‘Translation’, a ‘Rotation’ or a general ‘Affine’ transform.

// Multiple periodicities can be imposed in the same way:

Periodic Surface {6} = {5} Translate {0, 0, 1};
Periodic Surface {4} = {3} Translate {0, 1, 0};

// For more complicated cases, finding the corresponding surfaces by hand can be
// tedious, especially when geometries are created through solid
// modelling. Let’s construct a slightly more complicated geometry.

// We start with a cube and some spheres:

Box(10) = {2, 0, 0, 1, 1, 1};
x = 2-0.3; y = 0; z = 0;
Sphere(11) = {x, y, z, 0.35};
Sphere(12) = {x+1, y, z, 0.35};
Sphere(13) = {x, y+1, z, 0.35};
Sphere(14) = {x, y, z+1, 0.35};
Sphere(15) = {x+1, y+1, z, 0.35};
Sphere(16) = {x, y+1, z+1, 0.35};
Sphere(17) = {x+1, y, z+1, 0.35};
Sphere(18) = {x+1, y+1, z+1, 0.35};

// We first fragment all the volumes, which will leave parts of spheres
// protruding outside the cube:
v() = BooleanFragments { Volume{10}; Delete; }{ Volume{11:18}; Delete; };

// Ask OpenCASCADE to compute more accurate bounding boxes of entities using the
// STL mesh:
Geometry.OCCBoundsUseStl = 1;

// We then retrieve all the volumes in the bounding box of the original cube,
// and delete all the parts outside it:
eps = 1e-3;
vin() = Volume In BoundingBox {2-eps,-eps,-eps, 2+1+eps,1+eps,1+eps};
v() -= vin();
Recursive Delete{ Volume{v()}; }

// We now set a non-uniform mesh size constraint (again to check results

Chapter 2: Gmsh tutorial 53

// visually):
MeshSize { PointsOf{ Volume{vin()}; }} = 0.1;
p() = Point In BoundingBox{2-eps, -eps, -eps, 2+eps, eps, eps};
MeshSize {p()} = 0.001;

// We now identify corresponding surfaces on the left and right sides of the
// geometry automatically.

// First we get all surfaces on the left:

Sxmin() = Surface In BoundingBox{2-eps, -eps, -eps, 2+eps, 1+eps, 1+eps};

For i In {0:#Sxmin()-1}
// Then we get the bounding box of each left surface
bb() = BoundingBox Surface { Sxmin(i) };
// We translate the bounding box to the right and look for surfaces inside it:
Sxmax() = Surface In BoundingBox { bb(0)-eps+1, bb(1)-eps, bb(2)-eps,
bb(3)+eps+1, bb(4)+eps, bb(5)+eps };
// For all the matches, we compare the corresponding bounding boxes...
For j In {0:#Sxmax()-1}
bb2() = BoundingBox Surface { Sxmax(j) };
bb2(0) -= 1;
bb2(3) -= 1;
// ...and if they match, we apply the periodicity constraint
If(Fabs(bb2(0)-bb(0)) < eps && Fabs(bb2(1)-bb(1)) < eps &&
Fabs(bb2(2)-bb(2)) < eps && Fabs(bb2(3)-bb(3)) < eps &&
Fabs(bb2(4)-bb(4)) < eps && Fabs(bb2(5)-bb(5)) < eps)
Periodic Surface {Sxmax(j)} = {Sxmin(i)} Translate {1,0,0};
EndIf
EndFor
EndFor

2.19 t19: Thrusections, fillets, pipes, mesh size from curvature

See t19.geo. Also available in C++ (t19.cpp), Python (t19.py) and Fortran (t19.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 19
//
// Thrusections, fillets, pipes, mesh size from curvature
//
// -----------------------------------------------------------------------------
54 Gmsh 4.11.1

// The OpenCASCADE geometry kernel supports several useful features for solid
// modelling.

SetFactory("OpenCASCADE");

// Volumes can be constructed from (closed) curve loops thanks to the

// ‘ThruSections’ command
Circle(1) = {0,0,0, 0.5}; Curve Loop(1) = 1;
Circle(2) = {0.1,0.05,1, 0.1}; Curve Loop(2) = 2;
Circle(3) = {-0.1,-0.1,2, 0.3}; Curve Loop(3) = 3;
ThruSections(1) = {1:3};

// With ‘Ruled ThruSections’ you can force the use of ruled surfaces:
Circle(11) = {2+0,0,0, 0.5}; Curve Loop(11) = 11;
Circle(12) = {2+0.1,0.05,1, 0.1}; Curve Loop(12) = 12;
Circle(13) = {2-0.1,-0.1,2, 0.3}; Curve Loop(13) = 13;
Ruled ThruSections(11) = {11:13};

// We copy the first volume, and fillet all its edges:

v() = Translate{4, 0, 0} { Duplicata{ Volume{1}; } };
f() = Abs(Boundary{ Volume{v(0)}; });
e() = Unique(Abs(Boundary{ Surface{f()}; }));
Fillet{v(0)}{e()}{0.1}

// OpenCASCADE also allows general extrusions along a smooth path. Let’s first
// define a spline curve:
nturns = 1;
npts = 20;
r = 1;
h = 1 * nturns;
For i In {0 : npts - 1}
theta = i * 2*Pi*nturns/npts;
Point(1000 + i) = {r * Cos(theta), r * Sin(theta), i * h/npts};
EndFor
Spline(1000) = {1000 : 1000 + npts - 1};

// A wire is like a curve loop, but open:

Wire(1000) = {1000};

// We define the shape we would like to extrude along the spline (a disk):
Disk(1000) = {1,0,0, 0.2};
Rotate {{1, 0, 0}, {0, 0, 0}, Pi/2} { Surface{1000}; }

// We extrude the disk along the spline to create a pipe:

Extrude { Surface{1000}; } Using Wire {1000}

// We delete the source surface, and increase the number of sub-edges for a
// nicer display of the geometry:
Delete{ Surface{1000}; }
Geometry.NumSubEdges = 1000;
Chapter 2: Gmsh tutorial 55

// We can activate the calculation of mesh element sizes based on curvature

// (here with a target of 20 elements per 2*Pi radians):
Mesh.MeshSizeFromCurvature = 20;

// We can constraint the min and max element sizes to stay within reasonnable
// values (see ‘t10.geo’ for more details):
Mesh.MeshSizeMin = 0.001;
Mesh.MeshSizeMax = 0.3;

2.20 t20: STEP import and manipulation, geometry

partitioning
See t20.geo. Also available in C++ (t20.cpp), Python (t20.py) and Fortran (t20.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 20
//
// STEP import and manipulation, geometry partitioning
//
// -----------------------------------------------------------------------------

// The OpenCASCADE geometry kernel allows to import STEP files and to modify
// them. In this tutorial we will load a STEP geometry and partition it into
// slices.

SetFactory("OpenCASCADE");

// Load a STEP file (using ‘ShapeFromFile’ instead of ‘Merge’ allows to directly

// retrieve the tags of the highest dimensional imported entities):
v() = ShapeFromFile("t20_data.step");

// If we had specified
//
// Geometry.OCCTargetUnit = "M";
//
// before merging the STEP file, OpenCASCADE would have converted the units to
// meters (instead of the default, which is millimeters).

// Get the bounding box of the volume:

bbox() = BoundingBox Volume{v()};
xmin = bbox(0);
56 Gmsh 4.11.1

ymin = bbox(1);
zmin = bbox(2);
xmax = bbox(3);
ymax = bbox(4);
zmax = bbox(5);

// We want to slice the model into N slices, and either keep the volume slices
// or just the surfaces obtained by the cutting:
DefineConstant[
N = {5, Min 2, Max 100, Step 1, Name "Parameters/0Number of slices"}
dir = {0, Choices{0="X", 1="Y", 2="Z"}, Name "Parameters/1Direction"}
surf = {0, Choices{0, 1}, Name "Parameters/2Keep only surfaces?"}
];

dx = (xmax - xmin);
dy = (ymax - ymin);
dz = (zmax - zmin);
L = (dir == 0) ? dz : dx;
H = (dir == 1) ? dz : dy;

// Create the first cutting plane:

s() = {news};
Rectangle(s(0)) = {xmin, ymin, zmin, L, H};
If(dir == 0)
Rotate{ {0, 1, 0}, {xmin, ymin, zmin}, -Pi/2 } { Surface{s(0)}; }
ElseIf(dir == 1)
Rotate{ {1, 0, 0}, {xmin, ymin, zmin}, Pi/2 } { Surface{s(0)}; }
EndIf
tx = (dir == 0) ? dx / N : 0;
ty = (dir == 1) ? dy / N : 0;
tz = (dir == 2) ? dz / N : 0;
Translate{tx, ty, tz} { Surface{s(0)}; }

// Create the other cutting planes:

For i In {1:N-2}
s() += Translate{i * tx, i * ty, i * tz} { Duplicata{ Surface{s(0)}; } };
EndFor

// Fragment (i.e. intersect) the volume with all the cutting planes:
BooleanFragments{ Volume{v()}; Delete; }{ Surface{s()}; Delete; }

// Now remove all the surfaces (and their bounding entities) that are not on the
// boundary of a volume, i.e. the parts of the cutting planes that "stick out"
// of the volume:
Recursive Delete { Surface{:}; }

If(surf)
// If we want to only keep the surfaces, retrieve the surfaces in bounding
// boxes around the cutting planes...
eps = 1e-4;
s() = {};
For i In {1:N-1}
Chapter 2: Gmsh tutorial 57

xx = (dir == 0) ? xmin : xmax;

yy = (dir == 1) ? ymin : ymax;
zz = (dir == 2) ? zmin : zmax;
s() += Surface In BoundingBox
{xmin - eps + i * tx, ymin - eps + i * ty, zmin - eps + i * tz,
xx + eps + i * tx, yy + eps + i * ty, zz + eps + i * tz};
EndFor
// ...and remove all the other entities:
dels = Surface{:};
dels -= s();
Delete { Volume{:}; Surface{dels()}; Curve{:}; Point{:}; }
EndIf

// Finally, let’s specify a global mesh size:

Mesh.MeshSizeMin = 3;
Mesh.MeshSizeMax = 3;

// To partition the mesh instead of the geometry, see ‘t21.geo’.

2.21 t21: Mesh partitioning

See t21.geo. Also available in C++ (t21.cpp), Python (t21.py) and Fortran (t21.f90).

// -----------------------------------------------------------------------------
//
// Gmsh GEO tutorial 21
//
// Mesh partitioning
//
// -----------------------------------------------------------------------------

// Gmsh can partition meshes using different algorithms, e.g. the graph
// partitioner Metis or the ‘SimplePartition’ plugin. For all the partitining
// algorithms, the relationship between mesh elements and mesh partitions is
// encoded through the creation of new (discrete) elementary entities, called
// "partition entities".
//
// Partition entities behave exactly like other discrete elementary entities;
// the only difference is that they keep track of both a mesh partition index
// and their parent elementary entity.
//
// The major advantage of this approach is that it allows to maintain a full
58 Gmsh 4.11.1

// boundary representation of the partition entities, which Gmsh creates

// automatically if ‘Mesh.PartitionCreateTopology’ is set.

// Let us start by creating a simple geometry with two adjacent squares sharing
// an edge:
SetFactory("OpenCASCADE");
Rectangle(1) = {0, 0, 0, 1, 1};
Rectangle(2) = {1, 0, 0, 1, 1};
BooleanFragments{ Surface{1}; Delete; }{ Surface{2}; Delete; }
MeshSize {:} = 0.05;

// We create one physical group for each square, and we mesh the resulting
// geometry:
Physical Surface("Left", 100) = 1;
Physical Surface("Right", 200) = 2;
Mesh 2;

// We now define several constants to fine-tune how the mesh will be partitioned
DefineConstant[
partitioner = {0, Choices{0="Metis", 1="SimplePartition"},
Name "Parameters/0Mesh partitioner"}
N = {3, Min 1, Max 256, Step 1,
Name "Parameters/1Number of partitions"}
topology = {1, Choices{0, 1},
Name "Parameters/2Create partition topology (BRep)?"}
ghosts = {0, Choices{0, 1},
Name "Parameters/3Create ghost cells?"}
physicals = {0, Choices{0, 1},
Name "Parameters/3Create new physical groups?"}
write = {1, Choices {0, 1},
Name "Parameters/3Write file to disk?"}
split = {0, Choices {0, 1},
Name "Parameters/4Write one file per partition?"}
];

// Should we create the boundary representation of the partition entities?

Mesh.PartitionCreateTopology = topology;

// Should we create ghost cells?

Mesh.PartitionCreateGhostCells = ghosts;

// Should we automatically create new physical groups on the partition entities?

Mesh.PartitionCreatePhysicals = physicals;

// Should we keep backward compatibility with pre-Gmsh 4, e.g. to save the mesh
// in MSH2 format?
Mesh.PartitionOldStyleMsh2 = 0;

// Should we save one mesh file per partition?

Mesh.PartitionSplitMeshFiles = split;

If (partitioner == 0)
Chapter 2: Gmsh tutorial 59

// Use Metis to create N partitions

PartitionMesh N;
// Several options can be set to control Metis: ‘Mesh.MetisAlgorithm’ (1:
// Recursive, 2: K-way), ‘Mesh.MetisObjective’ (1: min. edge-cut, 2:
// min. communication volume), ‘Mesh.PartitionTriWeight’ (weight of
// triangles), ‘Mesh.PartitionQuadWeight’ (weight of quads), ...
Else
// Use the ‘SimplePartition’ plugin to create chessboard-like partitions
Plugin(SimplePartition).NumSlicesX = N;
Plugin(SimplePartition).NumSlicesY = 1;
Plugin(SimplePartition).NumSlicesZ = 1;
Plugin(SimplePartition).Run;
EndIf

// Save mesh file (or files, if ‘Mesh.PartitionSplitMeshFiles’ is set):

If(write)
Save "t21.msh";
EndIf

2.22 x1: Geometry and mesh data

See x1.py. Also available in C++ (x1.cpp).
# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 1
#
# Geometry and mesh data
#
# -----------------------------------------------------------------------------

# The Python API allows to do much more than what can be done in .geo
# files. These additional features are introduced gradually in the extended
# tutorials, starting with ‘x1.py’.

# In this first extended tutorial, we start by using the API to access basic
# geometrical and mesh data.

import gmsh
import sys

if len(sys.argv) < 2:
print("Usage: " + sys.argv[0] + " file")
exit

gmsh.initialize()

# You can run this tutorial on any file that Gmsh can read, e.g. a mesh file in
# the MSH format: ‘python t1.py file.msh’

gmsh.open(sys.argv[1])

# Print the model name and dimension:

60 Gmsh 4.11.1

print(’Model ’ + gmsh.model.getCurrent() + ’ (’ +
str(gmsh.model.getDimension()) + ’D)’)

# Geometrical data is made of elementary model ‘entities’, called ‘points’

# (entities of dimension 0), ‘curves’ (entities of dimension 1), ‘surfaces’
# (entities of dimension 2) and ‘volumes’ (entities of dimension 3). As we have
# seen in the other Python tutorials, elementary model entities are identified
# by their dimension and by a ‘tag’: a strictly positive identification
# number. Model entities can be either CAD entities (from the built-in ‘geo’
# kernel or from the OpenCASCADE ‘occ’ kernel) or ‘discrete’ entities (defined
# by a mesh). ‘Physical groups’ are collections of model entities and are also
# identified by their dimension and by a tag.

# Get all the elementary entities in the model, as a vector of (dimension, tag)
# pairs:
entities = gmsh.model.getEntities()

for e in entities:
# Dimension and tag of the entity:
dim = e[0]
tag = e[1]

# Mesh data is made of ‘elements’ (points, lines, triangles, ...), defined

# by an ordered list of their ‘nodes’. Elements and nodes are identified by
# ‘tags’ as well (strictly positive identification numbers), and are stored
# ("classified") in the model entity they discretize. Tags for elements and
# nodes are globally unique (and not only per dimension, like entities).

# A model entity of dimension 0 (a geometrical point) will contain a mesh

# element of type point, as well as a mesh node. A model curve will contain
# line elements as well as its interior nodes, while its boundary nodes will
# be stored in the bounding model points. A model surface will contain
# triangular and/or quadrangular elements and all the nodes not classified
# on its boundary or on its embedded entities. A model volume will contain
# tetrahedra, hexahedra, etc. and all the nodes not classified on its
# boundary or on its embedded entities.

# Get the mesh nodes for the entity (dim, tag):

nodeTags, nodeCoords, nodeParams = gmsh.model.mesh.getNodes(dim, tag)

# Get the mesh elements for the entity (dim, tag):

elemTypes, elemTags, elemNodeTags = gmsh.model.mesh.getElements(dim, tag)

# Elements can also be obtained by type, by using ‘getElementTypes()’

# followed by ‘getElementsByType()’.

# Let’s print a summary of the information available on the entity and its
# mesh.

# * Type and name of the entity:

type = gmsh.model.getType(e[0], e[1])
name = gmsh.model.getEntityName(e[0], e[1])
Chapter 2: Gmsh tutorial 61

if len(name): name += ’ ’
print("Entity " + name + str(e) + " of type " + type)

# * Number of mesh nodes and elements:

numElem = sum(len(i) for i in elemTags)
print(" - Mesh has " + str(len(nodeTags)) + " nodes and " + str(numElem) +
" elements")

# * Upward and downward adjacencies:

up, down = gmsh.model.getAdjacencies(e[0], e[1])
if len(up):
print(" - Upward adjacencies: " + str(up))
if len(down):
print(" - Downward adjacencies: " + str(down))

# * Does the entity belong to physical groups?

physicalTags = gmsh.model.getPhysicalGroupsForEntity(dim, tag)
if len(physicalTags):
s = ’’
for p in physicalTags:
n = gmsh.model.getPhysicalName(dim, p)
if n: n += ’ ’
s += n + ’(’ + str(dim) + ’, ’ + str(p) + ’) ’
print(" - Physical groups: " + s)

# * Is the entity a partition entity? If so, what is its parent entity?

partitions = gmsh.model.getPartitions(e[0], e[1])
if len(partitions):
print(" - Partition tags: " + str(partitions) + " - parent entity " +
str(gmsh.model.getParent(e[0], e[1])))

# * List all types of elements making up the mesh of the entity:

for t in elemTypes:
name, dim, order, numv, parv, _ = gmsh.model.mesh.getElementProperties(
t)
print(" - Element type: " + name + ", order " + str(order) + " (" +
str(numv) + " nodes in param coord: " + str(parv) + ")")

# We can use this to clear all the model data:

gmsh.clear()

gmsh.finalize()

2.23 x2: Mesh import, discrete entities, hybrid models, terrain

meshing
See x2.py. Also available in C++ (x2.cpp).
62 Gmsh 4.11.1

# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 2
#
# Mesh import, discrete entities, hybrid models, terrain meshing
#
# -----------------------------------------------------------------------------

import gmsh
import sys
import math

# The API can be used to import a mesh without reading it from a file, by
# creating nodes and elements on the fly and storing them in model
# entities. These model entities can be existing CAD entities, or can be
# discrete entities, entirely defined by the mesh.
#
# Discrete entities can be reparametrized (see ‘t13.py’) so that they can be
# remeshed later on; and they can also be combined with built-in CAD entities to
# produce hybrid models.
#
# We combine all these features in this tutorial to perform terrain meshing,
# where the terrain is described by a discrete surface (that we then
# reparametrize) combined with a CAD representation of the underground.

gmsh.initialize()

gmsh.model.add("x2")

# We will create the terrain surface mesh from N x N input data points:
N = 100

# Helper function to return a node tag given two indices i and j:

def tag(i, j):
return (N + 1) * i + j + 1

# The x, y, z coordinates of all the nodes:

coords = []

# The tags of the corresponding nodes:

nodes = []
Chapter 2: Gmsh tutorial 63

# The connectivities of the triangle elements (3 node tags per triangle) on the
# terrain surface:
tris = []

# The connectivities of the line elements on the 4 boundaries (2 node tags

# for each line element):
lin = [[], [], [], []]

# The connectivities of the point elements on the 4 corners (1 node tag for each
# point element):
pnt = [tag(0, 0), tag(N, 0), tag(N, N), tag(0, N)]

for i in range(N + 1):

for j in range(N + 1):
nodes.append(tag(i, j))
coords.extend([
float(i) / N,
float(j) / N, 0.05 * math.sin(10 * float(i + j) / N)
])
if i > 0 and j > 0:
tris.extend([tag(i - 1, j - 1), tag(i, j - 1), tag(i - 1, j)])
tris.extend([tag(i, j - 1), tag(i, j), tag(i - 1, j)])
if (i == 0 or i == N) and j > 0:
lin[3 if i == 0 else 1].extend([tag(i, j - 1), tag(i, j)])
if (j == 0 or j == N) and i > 0:
lin[0 if j == 0 else 2].extend([tag(i - 1, j), tag(i, j)])

# Create 4 discrete points for the 4 corners of the terrain surface:

for i in range(4):
gmsh.model.addDiscreteEntity(0, i + 1)
gmsh.model.setCoordinates(1, 0, 0, coords[3 * tag(0, 0) - 1])
gmsh.model.setCoordinates(2, 1, 0, coords[3 * tag(N, 0) - 1])
gmsh.model.setCoordinates(3, 1, 1, coords[3 * tag(N, N) - 1])
gmsh.model.setCoordinates(4, 0, 1, coords[3 * tag(0, N) - 1])

# Create 4 discrete bounding curves, with their boundary points:

for i in range(4):
gmsh.model.addDiscreteEntity(1, i + 1, [i + 1, i + 2 if i < 3 else 1])

# Create one discrete surface, with its bounding curves:

gmsh.model.addDiscreteEntity(2, 1, [1, 2, -3, -4])

# Add all the nodes on the surface (for simplicity... see below):
gmsh.model.mesh.addNodes(2, 1, nodes, coords)

# Add point elements on the 4 points, line elements on the 4 curves, and
# triangle elements on the surface:
for i in range(4):
# Type 15 for point elements:
gmsh.model.mesh.addElementsByType(i + 1, 15, [], [pnt[i]])
# Type 1 for 2-node line elements:
64 Gmsh 4.11.1

gmsh.model.mesh.addElementsByType(i + 1, 1, [], lin[i])

# Type 2 for 3-node triangle elements:
gmsh.model.mesh.addElementsByType(1, 2, [], tris)

# Reclassify the nodes on the curves and the points (since we put them all on
# the surface before with ‘addNodes’ for simplicity)
gmsh.model.mesh.reclassifyNodes()

# Create a geometry for the discrete curves and surfaces, so that we can remesh
# them later on:
gmsh.model.mesh.createGeometry()

# Note that for more complicated meshes, e.g. for on input unstructured STL
# mesh, we could use ‘classifySurfaces()’ to automatically create the discrete
# entities and the topology; but we would then have to extract the boundaries
# afterwards.

# Create other build-in CAD entities to form one volume below the terrain
# surface. Beware that only built-in CAD entities can be hybrid, i.e. have
# discrete entities on their boundary: OpenCASCADE does not support this
# feature.
p1 = gmsh.model.geo.addPoint(0, 0, -0.5)
p2 = gmsh.model.geo.addPoint(1, 0, -0.5)
p3 = gmsh.model.geo.addPoint(1, 1, -0.5)
p4 = gmsh.model.geo.addPoint(0, 1, -0.5)
c1 = gmsh.model.geo.addLine(p1, p2)
c2 = gmsh.model.geo.addLine(p2, p3)
c3 = gmsh.model.geo.addLine(p3, p4)
c4 = gmsh.model.geo.addLine(p4, p1)
c10 = gmsh.model.geo.addLine(p1, 1)
c11 = gmsh.model.geo.addLine(p2, 2)
c12 = gmsh.model.geo.addLine(p3, 3)
c13 = gmsh.model.geo.addLine(p4, 4)
ll1 = gmsh.model.geo.addCurveLoop([c1, c2, c3, c4])
s1 = gmsh.model.geo.addPlaneSurface([ll1])
ll3 = gmsh.model.geo.addCurveLoop([c1, c11, -1, -c10])
s3 = gmsh.model.geo.addPlaneSurface([ll3])
ll4 = gmsh.model.geo.addCurveLoop([c2, c12, -2, -c11])
s4 = gmsh.model.geo.addPlaneSurface([ll4])
ll5 = gmsh.model.geo.addCurveLoop([c3, c13, 3, -c12])
s5 = gmsh.model.geo.addPlaneSurface([ll5])
ll6 = gmsh.model.geo.addCurveLoop([c4, c10, 4, -c13])
s6 = gmsh.model.geo.addPlaneSurface([ll6])
sl1 = gmsh.model.geo.addSurfaceLoop([s1, s3, s4, s5, s6, 1])
v1 = gmsh.model.geo.addVolume([sl1])
gmsh.model.geo.synchronize()

# Set this to True to build a fully hex mesh:

#transfinite = True
transfinite = False
transfiniteAuto = False
Chapter 2: Gmsh tutorial 65

if transfinite:
NN = 30
for c in gmsh.model.getEntities(1):
gmsh.model.mesh.setTransfiniteCurve(c[1], NN)
for s in gmsh.model.getEntities(2):
gmsh.model.mesh.setTransfiniteSurface(s[1])
gmsh.model.mesh.setRecombine(s[0], s[1])
gmsh.model.mesh.setSmoothing(s[0], s[1], 100)
gmsh.model.mesh.setTransfiniteVolume(v1)
elif transfiniteAuto:
gmsh.option.setNumber(’Mesh.MeshSizeMin’, 0.5)
gmsh.option.setNumber(’Mesh.MeshSizeMax’, 0.5)
# setTransfiniteAutomatic() uses the sizing constraints to set the number
# of points
gmsh.model.mesh.setTransfiniteAutomatic()
else:
gmsh.option.setNumber(’Mesh.MeshSizeMin’, 0.05)
gmsh.option.setNumber(’Mesh.MeshSizeMax’, 0.05)

gmsh.model.mesh.generate(3)
gmsh.write(’x2.msh’)

# Launch the GUI to see the results:

if ’-nopopup’ not in sys.argv:
gmsh.fltk.run()

gmsh.finalize()

2.24 x3: Post-processing data import: list-based

See x3.py. Also available in C++ (x3.cpp).

# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 3
#
# Post-processing data import: list-based
#
# -----------------------------------------------------------------------------

import gmsh
import sys
66 Gmsh 4.11.1

gmsh.initialize(sys.argv)

# Gmsh supports two types of post-processing data: "list-based" and

# "model-based". Both types of data are handled through the ‘view’ interface.

# List-based views are completely independent from any model and any mesh: they
# are self-contained and simply contain lists of coordinates and values, element
# by element, for 3 types of fields (scalar "S", vector "V" and tensor "T") and
# several types of element shapes (point "P", line "L", triangle "T", quadrangle
# "Q", tetrahedron "S", hexahedron "H", prism "I" and pyramid "Y"). (See ‘x4.py’
# for a tutorial on model-based views.)

# To create a list-based view one should first create a view:

t1 = gmsh.view.add("A list-based view")

# List-based data is then added by specifying the type as a 2 character string

# that combines a field type and an element shape (e.g. "ST" for a scalar field
# on triangles), the number of elements to be added, and the concatenated list
# of coordinates (e.g. 3 "x" coordinates, 3 "y" coordinates, 3 "z" coordinates
# for first order triangles) and values for each element (e.g. 3 values for
# first order scalar triangles, repeated for each step if there are several time
# steps).

# Let’s create two triangles...

triangle1 = [0., 1., 1., # x coordinates of the 3 triangle nodes
0., 0., 1., # y coordinates of the 3 triangle nodes
0., 0., 0.] # z coordinates of the 3 triangle nodes
triangle2 = [0., 1., 0., 0., 1., 1., 0., 0., 0.]

# ... and append values for 10 time steps

for step in range(0, 10):
triangle1.extend([10., 11. - step, 12.]) # 3 node values for each step
triangle2.extend([11., 12., 13. + step])

# List-based data is just added by concatenating the data for all the triangles:
gmsh.view.addListData(t1, "ST", 2, triangle1 + triangle2)

# Internally, post-processing views parsed by the .geo file parser create such
# list-based data (see e.g. ‘t7.py’, ‘t8.py’ and ‘t9.py’), independently of any
# mesh.

# Vector or tensor fields can be imported in the same way, the only difference
# beeing the type (starting with "V" for vector fields and "T" for tensor
# fields) and the number of components. For example a vector field on a line
# element can be added as follows:
line = [
0., 1., # x coordinate of the 2 line nodes
1.2, 1.2, # y coordinate of the 2 line nodes
0., 0. # z coordinate of the 2 line nodes
]
for step in range(0, 10):
Chapter 2: Gmsh tutorial 67

# 3 vector components for each node (2 nodes here), for each step
line.extend([10. + step, 0., 0.,
10. + step, 0., 0.])
gmsh.view.addListData(t1, "VL", 1, line)

# List-based data can also hold 2D (in window coordinates) and 3D (in model
# coordinates) strings (see ‘t4.py’). Here we add a 2D string located on the
# bottom-left of the window (with a 20 pixels offset), as well as a 3D string
# located at model coordinates (0.5, 0.5. 0):
gmsh.view.addListDataString(t1, [20., -20.], ["Created with Gmsh"])
gmsh.view.addListDataString(t1, [0.5, 1.5, 0.],
["A multi-step list-based view"],
["Align", "Center", "Font", "Helvetica"])

# The various attributes of the view can be queried and changed using the option
# interface:
gmsh.view.option.setNumber(t1, "TimeStep", 5)
gmsh.view.option.setNumber(t1, "IntervalsType", 3)
ns = gmsh.view.option.getNumber(t1, "NbTimeStep")
print("View " + str(t1) + " has " + str(ns) + " time steps")

# Views can be queried and modified in various ways using plugins (see ‘t9.py’),
# or probed directly using ‘gmsh.view.probe()’ - here at point (0.9, 0.1, 0):
print("Value at (0.9, 0.1, 0)", gmsh.view.probe(t1, 0.9, 0.1, 0))

# Views can be saved to disk using ‘gmsh.view.write()’:

gmsh.view.write(t1, "x3.pos")

# High-order datasets can be provided by setting the interpolation matrices

# explicitly. Let’s create a second view with second order interpolation on
# a 4-node quadrangle.

# Add a new view:

t2 = gmsh.view.add("Second order quad")

# Set the node coordinates:

quad = [0., 1., 1., 0., # x coordinates of the 4 quadrangle nodes
-1.2, -1.2, -0.2, -0.2, # y coordinates of the 4 quadrangle nodes
0., 0., 0., 0.] # z coordinates of the 4 quadrangle nodes

# Add nine values that will be interpolated by second order basis functions
quad.extend([1., 1., 1., 1., 3., 3., 3., 3., -3.])

# Set the two interpolation matrices c[i][j] and e[i][j] defining the d = 9
# basis functions: f[i](u, v, w) = sum_(j = 0, ..., d - 1) c[i][j] u^e[j][0]
# v^e[j][1] w^e[j][2], i = 0, ..., d-1, with u, v, w the coordinates in the
# reference element:
gmsh.view.setInterpolationMatrices(t2, "Quadrangle", 9,
[0, 0, 0.25, 0, 0, -0.25, -0.25, 0, 0.25,
0, 0, 0.25, 0, 0, -0.25, 0.25, 0, -0.25,
0, 0, 0.25, 0, 0, 0.25, 0.25, 0, 0.25,
0, 0, 0.25, 0, 0, 0.25, -0.25, 0, -0.25,
68 Gmsh 4.11.1

0, 0, -0.5, 0.5, 0, 0.5, 0, -0.5, 0,

0, 0.5, -0.5, 0, 0.5, 0, -0.5, 0, 0,
0, 0, -0.5, 0.5, 0, -0.5, 0, 0.5, 0,
0, 0.5, -0.5, 0, -0.5, 0, 0.5, 0, 0,
1, -1, 1, -1, 0, 0, 0, 0, 0],
[0, 0, 0,
2, 0, 0,
2, 2, 0,
0, 2, 0,
1, 0, 0,
2, 1, 0,
1, 2, 0,
0, 1, 0,
1, 1, 0])

# Note that two additional interpolation matrices could also be provided to

# interpolate the geometry, i.e. to interpolate curved elements.

# Add the data to the view:

gmsh.view.addListData(t2, "SQ", 1, quad)

# In order to visualize the high-order field, one must activate adaptive

# visualization, set a visualization error threshold and a maximum subdivision
# level (Gmsh does automatic mesh refinement to visualize the high-order field
# with the requested accuracy):
gmsh.view.option.setNumber(t2, "AdaptVisualizationGrid", 1)
gmsh.view.option.setNumber(t2, "TargetError", 1e-2)
gmsh.view.option.setNumber(t2, "MaxRecursionLevel", 5)

# Launch the GUI to see the results:

if ’-nopopup’ not in sys.argv:
gmsh.fltk.run()

gmsh.finalize()

2.25 x4: Post-processing data import: model-based

See x4.py. Also available in C++ (x4.cpp).

# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 4
Chapter 2: Gmsh tutorial 69

#
# Post-processing data import: model-based
#
# -----------------------------------------------------------------------------

import gmsh
import sys

gmsh.initialize(sys.argv)

# Contrary to list-based view (see ‘x3.py’), model-based views are based on one
# or more meshes. Compared to list-based views, they are thus linked to one
# model (per step). Post-processing data stored in MSH files create such
# model-based views.

# Let’s create a first model-based view using a simple mesh constructed by

# hand. We create a model with a discrete surface
gmsh.model.add("simple model")
surf = gmsh.model.addDiscreteEntity(2)

# We add 4 nodes and 2 3-node triangles (element type "2")

gmsh.model.mesh.addNodes(2, surf, [1, 2, 3, 4],
[0., 0., 0., 1., 0., 0., 1., 1., 0., 0., 1., 0.])
gmsh.model.mesh.addElementsByType(surf, 2, [1, 2], [1, 2, 3, 1, 3, 4])

# We can now create a new model-based view, to which we add 10 steps of

# node-based data:
t1 = gmsh.view.add("Continuous")
for step in range(0, 10):
gmsh.view.addHomogeneousModelData(
t1, step, "simple model", "NodeData",
[1, 2, 3, 4], # tags of nodes
[10., 10., 12. + step, 13. + step]) # data, per node

# Besided node-based data, which result in continuous fields, one can also add
# general discontinous fields defined at the nodes of each element, using
# "ElementNodeData":
t2 = gmsh.view.add("Discontinuous")
for step in range(0, 10):
gmsh.view.addHomogeneousModelData(
t2, step, "simple model", "ElementNodeData",
[1, 2], # tags of elements
[10., 10., 12. + step, 14., 15., 13. + step]) # data per element nodes

# Constant per element datasets can also be created using "ElementData". Note
# that a more general function ‘addModelData’ to add data for hybrid meshes
# (when data is not homogeneous, i.e. when the number of nodes changes between
# elements) is also available.

# Each step of a model-based view can be defined on a different model, i.e. on a

# different mesh. Let’s define a second model and mesh it
gmsh.model.add("another model")
70 Gmsh 4.11.1

gmsh.model.occ.addBox(0, 0, 0, 1, 1, 1)
gmsh.model.occ.synchronize()
gmsh.model.mesh.generate(3)

# We can add other steps to view "t" based on this new mesh:
nodes, coord, _ = gmsh.model.mesh.getNodes()
for step in range(11, 20):
gmsh.view.addHomogeneousModelData(
t1, step, "another model", "NodeData", nodes,
[step * coord[i] for i in range(0, len(coord), 3)])

# This feature allows to create seamless animations for time-dependent datasets

# on deforming or remeshed models.

# High-order node-based datasets are supported without needing to supply the

# interpolation matrices (iso-parametric Lagrange elements). Arbitrary
# high-order datasets can be specified as "ElementNodeData", with the
# interpolation matrices specified in the same as as for list-based views (see
# ‘x3.py’).

# Model-based views can be saved to disk using ‘gmsh.view.write()’; note that

# saving a view based on multiple meshes (like the view ‘t1’) will automatically
# create several files. If the ‘PostProcessing.SaveMesh’ option is not set,
# ‘gmsh.view.write()’ will only save the view data, without the mesh (which
# could be saved independently with ‘gmsh.write()’).
gmsh.view.write(t1, "x4_t1.msh")
gmsh.view.write(t2, "x4_t2.msh")

# Launch the GUI to see the results:

if ’-nopopup’ not in sys.argv:
gmsh.fltk.run()

gmsh.finalize()

2.26 x5: Additional geometrical data: parametrizations,

normals, curvatures
See x5.py. Also available in C++ (x5.cpp).

# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 5
Chapter 2: Gmsh tutorial 71

#
# Additional geometrical data: parametrizations, normals, curvatures
#
# -----------------------------------------------------------------------------

import gmsh
import sys
import math

gmsh.initialize(sys.argv)

# The API provides access to geometrical data in a CAD kernel agnostic manner.

# Let’s create a simple CAD model by fusing a sphere and a cube, then mesh the
# surfaces:
gmsh.model.add("x5")
s = gmsh.model.occ.addSphere(0, 0, 0, 1)
b = gmsh.model.occ.addBox(0.5, 0, 0, 1.3, 2, 3)
gmsh.model.occ.fuse([(3, s)], [(3, b)])
gmsh.model.occ.synchronize()
gmsh.model.mesh.generate(2)

# We can for example retrieve the exact normals and the curvature at all the
# mesh nodes (i.e. not normals and curvatures computed from the mesh, but
# directly evaluated on the geometry), by querying the CAD kernels at the
# corresponding parametric coordinates.
normals = []
curvatures = []

# For each surface in the model:

for e in gmsh.model.getEntities(2):
# Retrieve the surface tag
s = e[1]

# Get the mesh nodes on the surface, including those on the boundary
# (contrary to internal nodes, which store their parametric coordinates,
# boundary nodes will be reparametrized on the surface in order to compute
# their parametric coordinates, the result being different when
# reparametrized on another adjacent surface)
tags, coord, param = gmsh.model.mesh.getNodes(2, s, True)

# Get the surface normals on all the points on the surface corresponding to
# the parametric coordinates of the nodes
norm = gmsh.model.getNormal(s, param)

# In the same way, get the curvature

curv = gmsh.model.getCurvature(2, s, param)

# Store the normals and the curvatures so that we can display them as
# list-based post-processing views
for i in range(0, len(coord), 3):
normals.append(coord[i])
72 Gmsh 4.11.1

normals.append(coord[i + 1])
normals.append(coord[i + 2])
normals.append(norm[i])
normals.append(norm[i + 1])
normals.append(norm[i + 2])
curvatures.append(coord[i])
curvatures.append(coord[i + 1])
curvatures.append(coord[i + 2])
curvatures.append(curv[i // 3])

# Create a list-based vector view on points to display the normals, and a scalar
# view on points to display the curvatures
vn = gmsh.view.add("normals")
gmsh.view.addListData(vn, "VP", len(normals) // 6, normals)
gmsh.view.option.setNumber(vn, ’ShowScale’, 0)
gmsh.view.option.setNumber(vn, ’ArrowSizeMax’, 30)
gmsh.view.option.setNumber(vn, ’ColormapNumber’, 19)
vc = gmsh.view.add("curvatures")
gmsh.view.addListData(vc, "SP", len(curvatures) // 4, curvatures)
gmsh.view.option.setNumber(vc, ’ShowScale’, 0)

# We can also retrieve the parametrization bounds of model entities, e.g. of

# curve 5, and evaluate the parametrization for several parameter values:
bounds = gmsh.model.getParametrizationBounds(1, 5)
N = 20
t = [bounds[0][0] + i * (bounds[1][0] - bounds[0][0]) / N for i in range(N)]
xyz1 = gmsh.model.getValue(1, 5, t)

# We can also reparametrize curve 5 on surface 1, and evaluate the points in the
# parametric plane of the surface:
uv = gmsh.model.reparametrizeOnSurface(1, 5, t, 1)
xyz2 = gmsh.model.getValue(2, 1, uv)

# Hopefully we get the same x, y, z coordinates!

if max([abs(a - b) for (a, b) in zip(xyz1, xyz2)]) < 1e-12:
gmsh.logger.write(’Evaluation on curve and surface match!’)
else:
gmsh.logger.write(’Evaluation on curve and surface do not match!’, ’error’)

# Launch the GUI to see the results:

if ’-nopopup’ not in sys.argv:
gmsh.fltk.run()

gmsh.finalize()

2.27 x6: Additional mesh data: integration points, Jacobians

and basis functions
See x6.py. Also available in C++ (x6.cpp).
# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 6
Chapter 2: Gmsh tutorial 73

#
# Additional mesh data: integration points, Jacobians and basis functions
#
# -----------------------------------------------------------------------------

import gmsh
import sys

gmsh.initialize(sys.argv)

gmsh.model.add("x6")

# The API provides access to all the elementary building blocks required to
# implement finite-element-type numerical methods. Let’s create a simple 2D
# model and mesh it:
gmsh.model.occ.addRectangle(0, 0, 0, 1, 0.1)
gmsh.model.occ.synchronize()
gmsh.model.mesh.setTransfiniteAutomatic()
gmsh.model.mesh.generate(2)

# Set the element order and the desired interpolation order:

elementOrder = 1
interpolationOrder = 2
gmsh.model.mesh.setOrder(elementOrder)

def pp(label, v, mult):

print(" * " + str(len(v) / mult) + " " + label + ": " + str(v))

# Iterate over all the element types present in the mesh:

elementTypes = gmsh.model.mesh.getElementTypes()

for t in elementTypes:
# Retrieve properties for the given element type
elementName, dim, order, numNodes, numPrimNodes, localNodeCoord =\
gmsh.model.mesh.getElementProperties(t)
print("\n** " + elementName + " **\n")

# Retrieve integration points for that element type, enabling exact

# integration of polynomials of order "interpolationOrder". The "Gauss"
# integration family returns the "economical" Gauss points if available, and
# defaults to the "CompositeGauss" (tensor product) rule if not.
localCoords, weights =\
gmsh.model.mesh.getIntegrationPoints(t, "Gauss" + str(interpolationOrder))
pp("integration points to integrate order " +
str(interpolationOrder) + " polynomials", localCoords, 3)

# Return the basis functions evaluated at the integration points. Selecting

# "Lagrange" and "GradLagrange" returns the isoparamtric basis functions and
# their gradient (in the reference space of the given element type). A
# specific interpolation order can be requested using "LagrangeN" and
# "GradLagrangeN" with N = 1, 2, ... Other supported function spaces include
# "H1LegendreN", "GradH1LegendreN", "HcurlLegendreN", "CurlHcurlLegendreN".
74 Gmsh 4.11.1

numComponents, basisFunctions, numOrientations =\

gmsh.model.mesh.getBasisFunctions(t, localCoords, "Lagrange")
pp("basis functions at integration points", basisFunctions, 1)
numComponents, basisFunctions, numOrientations =\
gmsh.model.mesh.getBasisFunctions(t, localCoords, "GradLagrange")
pp("basis function gradients at integration points", basisFunctions, 3)

# Compute the Jacobians (and their determinants) at the integration points

# for all the elements of the given type in the mesh. Beware that the
# Jacobians are returned "by column": see the API documentation for details.
jacobians, determinants, coords =\
gmsh.model.mesh.getJacobians(t, localCoords)
pp("Jacobian determinants at integration points", determinants, 1)

gmsh.finalize()

2.28 x7: Additional mesh data: internal edges and faces

See x7.py. Also available in C++ (x7.cpp).

# -----------------------------------------------------------------------------
#
# Gmsh Python extended tutorial 7
#
# Additional mesh data: internal edges and faces
#
# -----------------------------------------------------------------------------

import sys
import gmsh

gmsh.initialize(sys.argv)

gmsh.model.add("x7")

# Meshes are fully described in Gmsh by nodes and elements, both associated to
# model entities. The API can be used to generate and handle other mesh
# entities, i.e. mesh edges and faces, which are not stored by default.

# Let’s create a simple model and mesh it:

gmsh.model.occ.addBox(0, 0, 0, 1, 1, 1)
gmsh.model.occ.synchronize()
Chapter 2: Gmsh tutorial 75

gmsh.option.setNumber("Mesh.MeshSizeMin", 2.)
gmsh.model.mesh.generate(3)

# Like elements, mesh edges and faces are described by (an ordered list of)
# their nodes. Let us retrieve the edges and the (triangular) faces of all the
# first order tetrahedra in the mesh:
elementType = gmsh.model.mesh.getElementType("tetrahedron", 1)
edgeNodes = gmsh.model.mesh.getElementEdgeNodes(elementType)
faceNodes = gmsh.model.mesh.getElementFaceNodes(elementType, 3)

# Edges and faces are returned for each element as a list of nodes corresponding
# to the canonical orientation of the edges and faces for a given element type.

# Gmsh can also identify unique edges and faces (a single edge or face whatever
# the ordering of their nodes) and assign them a unique tag. This identification
# can be done internally by Gmsh (e.g. when generating keys for basis
# functions), or requested explicitly as follows:
gmsh.model.mesh.createEdges()
gmsh.model.mesh.createFaces()

# Edge and face tags can then be retrieved by providing their nodes:
edgeTags, edgeOrientations = gmsh.model.mesh.getEdges(edgeNodes)
faceTags, faceOrientations = gmsh.model.mesh.getFaces(3, faceNodes)

# Since element edge and face nodes are returned in the same order as the
# elements, one can easily keep track of which element(s) each edge or face is
# connected to:
elementTags, elementNodeTags = gmsh.model.mesh.getElementsByType(elementType)
edges2Elements = {}
faces2Elements = {}
for i in range(len(edgeTags)): # 6 edges per tetrahedron
if not edgeTags[i] in edges2Elements:
edges2Elements[edgeTags[i]] = [elementTags[i // 6]]
else:
edges2Elements[edgeTags[i]].append(elementTags[i // 6])
for i in range(len(faceTags)): # 4 faces per tetrahedron
if not faceTags[i] in faces2Elements:
faces2Elements[faceTags[i]] = [elementTags[i // 4]]
else:
faces2Elements[faceTags[i]].append(elementTags[i // 4])

# New unique lower dimensional elements can also be easily created given the
# edge or face nodes. This is especially useful for numerical methods that
# require integrating or interpolating on internal edges or faces (like
# e.g. Discontinuous Galerkin techniques), since creating elements for the
# internal entities will make this additional mesh data readily available (see
# ‘x6.py’). For example, we can create a new discrete surface...
s = gmsh.model.addDiscreteEntity(2)

# ... and fill it with unique triangles corresponding to the faces of the
# tetrahedra:
maxElementTag = gmsh.model.mesh.getMaxElementTag()
76 Gmsh 4.11.1

uniqueFaceTags = set()
tagsForTriangles = []
faceNodesForTriangles = []
for i in range(len(faceTags)):
if faceTags[i] not in uniqueFaceTags:
uniqueFaceTags.add(faceTags[i])
tagsForTriangles.append(faceTags[i] + maxElementTag)
faceNodesForTriangles.append(faceNodes[3 * i])
faceNodesForTriangles.append(faceNodes[3 * i + 1])
faceNodesForTriangles.append(faceNodes[3 * i + 2])
elementType2D = gmsh.model.mesh.getElementType("triangle", 1)
gmsh.model.mesh.addElementsByType(s, elementType2D, tagsForTriangles,
faceNodesForTriangles)

# Since the tags for the triangles have been created based on the face tags,
# the information about neighboring elements can also be readily created,
# useful e.g. in Finite Volume or Discontinuous Galerkin techniques:
for t in tagsForTriangles:
print("triangle " + str(int(t)) + " is connected to tetrahedra " +
str(faces2Elements[t - maxElementTag]))

# If all you need is the list of all edges or faces in terms of their nodes, you
# can also directly call:
edgeTags, edgeNodes = gmsh.model.mesh.getAllEdges()
faceTags, faceNodes = gmsh.model.mesh.getAllFaces(3)

# Launch the GUI to see the results:

if ’-nopopup’ not in sys.argv:
gmsh.fltk.run()
Chapter 3: Gmsh graphical user interface 77

3 Gmsh graphical user interface

Once you have the Gmsh application installed (see Section 1.7 [Installing and running Gmsh on
your computer], page 14), to launch the graphical interface just double-click on the Gmsh icon,
or type
> gmsh
at the shell prompt in a terminal. This will open the main window of the Gmsh GUI, with
a menu bar on top (except on macOS, where by default the menu bar is on the top of the
screen – this can be changed with the General.SystemMenuBar option, see Section 7.1 [General
options], page 219), a tree menu on the left (which by default contains a ‘Modules’ entry with
three children: ‘Geometry’, ‘Mesh’ and ‘Solver’), a graphic area on the right, and a status bar
with some shortcut buttons at the bottom. (You can detach the tree menu using ‘Window-
>Attach/Detach Menu’.)

To create a new geometrical model, use the ‘File->New’ menu to create a new model file, and
choose for example ‘mymodel.geo’ as file name. Then in the tree menu, successively open the
‘Geometry’, ‘Elementary entities’ and ‘Add’ submenus, and click for example on ‘Rectangle’. A
context window with parameters will pop up: you can enter some parameters in this window
(e.g. the width and height of the rectangle) and move the mouse to place it on the canvas. If you
don’t want to place the rectangle with the mouse, select ‘X’, ‘Y’ and ‘Z freeze’ in the window
and enter the coordinates manually in the context window. Once you are done, either press e
(see the status message on the top of the graphic window) or click on the ‘Add’ button in the
context window.
78 Gmsh 4.11.1

There is no need to save your geometrical model: when the rectangle was added, scripting
commands were automatically appended to your model file ‘mymodel.geo’:
//+
SetFactory("OpenCASCADE");
Rectangle(1) = {0, 0, 0, 1, 0.5, 0};
You can edit this script with any text editor; clicking on ‘Edit script’ in the tree menu will
launch the default text editor specified by the General.Editor option (see Section 7.1 [General
options], page 219). If you edit the script, you should click on ‘Reload script’ in the tree menu
to reload the modifications in the GUI. The //+ line in the script is a comment that is used as
a placemark between commands added by the GUI; see Chapter 5 [Gmsh scripting language],
page 89 for the scripting language reference.
Combining GUI actions and script file editing is a classical way of working with the Gmsh app.
For example, it is often faster to define variables and points directly in the script file, and then
use the GUI to define the curves, the surfaces and the volumes interactively.
To load an existing model instead of creating a model from scratch, use the ‘File->Open’ menu.
For example, to open the first tutorial (see Chapter 2 [Gmsh tutorial], page 15), choose t1.geo.
On the terminal, you can also specify the file name directly on the command line, i.e.:
> gmsh t1.geo
To generate a mesh, open ‘Mesh’ in the tree menu and choose the desired dimension: ‘1D’
will mesh all the curves; ‘2D’ will mesh all the surfaces—as well as all the curves if ‘1D’ was
not called before; ‘3D’ will mesh all the volumes—and all the surfaces if ‘2D’ was not called
before. To save the resulting mesh in the current mesh format click on ‘Save’ in the tree menu,
or select the appropriate format and file name with the ‘File->Export’ menu. The default
mesh file name is based on the name of the current active model, with an appended extension
depending on the mesh format. Note that most interactive commands have keyboard shortcuts:
see Section 3.2 [Keyboard shortcuts], page 80, or select ‘Help->Keyboard and Mouse Usage’ in
the menu. For example, to quickly generate the 2D mesh and save a mesh, you can first press
2, then Ctrl+Shift+s.
A double-click in the graphic window will pop up a quick shortcut menu, which can be used
e.g. to quickly toggle the visibility of mesh entities (like surface faces), reset the viewport, select
the rotation center, display axes, or access the full module options (from the ‘Tools->Options’
menu). The shortcut buttons on the bottom left of the status bar can be used to quickly adjust
the viewport: ‘X’, ‘Y’, ‘Z’ set viewports with the corresponding axis perpendicular to graphic
plane; the rotation button rotates the view by 90 degrees; and ‘1:1’ resets the scale.

Several files can be loaded simultaneously. When specified on the command line, the first one
defines the active model (in the same way as using the ‘File->Open’ menu) and the others are
Chapter 3: Gmsh graphical user interface 79

‘merged’ into this model (in the same way as using the the ‘File->Merge’ menu). For example,
to merge the post-processing views contained in the files view1.pos and view5.msh together with
the geometry of the first tutorial Section 2.1 [t1], page 15, you can type the following command:
> gmsh t1.geo view1.pos view5.msh
When one or more more post-processing views are loaded, a ‘Post-Processing’ entry in the
tree menu appears. With the previous command, three views will appear in the tree menu
under ‘Post-processing’, respectively labeled ‘A scalar map’, ‘Nodal scalar map’ and ‘Element 1
vector’. In this example the views contain several time steps: you can loop through them with
the shortcuts icons on the left of the status bar. A mouse click on the view name will toggle the
visibility of the selected view, while a click on the arrow button on the right will provide access
to the view’s options.
Note that all the options specified interactively can also be directly specified in the script files.
You can save the current options of the current active model with the ‘File->Save Model Options’.
This will create a new option file with the same filename as the active model, but with an extra
‘.opt’ extension added. The next time you open this model, the associated options will be
automatically loaded, too. To save the current options as your default preferences for all future
Gmsh sessions, use the ‘File->Save Options As Default’ menu instead. You can also save the
current options in an arbitrary file by choosing the ‘Gmsh options’ format in ‘File->Export’.
For more information about available options (and how to reset them to their default values),
see Chapter 7 [Gmsh options], page 219. A full list of options with their current values is also
available using the ‘Help->Current Options’ menu.
Finally, note that the GUI can also be run (and modified) using the API: see Section 6.14
[Namespace gmsh/fltk], page 209 for details.
The two next sections describe the mouse actions in the GUI, as well as all the predefined
keyboard shortcuts. Screencasts explaining how to use the Gmsh GUI are available online at
the following address: https://gmsh.info/screencasts/.

3.1 Mouse actions

Move Highlight the entity under the mouse pointer and display its properties / Resize a
lasso zoom or a lasso (un)selection
Left button
Rotate / Select an entity / Accept a lasso zoom or a lasso selection
Ctrl+Left button
Start a lasso zoom or a lasso (un)selection
Middle button
Zoom / Unselect an entity / Accept a lasso zoom or a lasso unselection
Ctrl+Middle button
Orthogonalize display
Right button
Pan / Cancel a lasso zoom or a lasso (un)selection / Pop-up menu on post-processing
view button
Ctrl+Right button
Reset to default viewpoint
For a 2 button mouse, Middle button = Shift+Left button.
For a 1 button mouse, Middle button = Shift+Left button, Right button = Alt+Left button.
80 Gmsh 4.11.1

3.2 Keyboard shortcuts

(On macOS, Ctrl is replaced by Cmd in the shortcuts below.)
Left arrow
Go to previous time step
Right arrow
Go to next time step
Up arrow Make previous view visible
Down arrow
Make next view visible
0 Reload geometry
Ctrl+0 or 9
Reload full project
1 or F1 Mesh lines
2 or F2 Mesh surfaces
3 or F3 Mesh volumes
Escape Cancel lasso zoom/selection, toggle mouse selection ON/OFF
e End/accept selection in geometry creation mode
g Go to geometry module
m Go to mesh module
p Go to post-processing module
q Abort selection in geometry creation mode
s Go to solver module
x Toggle x coordinate freeze in geometry creation mode
y Toggle y coordinate freeze in geometry creation mode
z Toggle z coordinate freeze in geometry creation mode
Shift+a Bring all windows to front
Shift+g Show geometry options
Shift+m Show mesh options
Shift+o Show general options
Shift+p Show post-processing options
Shift+s Show solver options
Shift+u Show post-processing view plugins
Shift+w Show post-processing view options
Shift+x Move only along x coordinate in geometry creation mode
Shift+y Move only along y coordinate in geometry creation mode
Shift+z Move only along z coordinate in geometry creation mode
Shift+Escape
Enable full mouse selection
Chapter 3: Gmsh graphical user interface 81

Ctrl+d Attach/detach menu

Ctrl+e Export project
Ctrl+f Enter full screen
Ctrl+i Show statistics window
Ctrl+j Save model options
Ctrl+l Show message console
Ctrl+m Minimize window
Ctrl+n Create new project file
Ctrl+o Open project file
Ctrl+q Quit
Ctrl+r Rename project file
Ctrl+s Save mesh in default format
Shift+Ctrl+c
Show clipping plane window
Shift+Ctrl+h
Show current options and workspace window
Shift+Ctrl+j
Save options as default
Shift+Ctrl+m
Show manipulator window
Shift+Ctrl+n
Show option window
Shift+Ctrl+o
Merge file(s)
Shift+Ctrl+r
Open next-to-last opened file
Shift+Ctrl+u
Show plugin window
Shift+Ctrl+v
Show visibility window
Alt+a Loop through axes modes
Alt+b Hide/show bounding boxes
Alt+c Loop through predefined color schemes
Alt+e Hide/Show element outlines for visible post-pro views
Alt+f Change redraw mode (fast/full)
Alt+h Hide/show all post-processing views
Alt+i Hide/show all post-processing view scales
Alt+l Hide/show geometry lines
Alt+m Toggle visibility of all mesh entities
82 Gmsh 4.11.1

Alt+n Hide/show all post-processing view annotations

Alt+o Change projection mode (orthographic/perspective)
Alt+p Hide/show geometry points
Alt+r Loop through range modes for visible post-pro views
Alt+s Hide/show geometry surfaces
Alt+t Loop through interval modes for visible post-pro views
Alt+v Hide/show geometry volumes
Alt+w Enable/disable all lighting
Alt+x Set X view
Alt+y Set Y view
Alt+z Set Z view
Alt+1 Set 1:1 view
Alt+Shift+a
Hide/show small axes
Alt+Shift+b
Hide/show mesh volume faces
Alt+Shift+c
Loop through predefined colormaps
Alt+Shift+d
Hide/show mesh surface faces
Alt+Shift+l
Hide/show mesh lines
Alt+Shift+p
Hide/show mesh nodes
Alt+Shift+s
Hide/show mesh surface edges
Alt+Shift+t
Same as Alt+t, but with numeric mode included
Alt+Shift+v
Hide/show mesh volume edges
Alt+Shift+x
Set -X view
Alt+Shift+y
Set -Y view
Alt+Shift+z
Set -Z view
Alt+Shift+1
Reset bounding box around visible entities
Alt+Ctrl++1
Sync scale between viewports
Chapter 4: Gmsh command-line interface 83

4 Gmsh command-line interface

Gmsh defines a number of commands-line switches that can be used to control Gmsh in “batch”
mode from the command line, and pass options without resorting to a script (see Chapter 5
[Gmsh scripting language], page 89) or the API (see Chapter 6 [Gmsh application programming
interface], page 123).
For example, meshing the first tutorial in batch mode can be done in a terminal by passing the
-2 command-line switch:
> gmsh t1.geo -2
The same effect could be achieved by adding the Mesh 2; command at the end of ‘t1.geo’ and
running
> gmsh t1.geo -parse_and_exit
or further adding the Exit; command at the end of the script and simply opening this new file:
> gmsh t1.geo
Note that all numeric and string options (see Chapter 7 [Gmsh options], page 219) can be set
from the command line with the -setnumber and -setstring switches
> gmsh t1.geo -setnumber Mesh.Nodes 1 -setnumber Geometry.SurfaceLabels 1
The list of all command-line switches is given hereafter.
(Related option names, if any, are given between parentheses)
Geometry:
-0 Output model, then exit
-tol value
Set geometrical tolerance (Geometry.Tolerance)
-match Match geometries and meshes
Mesh:
-1, -2, -3
Perform 1D, 2D or 3D mesh generation, then exit
-format string
Select output mesh format: auto, msh1, msh2, msh22, msh3, msh4, msh40, msh41,
msh, unv, vtk, wrl, mail, stl, p3d, mesh, bdf, cgns, med, diff, ir3, inp, ply2, celum,
su2, x3d, dat, neu, m, key, off, rad (Mesh.Format)
-bin Create binary files when possible (Mesh.Binary)
-refine Perform uniform mesh refinement, then exit
-barycentric_refine
Perform barycentric mesh refinement, then exit
-reclassify angle
Reclassify surface mesh, then exit
-reparam angle
Reparametrize surface mesh, then exit
-part int Partition after batch mesh generation (Mesh.NbPartitions)
-part_weight [tri,quad,tet,hex,pri,pyr,trih] int
Weight of a triangle/quad/etc. during partitioning
(Mesh.Partition[Tri,Quad,...]Weight)
84 Gmsh 4.11.1

-part_split
Save mesh partitions in separate files (Mesh.PartitionSplitMeshFiles)
-part_[no_]topo
Create the partition topology (Mesh.PartitionCreateTopology)
-part_[no_]ghosts
Create ghost cells (Mesh.PartitionCreateGhostCells)
-part_[no_]physicals
Create physical groups for partitions (Mesh.PartitionCreatePhysicals)
-part_topo_pro
Save the partition topology .pro file (Mesh.PartitionTopologyFile)
-preserve_numbering_msh2
Preserve element numbering in MSH2 format (Mesh.PreserveNumberingMsh2)
-save_all
Save all elements (Mesh.SaveAll)
-save_parametric
Save nodes with their parametric coordinates (Mesh.SaveParametric)
-save_topology
Save model topology (Mesh.SaveTopology)
-algo string
Select mesh algorithm: auto, meshadapt, del2d, front2d, delquad, quadqs, initial2d,
del3d, front3d, mmg3d, hxt, initial3d (Mesh.Algorithm and Mesh.Algorithm3D)
-smooth int
Set number of mesh smoothing steps (Mesh.Smoothing)
-order int
Set mesh order (Mesh.ElementOrder)
-optimize[_netgen]
Optimize quality of tetrahedral elements (Mesh.Optimize[Netgen])
-optimize_threshold
Optimize tetrahedral elements that have a quality less than a threshold
(Mesh.OptimizeThreshold)
-optimize_ho
Optimize high order meshes (Mesh.HighOrderOptimize)
-ho_[min,max,nlayers]
High-order optimization parameters (Mesh.HighOrderThreshold[Min,Max],
Mesh.HighOrderNumLayers)
-clscale value
Set mesh element size factor (Mesh.MeshSizeFactor)
-clmin value
Set minimum mesh element size (Mesh.MeshSizeMin)
-clmax value
Set maximum mesh element size (Mesh.MeshSizeMax)
-clextend value
Extend mesh element sizes from boundaries (Mesh.MeshSizeExtendFromBoundary)
Chapter 4: Gmsh command-line interface 85

-clcurv value
Compute mesh element size from curvature, with value the target number of ele-
ments per 2*pi radians (Mesh.MeshSizeFromCurvature)
-aniso_max value
Set maximum anisotropy for bamg (Mesh.AnisoMax)
-smooth_ratio value
Set smoothing ration between mesh sizes at nodes of a same edge for bamg
(Mesh.SmoothRatio)
-epslc1d value
Set accuracy of evaluation of mesh size field for 1D mesh
(Mesh.LcIntegrationPrecision)
-swapangle value
Set the threshold angle (in degrees) between two adjacent faces below which a swap
is allowed (Mesh.AllowSwapAngle)
-rand value
Set random perturbation factor (Mesh.RandomFactor)
-bgm file Load background mesh from file
-check Perform various consistency checks on mesh
-ignore_periocity
Ignore periodic boundaries (Mesh.IgnorePeriodicity)
Post-processing:
-link int Select link mode between views (PostProcessing.Link)
-combine Combine views having identical names into multi-time-step views
Solver:
-listen string
Always listen to incoming connection requests (Solver.AlwaysListen) on the given
socket (uses Solver.SocketName if not specified)
-minterpreter string
Name of Octave interpreter (Solver.OctaveInterpreter)
-pyinterpreter string
Name of Python interpreter (Solver.OctaveInterpreter)
-run Run ONELAB solver(s)
Display:
-n Hide all meshes and post-processing views on startup (View.Visible,
Mesh.[Points,Lines,SurfaceEdges,...])
-nodb Disable double buffering (General.DoubleBuffer)
-numsubedges
Set num of subdivisions for high order element display (Mesh.NumSubEdges)
-fontsize int
Specify the font size for the GUI (General.FontSize)
-theme string
Specify FLTK GUI theme (General.FltkTheme)
86 Gmsh 4.11.1

-display string
Specify display (General.Display)
-camera Use camera mode view (General.CameraMode)
-stereo OpenGL quad-buffered stereo rendering (General.Stereo)
-gamepad Use gamepad controller if available
Other:
-, -parse_and_exit
Parse input files, then exit
-save Save output file, then exit
-o file Specify output file name
-new Create new model before merge next file
-merge Merge next files
-open Open next files
-log filename
Log all messages to filename
-a, -g, -m, -s, -p
Start in automatic, geometry, mesh, solver or post-processing mode
(General.InitialModule)
-pid Print process id on stdout
-watch pattern
Pattern of files to merge as they become available (General.WatchFilePattern)
-bg file Load background (image or PDF) file (General.BackgroundImageFileName)
-v int Set verbosity level (General.Verbosity)
-string "string"
Parse command string at startup
-setnumber name value
Set constant, ONELAB or option number name=value
-setstring name value
Set constant, ONELAB or option string name=value
-nopopup Don’t popup dialog windows in scripts (General.NoPopup)
-noenv Don’t modify the environment at startup
-nolocale
Don’t modify the locale at startup
-option file
Parse option file at startup
-convert files
Convert files into latest binary formats, then exit
-nt int Set number of threads (General.NumThreads)
-cpu Report CPU times for all operations
-version Show version number
Chapter 4: Gmsh command-line interface 87

-info Show detailed version information

-help Show command line usage
-help_options
Show all options
Chapter 5: Gmsh scripting language 89

5 Gmsh scripting language

The Gmsh scripting language is interpreted at runtime by Gmsh’s parser. Scripts are written
in ASCII files and are usually given the ‘.geo’ extension, but any extension (or no extension
at all) can also be used. For example Gmsh often uses the ‘.pos’ extension for scripts that
contain post-processing commands, in particular parsed post-processing views (see Section 5.4
[Post-processing scripting commands], page 117).
Historically, ‘.geo’ scripts have been the primary way to perform complex tasks with Gmsh,
and they are indeed quite powerful: they can handle (lists of) floating point (see Section 5.1.2
[Floating point expressions], page 89) and string (see Section 5.1.3 [String expressions], page 92)
variables, loops and tests (see Section 5.1.8 [Loops and conditionals], page 96), macros (see
Section 5.1.7 [User-defined macros], page 96), etc. However Gmsh’s scripting language is still
quite limited compared to actual programming languages: for example there are no private vari-
ables, macros don’t take arguments, and the runtime interpretation by the parser can penalize
performance on large models. Depending on the workflow and the application, using the Gmsh
API (see Chapter 6 [Gmsh application programming interface], page 123) can thus sometimes be
preferable. The downside of the API is that, while the scripting language is baked into Gmsh and
is thus available directly in the standalone Gmsh app, the API requires external dependencies
(a C++, C or Fortran compiler; or a Python or Julia interpreter).
This chapter describes the scripting language by detailing general commands first (see Section 5.1
[General scripting commands], page 89), before detailing the scripting commands specific to the
geometry (see Section 5.2 [Geometry scripting commands], page 102), mesh (see Section 5.3
[Mesh scripting commands], page 111) and post-processing (see Section 5.4 [Post-processing
scripting commands], page 117) modules.
The following rules are used when describing the scripting language in the rest of this chapter
(note that metasyntactic variable definitions stay valid throughout the chapter, not only in the
section where the definitions appear):
1. Keywords and literal symbols are printed like this.
2. Metasyntactic variables (i.e., text bits that are not part of the syntax, but stand for other
text bits) are printed like this.
3. A colon (:) after a metasyntactic variable separates the variable from its definition.
4. Optional rules are enclosed in < > pairs.
5. Multiple choices are separated by |.
6. Three dots (. . . ) indicate a possible (multiple) repetition of the preceding rule.

5.1 General scripting commands

5.1.1 Comments
Gmsh script files support both C and C++ style comments:
1. any text comprised between /* and */ pairs is ignored;
2. the rest of a line after a double slash // is ignored.
These commands won’t have the described effects inside double quotes or inside keywords. Also
note that ‘white space’ (spaces, tabs, new line characters) is ignored inside all expressions.

5.1.2 Floating point expressions

The two constant types used in Gmsh scripts are real and string (there is no integer type).
These types have the same meaning and syntax as in the C or C++ programming languages.
Floating point expressions (or, more simply, “expressions”) are denoted by the metasyntactic
variable expression, and are evaluated during the parsing of the script file:
90 Gmsh 4.11.1

expression :
real |
string |
string ~ { expression }
string [ expression ] |
# string [ ] |
( expression ) |
operator-unary-left expression |
expression operator-unary-right |
expression operator-binary expression |
expression operator-ternary-left expression
operator-ternary-right expression |
built-in-function |
number-option |
Find(expression-list-item, expression-list-item ) |
StrFind(string-expression, string-expression ) |
StrCmp(string-expression, string-expression ) |
StrLen(string-expression ) |
TextAttributes(string-expression <,string-expression ...>) |
Exists(string ) | Exists(string ~{ expression }) |
FileExists(string-expression ) |
StringToName(string-expression ) | S2N(string-expression ) |
GetNumber(string-expression <,expression >) |
GetValue("string ", expression ) |
DefineNumber(expression, onelab-options )
Such expressions are used in most of Gmsh’s scripting commands. When ~{expression } is
appended to a string string, the result is a new string formed by the concatenation of string, _
(an underscore) and the value of the expression. This is most useful in loops (see Section 5.1.8
[Loops and conditionals], page 96), where it permits to define unique strings automatically. For
example,
For i In {1:3}
x~{i} = i;
EndFor
is the same as
x_1 = 1;
x_2 = 2;
x_3 = 3;
The brackets [] permit to extract one item from a list (parentheses can also be used instead of
brackets). The # permits to get the size of a list. The operators operator-unary-left, operator-
unary-right, operator-binary, operator-ternary-left and operator-ternary-right are defined in
Section 5.1.5 [Operators], page 93. For the definition of built-in-functions, see Section 5.1.6
[Built-in functions], page 95. The various number-options are listed in Chapter 7 [Gmsh op-
tions], page 219. Find searches for occurrences of the first expression in the second (both of
which can be lists). StrFind searches the first string-expression for any occurrence of the second
string-expression. StrCmp compares the two strings (returns an integer greater than, equal to, or
less than 0, according as the first string is greater than, equal to, or less than the second string).
StrLen returns the length of the string. TextAttributes creates attributes for text strings.
Exists checks if a variable with the given name exists (i.e., has been defined previously), and
FileExists checks if the file with the given name exists. StringToName creates a name from the
provided string. GetNumber allows to get the value of a ONELAB variable (the optional second
argument is the default value returned if the variable does not exist). GetValue allows to ask
Chapter 5: Gmsh scripting language 91

the user for a value interactively (the second argument is the value returned in non-interactive
mode). For example, inserting GetValue("Value of parameter alpha?", 5.76) in an input
file will query the user for the value of a certain parameter alpha, assuming the default value
is 5.76. If the option General.NoPopup is set (see Section 7.1 [General options], page 219), no
question is asked and the default value is automatically used.
DefineNumber allows to define a ONELAB variable in-line. The expression given as the first
argument is the default value; this is followed by the various ONELAB options. See the ONELAB
tutorial wiki for more information.
List of expressions are also widely used, and are defined as:
expression-list :
expression-list-item <, expression-list-item > ...
with
expression-list-item :
expression |
expression : expression |
expression : expression : expression |
string [ ] | string ( ) |
List [ string ] |
List [ expression-list-item ] |
List [ { expression-list } ] |
Unique [ expression-list-item ] |
Abs [ expression-list-item ] |
ListFromFile [ expression-char ] |
LinSpace[ expression, expression, expression ] |
LogSpace[ expression, expression, expression ] |
string [ { expression-list } ] |
Point { expression } |
transform |
extrude |
boolean |
Point|Curve|Surface|Volume In BoundingBox { expression-list } |
BoundingBox Point|Curve|Surface|Volume { expression-list } |
Mass Curve|Surface|Volume { expression } |
CenterOfMass Curve|Surface|Volume { expression } |
MatrixOfInertia Curve|Surface|Volume { expression } |
Point { expression } |
Physical Point|Curve|Surface|Volume { expression-list } |
<Physical> Point|Curve|Surface|Volume { : } |
The second case in this last definition permits to create a list containing the range of numbers
comprised between two expressions, with a unit incrementation step. The third case also per-
mits to create a list containing the range of numbers comprised between two expressions, but
with a positive or negative incrementation step equal to the third expression. The fourth, fifth
and sixth cases permit to reference an expression list (parentheses can also be used instead of
brackets). Unique sorts the entries in the list and removes all duplicates. Abs takes the absolute
value of all entries in the list. ListFromFile reads a list of numbers from a file. LinSpace
and LogSpace construct lists using linear or logarithmic spacing. The next two cases permit to
reference an expression sublist (whose elements are those corresponding to the indices provided
by the expression-list). The next cases permit to retrieve the indices of entities created through
geometrical transformations, extrusions and boolean operations (see Section 5.2.7 [Transforma-
tions], page 108, Section 5.2.5 [Extrusions], page 106 and Section 5.2.6 [Boolean operations],
page 107).
92 Gmsh 4.11.1

The next two cases allow to retrieve entities in a given bounding box, or get the bounding box
of a given entity, with the bounding box specified as (X min, Y min, Z min, X max, Y max,
Z max). Beware that the order of coordinates is different than in the BoundingBox command
for the scene: see Section 5.1.9 [Other general commands], page 97. The last cases permit to
retrieve the mass, the center of mass or the matrix of inertia of an entity, the coordinates of a
given geometry point (see Section 5.2.1 [Points], page 102), the elementary entities making up
physical groups, and the tags of all (physical or elementary) points, curves, surfaces or volumes
in the model. These operations all trigger a synchronization of the CAD model with the internal
Gmsh model.
To see the practical use of such expressions, have a look at the first couple of examples in
Chapter 2 [Gmsh tutorial], page 15. Note that, in order to lighten the syntax, you can omit
the braces {} enclosing an expression-list if this expression-list only contains a single item. Also
note that a braced expression-list can be preceded by a minus sign in order to change the sign
of all the expression-list-items.
For some commands it makes sense to specify all the possible expressions in a list. This is
achieved with expression-list-or-all, defined as:
expression-list-or-all :
expression-list | :
The meaning of “all” (:) depends on context. For example, Curve { : } will get the ids of all
the existing curves in the model, while Surface { : } will get the ids of all existing surfaces.

5.1.3 String expressions

String expressions are defined as:
string-expression :
"string " |
string | string [ expression ] |
Today | OnelabAction | GmshExecutableName |
CurrentDirectory | CurrentDir | CurrentFileName
StrPrefix ( string-expression ) |
StrRelative ( string-expression ) |
StrCat ( string-expression <,...> ) |
Str ( string-expression <,...> ) |
StrChoice ( expression, string-expression, string-expression ) |
StrSub( string-expression, expression, expression ) |
StrSub( string-expression, expression ) |
UpperCase ( string-expression ) |
AbsolutePath ( string-expression ) |
DirName ( string-expression ) |
Sprintf ( string-expression , expression-list ) |
Sprintf ( string-expression ) |
Sprintf ( string-option ) |
GetEnv ( string-expression ) |
GetString ( string-expression <,string-expression >) |
GetStringValue ( string-expression , string-expression ) |
StrReplace ( string-expression , string-expression , string-expression )
NameToString ( string ) | N2S ( string ) |
<Physical> Point|Curve|Surface|Volume { expression } |
DefineString(string-expression, onelab-options )
Today returns the current date. OnelabAction returns the current ONELAB action (e.g.
check or compute). GmshExecutableName returns the full path of the Gmsh executable.
Chapter 5: Gmsh scripting language 93

CurrentDirectory (or CurrentDir) and CurrentFileName return the directory and file name
of the script being parsed. StrPrefix and StrRelative take the prefix (e.g. to remove the ex-
tension) or the relative path of a given file name. StrCat and Str concatenate string expressions
(Str adds a newline character after each string except the last). StrChoice returns the first
or second string-expression depending on the value of expression. StrSub returns the portion
of the string that starts at the character position given by the first expression and spans the
number of characters given by the second expression or until the end of the string (whichever
comes first; or always if the second expression is not provided). UpperCase converts the string-
expression to upper case. AbsolutePath returns the absolute path of a file. DirName returns the
directory of a file. Sprintf is equivalent to the sprintf C function (where string-expression is
a format string that can contain floating point formatting characters: %e, %g, etc.) The various
string-options are listed in Chapter 7 [Gmsh options], page 219. GetEnvThe gets the value of an
environment variable from the operating system. GetString allows to get a ONELAB string
value (the second optional argument is the default value returned if the variable does not ex-
ist). GetStringValue asks the user for a value interactively (the second argument is the value
used in non-interactive mode). StrReplace’s arguments are: input string, old substring, new
substring (brackets can be used instead of parentheses in Str and Sprintf). Physical Point,
etc., or Point, etc., retrieve the name of the physical or elementary entity, if any. NameToString
converts a variable name into a string.
DefineString allows to define a ONELAB variable in-line. The string-expression given as the
first argument is the default value; this is followed by the various ONELAB options. See the
ONELAB tutorial wiki for more information.
String expressions are mostly used to specify non-numeric options and input/output file names.
See Section 2.8 [t8], page 33, for an interesting usage of string-expressions in an animation script.
List of string expressions are defined as:
string-expression-list :
string-expression <,...>

5.1.4 Color expressions

Colors expressions are hybrids between fixed-length braced expression-lists and strings:
color-expression :
string-expression |
{ expression, expression, expression } |
{ expression, expression, expression, expression } |
color-option
The first case permits to use the X Windows names to refer to colors, e.g., Red, SpringGreen,
LavenderBlush3, . . . (see src/common/Colors.h in the source code for a complete list). The
second case permits to define colors by using three expressions to specify their red, green and blue
components (with values comprised between 0 and 255). The third case permits to define colors
by using their red, green and blue color components as well as their alpha channel. The last
case permits to use the value of a color-option as a color-expression. The various color-options
are listed in Chapter 7 [Gmsh options], page 219.
See Section 2.3 [t3], page 21, for an example of the use of color expressions.

5.1.5 Operators
Gmsh’s operators are similar to the corresponding operators in C and C++. Here is the list of
available unary, binary and ternary operators.
operator-unary-left:
- Unary minus.
 94 Gmsh 4.11.1

! Logical not.
operator-unary-right:
++ Post-incrementation.
-- Post-decrementation.
operator-binary:
^ Exponentiation.
* Multiplication.
/ Division.
% Modulo.
+ Addition.
- Subtraction.
== Equality.
!= Inequality.
> Greater.
>= Greater or equality.
< Less.
<= Less or equality.
&& Logical ‘and’.
|| Logical ‘or’. (Warning: the logical ‘or’ always implies the evaluation of both argu-
ments. That is, unlike in C or C++, the second operand of || is evaluated even if
the first one is true).
operator-ternary-left:
?
operator-ternary-right:
: The only ternary operator, formed by operator-ternary-left and operator-ternary-
right, returns the value of its second argument if the first argument is non-zero;
otherwise it returns the value of its third argument.
The evaluation priorities are summarized below1 (from stronger to weaker, i.e., * has a highest
evaluation priority than +). Parentheses () may be used anywhere to change the order of
evaluation:
1. (), [], ., #
2. ^
3. !, ++, --, - (unary)
4. *, /, %
5. +, -
6. <, >, <=, >=
7. ==, !=
8. &&
9. ||
10. ?:
11. =, +=, -=, *=, /=
1
The affectation operators are introduced in Section 5.1.9 [Other general commands], page 97.
Chapter 5: Gmsh scripting language 95

5.1.6 Built-in functions

A built-in function is composed of an identifier followed by a pair of parentheses containing an
expression-list, the list of its arguments. This list of arguments can also be provided in between
brackets, instead of parentheses. Here is the list of the built-in functions currently implemented:
build-in-function:
Acos ( expression )
Arc cosine (inverse cosine) of an expression in [-1,1]. Returns a value in [0,Pi].
Asin ( expression )
Arc sine (inverse sine) of an expression in [-1,1]. Returns a value in [-Pi/2,Pi/2].
Atan ( expression )
Arc tangent (inverse tangent) of expression. Returns a value in [-Pi/2,Pi/2].
Atan2 ( expression, expression )
Arc tangent (inverse tangent) of the first expression divided by the second. Returns
a value in [-Pi,Pi].
Ceil ( expression )
Rounds expression up to the nearest integer.
Cos ( expression )
Cosine of expression.
Cosh ( expression )
Hyperbolic cosine of expression.
Exp ( expression )
Returns the value of e (the base of natural logarithms) raised to the power of ex-
pression.
Fabs ( expression )
Absolute value of expression.
Fmod ( expression, expression )
Remainder of the division of the first expression by the second, with the sign of the
first.
Floor ( expression )
Rounds expression down to the nearest integer.
Hypot ( expression, expression )
Returns the square root of the sum of the square of its two arguments.
Log ( expression )
Natural logarithm of expression (expression > 0).
Log10 ( expression )
Base 10 logarithm of expression (expression > 0).
Max ( expression, expression )
Maximum of the two arguments.
Min ( expression, expression )
Minimum of the two arguments.
Modulo ( expression, expression )
see Fmod( expression, expression ).
Rand ( expression )
Random number between zero and expression.
96 Gmsh 4.11.1

Round ( expression )
Rounds expression to the nearest integer.
Sqrt ( expression )
Square root of expression (expression >= 0).
Sin ( expression )
Sine of expression.
Sinh ( expression )
Hyperbolic sine of expression.
Tan ( expression )
Tangent of expression.
Tanh ( expression )
Hyperbolic tangent of expression.

5.1.7 User-defined macros

User-defined macros take no arguments, and are evaluated as if a file containing the macro body
was included at the location of the Call statement.
Macro string | string-expression
Begin the declaration of a user-defined macro named string. The body of the macro
starts on the line after ‘Macro string ’, and can contain any Gmsh command. A
synonym for Macro is Function.
Return End the body of the current user-defined macro. Macro declarations cannot be
imbricated.
Call string | string-expression ;
Execute the body of a (previously defined) macro named string.
See Section 2.5 [t5], page 26, for an example of a user-defined macro. A shortcoming of Gmsh’s
scripting language is that all variables are “public”. Variables defined inside the body of a macro
will thus be available outside, too!

5.1.8 Loops and conditionals

Loops and conditionals are defined as follows, and can be imbricated:
For ( expression : expression )
Iterate from the value of the first expression to the value of the second expression,
with a unit incrementation step. At each iteration, the commands comprised be-
tween ‘For ( expression : expression )’ and the matching EndFor are executed.
For ( expression : expression : expression )
Iterate from the value of the first expression to the value of the second expression,
with a positive or negative incrementation step equal to the third expression. At
each iteration, the commands comprised between ‘For ( expression : expression
: expression )’ and the matching EndFor are executed.
For string In { expression : expression }
Iterate from the value of the first expression to the value of the second expression,
with a unit incrementation step. At each iteration, the value of the iterate is affected
to an expression named string, and the commands comprised between ‘For string
In { expression : expression }’ and the matching EndFor are executed.
For string In { expression : expression : expression }
Iterate from the value of the first expression to the value of the second expression,
with a positive or negative incrementation step equal to the third expression. At
Chapter 5: Gmsh scripting language 97

each iteration, the value of the iterate is affected to an expression named string, and
the commands comprised between ‘For string In { expression : expression :
expression }’ and the matching EndFor are executed.
EndFor End a matching For command.
If ( expression )
The body enclosed between ‘If ( expression )’ and the matching ElseIf, Else
or EndIf, is evaluated if expression is non-zero.
ElseIf ( expression )
The body enclosed between ‘ElseIf ( expression )’ and the next matching
ElseIf, Else or EndIf, is evaluated if expression is non-zero and none of the ex-
pression of the previous matching codes If and ElseIf were non-zero.
Else The body enclosed between Else and the matching EndIf is evaluated if none of
the expression of the previous matching codes If and ElseIf were non-zero.
EndIf End a matching If command.

5.1.9 Other general commands

The following commands can be used anywhere in a Gmsh script:
string = expression ;
Create a new expression identifier string, or affects expression to an existing ex-
pression identifier. The following expression identifiers are predefined (hardcoded in
Gmsh’s parser):
Pi Return 3.1415926535897932.
GMSH_MAJOR_VERSION
Return Gmsh’s major version number.
GMSH_MINOR_VERSION
Return Gmsh’s minor version number.
GMSH_PATCH_VERSION
Return Gmsh’s patch version number.
MPI_Size Return the number of processors on which Gmsh is running. It is always
1, except if you compiled Gmsh with ENABLE_MPI (see Appendix A
[Compiling the source code], page 369).
MPI_Rank Return the rank of the current processor.
Cpu Return the current CPU time (in seconds).
Memory Return the current memory usage (in Mb).
TotalMemory
Return the total memory available (in Mb).
newp Return the next available point tag. As explained in Section 1.1 [Ge-
ometry module], page 7, a unique tag must be associated with every
geometrical point: newp permits to know the highest tag already at-
tributed (plus one). This is mostly useful when writing user-defined
macros (see Section 5.1.7 [User-defined macros], page 96) or general ge-
ometric primitives, when one does not know a priori which tags are
already attributed, and which ones are still available.
newc Return the next available curve tag.
 98 Gmsh 4.11.1

news Return the next available surface tag.

newv Return the next available volume tag.
newcl Return the next available curve loop tag.
newsl Return the next available surface loop tag.
newreg Return the next available region tag. That is, newreg returns the max-
imum of newp, newl, news, newv, newll, newsl and all physical group
tags2 .
string = { };
Create a new expression list identifier string with an empty list.
string [] = { expression-list };
Create a new expression list identifier string with the list expression-list, or affects
expression-list to an existing expression list identifier. Parentheses are also allowed
instead of square brackets; although not recommended, brackets and parentheses
can also be completely ommitted.
string [ { expression-list } ] = { expression-list };
Affect each item in the right hand side expression-list to the elements (indexed by
the left hand side expression-list) of an existing expression list identifier. The two
expression-lists must contain the same number of items. Parentheses can also be
used instead of brackets.
string += expression ;
Add and affect expression to an existing expression identifier.
string -= expression ;
Subtract and affect expression to an existing expression identifier.
string *= expression ;
Multiply and affect expression to an existing expression identifier.
string /= expression ;
Divide and affect expression to an existing expression identifier.
string += { expression-list };
Append expression-list to an existing expression list or creates a new expression list
with expression-list.
string -= { expression-list };
Remove the items in expression-list from the existing expression list.
string [ { expression-list } ] += { expression-list };
Add and affect, item per item, the right hand side expression-list to an existing
expression list identifier. Parentheses can also be used instead of brackets.
string [ { expression-list } ] -= { expression-list };
Subtract and affect, item per item, the right hand side expression-list to an existing
expression list identifier. Parentheses can also be used instead of brackets.
string [ { expression-list } ] *= { expression-list };
Multiply and affect, item per item, the right hand side expression-list to an existing
expression list identifier. Parentheses can also be used instead of brackets.
2
For compatibility purposes, the behavior of newl, news, newv and newreg can be modified with the
Geometry.OldNewReg option (see Section 7.3 [Geometry options], page 246).
Chapter 5: Gmsh scripting language 99

string [ { expression-list } ] /= { expression-list };

Divide and affect, item per item, the right hand side expression-list to an existing
expression list identifier. Parentheses can also be used instead of brackets.
string = string-expression ;
Create a new string expression identifier string with a given string-expression.
string [] = Str( string-expression-list ) ;
Create a new string expression list identifier string with a given string-expression-
list. Parentheses can also be used instead of brackets.
string [] += Str( string-expression-list ) ;
Append a string expression list to an existing list. Parentheses can also be used
instead of brackets.
DefineConstant[ string = expression |string-expression <, ...>];
Create a new expression identifier string, with value expression, only if has not been
defined before.
DefineConstant[ string = { expression |string-expression, onelab-options } <,
...>];
Same as the previous case, except that the variable is also exchanged with the
ONELAB database if it has not been defined before. See the ONELAB tutorial
wiki for more information.
SetNumber( string-expression , expression );
Set the value a numeric ONELAB variable string-expression.
SetString( string-expression , string-expression );
Set the value a string ONELAB variable string-expression.
number-option = expression ;
Affect expression to a real option.
string-option = string-expression ;
Affect string-expression to a string option.
color-option = color-expression ;
Affect color-expression to a color option.
number-option += expression ;
Add and affect expression to a real option.
number-option -= expression ;
Subtract and affect expression to a real option.
number-option *= expression ;
Multiply and affect expression to a real option.
number-option /= expression ;
Divide and affect expression to a real option.
Abort; Abort the current script.
Exit; Exit Gmsh.
CreateDir string-expression ;
Create the directory string-expression.
Printf ( string-expression <, expression-list > );
Print a string expression in the information window and/or on the terminal. Printf
is equivalent to the printf C function: string-expression is a format string that can
100 Gmsh 4.11.1

contain formatting characters (%f, %e, etc.). Note that all expressions are evaluated
as floating point values in Gmsh (see Section 5.1.2 [Floating point expressions],
page 89), so that only valid floating point formatting characters make sense in
string-expression. See Section 2.5 [t5], page 26, for an example of the use of Printf.
Printf ( string-expression , expression-list ) > string-expression ;
Same as Printf above, but output the expression in a file.
Printf ( string-expression , expression-list ) >> string-expression ;
Same as Printf above, but appends the expression at the end of the file.
Warning|Error ( string-expression <, expression-list > );
Same as Printf, but raises a warning or an error.
Merge string-expression ;
Merge a file named string-expression. This command is equivalent to the ‘File-
>Merge’ menu in the GUI. If the path in string-expression is not absolute, string-
expression is appended to the path of the current file. This operation triggers a
synchronization of the CAD model with the internal Gmsh model.
ShapeFromFile( string-expression );
Merge a BREP, STEP or IGES file and returns the tags of the highest-dimensional
entities. Only available with the OpenCASCADE geometry kernel.
Draw; Redraw the scene.
SplitCurrentWindowHorizontal expression ;
Split the current window horizontally, with the ratio given by expression.
SplitCurrentWindowVertical expression ;
Split the current window vertically, with the ratio given by expression.
SetCurrentWindow expression ;
Set the current window by speficying its index (starting at 0) in the list of all
windows. When new windows are created by splits, new windows are appended at
the end of the list.
UnsplitWindow;
Restore a single window.
SetChanged;
Force the mesh and post-processing vertex arrays to be regenerated. Useful e.g. for
creating animations with changing clipping planes, etc.
BoundingBox;
Recompute the bounding box of the scene (which is normally computed only after
new model entities are added or after files are included or merged). The bounding
box is computed as follows:
1. If there is a mesh (i.e., at least one mesh node), the bounding box is taken as
the box enclosing all the mesh nodes;
2. If there is no mesh but there is a geometry (i.e., at least one geometrical point),
the bounding box is taken as the box enclosing all the geometrical points;
3. If there is no mesh and no geometry, but there are some post-processing views,
the bounding box is taken as the box enclosing all the primitives in the views.
This operation triggers a synchronization of the CAD model with the internal Gmsh
model.
Chapter 5: Gmsh scripting language 101

BoundingBox { expression, expression, expression, expression, expression,

expression };
Force the bounding box of the scene to the given expressions (X min, X max, Y
min, Y max, Z min, Z max). Beware that order of the coordinates is different than
in the BoundingBox commands for model entities: see Section 5.1.2 [Floating point
expressions], page 89.
Delete Model;
Delete the current model (all model entities and their associated meshes).
Delete Physicals;
Delete all physical groups.
Delete Variables;
Delete all the expressions.
Delete Options;
Delete the current options and revert to the default values.
Delete string ;
Delete the expression string.
Print string-expression ;
Print the graphic window in a file named string-expression, using the current
Print.Format (see Section 7.1 [General options], page 219). If the path in string-
expression is not absolute, string-expression is appended to the path of the current
file. This operation triggers a synchronization of the CAD model with the internal
Gmsh model.
Sleep expression ;
Suspend the execution of Gmsh during expression seconds.
SystemCall string-expression ;
Executes a (blocking) system call.
NonBlockingSystemCall string-expression ;
Execute a (non-blocking) system call.
OnelabRun ( string-expression <, string-expression > )
Run a ONELAB client (first argument is the client name, second optional argument
is the command line).
SetName string-expression ;
Change the name of the current model.
SetFactory(string-expression );
Change the current geometry kernel (i.e. determines the CAD kernel that is used
for all subsequent geometrical commands). Currently available kernels: "Built-in"
and "OpenCASCADE".
SyncModel;
Force an immediate transfer from the old geometrical database into the new one
(this transfer normally occurs right after a file is read).
NewModel;
Create a new current model.
Include string-expression ;
Include the file named string-expression at the current position in the input file.
The include command should be given on a line of its own. If the path in string-
expression is not absolute, string-expression is appended to the path of the current
file.
102 Gmsh 4.11.1

5.2 Geometry scripting commands

Both the built-in and the OpenCASCADE CAD kernels can be used in the scripting language,
by specifying SetFactory("Built-in") or SetFactory("OpenCASCADE"), respectively, before
geometrical scripting commands. If SetFactory is not specified, the built-in kernel is used.
A bottom-up boundary representation approach can be used by first defining points (using the
Point command), then curves (using Line, Circle, Spline, . . . , commands or by extruding
points), then surfaces (using for example the Plane Surface or Surface commands, or by
extruding curves), and finally volumes (using the Volume command or by extruding surfaces).
Entities can then be manipulated in various ways, for example using the Translate, Rotate,
Scale or Symmetry commands. They can be deleted with the Delete command, provided
that no higher-dimension entity references them. With the OpenCASCADE kernel, additional
boolean operations are available: BooleanIntersection, BooleanUnion, BooleanDifference
and BooleanFragments.
The next subsections describe all the available geometry commands in the scripting language.
Note that the following general rule is followed for the definition of model entities: if an ex-
pression defines a new entity, it is enclosed between parentheses. If an expression refers to a
previously defined entity, it is enclosed between braces.

5.2.1 Points
Point ( expression ) = { expression, expression, expression <, expression > };
Create a point. The expression inside the parentheses is the point’s tag; the three
first expressions inside the braces on the right hand side give the three X, Y and Z
coordinates of the point in the three-dimensional Euclidean space; the optional last
expression sets the prescribed mesh element size at that point. See Section 1.2.2
[Specifying mesh element sizes], page 10, for more information about how this value
is used in the meshing process.
Physical Point ( expression | string-expression <, expression > ) <+|->= {
expression-list };
Create a physical point. The expression inside the parentheses is the physical point’s
tag; the expression-list on the right hand side should contain the tags of all the
elementary points that need to be grouped inside the physical point. If a string-
expression is given instead instead of expression inside the parentheses, a string label
is associated with the physical tag, which can be either provided explicitly (after
the comma) or not (in which case a unique tag is automatically created).

5.2.2 Curves
Line ( expression ) = { expression, expression };
Create a straight line segment. The expression inside the parentheses is the line
segment’s tag; the two expressions inside the braces on the right hand side give tags
of the start and end points of the segment.
Bezier ( expression ) = { expression-list };
Create a Bezier curve. The expression-list contains the tags of the control points.
BSpline ( expression ) = { expression-list };
Create a cubic BSpline. The expression-list contains the tags of the control points.
Creates a periodic curve if the first and last points are identical.
Spline ( expression ) = { expression-list };
Create a spline going through the points in expression-list. With the built-in geome-
try kernel this constructs a Catmull-Rom spline. With the OpenCASCADE kernel,
Chapter 5: Gmsh scripting language 103

this constructs a C2 BSpline. Creates a periodic curve if the first and last points
are identical.
Circle ( expression ) = { expression, expression, expression <, ...> };
Create a circle arc. If three expressions are provided on the right-hand-side they
define the start point, the center and the end point of the arc. With the built-in
geometry kernel the arc should be strictly smaller than Pi. With the OpenCAS-
CADE kernel, if between 4 and 6 expressions are provided, the first three define the
coordinates of the center, the next one defines the radius, and the optional next two
the start and end angle.
Ellipse ( expression ) = { expression, expression, expression <, ...> };
Create an ellipse arc. If four expressions are provided on the right-hand-side they
define the start point, the center point, a point anywhere on the major axis and
the end point. If the first point is a major axis point, the third expression can be
ommitted. With the OpenCASCADE kernel, if between 5 and 7 expressions are
provided, the first three define the coordinates of the center, the next two define the
major (along the x-axis) and minor radii (along the y-axis), and the next two the
start and end angle. Note that OpenCASCADE does not allow creating ellipse arcs
with the major radius smaller than the minor radius.
Compound Spline | BSpline ( expression ) = { expression-list } Using expression ;
Create a spline or a BSpline from control points sampled on the curves in expression-
list. Using expression specifies the number of intervals on each curve to compute
the sampling points. Compound splines and BSplines are only available with the
built-in geometry kernel.
Curve Loop ( expression ) = { expression-list };
Create an oriented loop of curves, i.e. a closed wire. The expression inside the
parentheses is the curve loop’s tag; the expression-list on the right hand side should
contain the tags of all the curves that constitute the curve loop. A curve loop
must be a closed loop. With the built-in geometry kernel, the curves should be
ordered and oriented, using negative tags to specify reverse orientation. (If the
orientation is correct, but the ordering is wrong, Gmsh will actually reorder the list
internally to create a consistent loop; the built-in kernel also supports multiple curve
loops (or subloops) in a single Curve Loop command, but this is not recommended).
With the OpenCASCADE kernel the curve loop is always oriented according to the
orientation of its first curve; negative tags can be specified for compatibility with
the built-in kernel, but are simply ignored. Curve loops are used to create surfaces:
see Section 5.2.3 [Surfaces], page 104.
Wire ( expression ) = { expression-list };
Create a path made of curves. Wires are only available with the OpenCASCADE
kernel. They are used to create ThruSections and extrusions along paths.
Physical Curve ( expression | string-expression <, expression > ) <+|->= {
expression-list };
Create a physical curve. The expression inside the parentheses is the physical curve’s
tag; the expression-list on the right hand side should contain the tags of all the
elementary curves that need to be grouped inside the physical curve. If a string-
expression is given instead instead of expression inside the parentheses, a string
label is associated with the physical tag, which can be either provided explicitly
(after the comma) or not (in which case a unique tag is automatically created). In
some mesh file formats (e.g. MSH2), specifying negative tags in the expression-list
will reverse the orientation of the mesh elements belonging to the corresponding
elementary curves in the saved mesh file.
104 Gmsh 4.11.1

5.2.3 Surfaces
Plane Surface ( expression ) = { expression-list };
Create a plane surface. The expression inside the parentheses is the plane surface’s
tag; the expression-list on the right hand side should contain the tags of all the curve
loops defining the surface. The first curve loop defines the exterior boundary of the
surface; all other curve loops define holes in the surface. A curve loop defining a
hole should not have any curves in common with the exterior curve loop (in which
case it is not a hole, and the two surfaces should be defined separately). Likewise,
a curve loop defining a hole should not have any curves in common with another
curve loop defining a hole in the same surface (in which case the two curve loops
should be combined).

Surface ( expression ) = { expression-list } < In Sphere { expression }, Using Point

{ expression-list } >;
Create a surface filling. With the built-in kernel, the first curve loop should be
composed of either three or four curves, the surface is constructed using transfi-
nite interpolation, and the optional In Sphere argument forces the surface to be a
spherical patch (the extra parameter gives the tag of the center of the sphere). With
the OpenCASCADE kernel, a BSpline surface is constructucted by optimization to
match the bounding curves, as well as the (optional) points provided after Using
Point.

BSpline Surface ( expression ) = { expression-list };

Create a BSpline surface filling. Only a single curve loop made of 2, 3 or 4 BSpline
curves can be provided. BSpline Surface is only available with the OpenCAS-
CADE kernel.

Bezier Surface ( expression ) = { expression-list };

Create a Bezier surface filling. Only a single curve loop made of 2, 3 or 4 Bezier
curves can be provided. Bezier Surface is only available with the OpenCASCADE
kernel.

Disk ( expression ) = { expression-list };

Creates a disk. When four expressions are provided on the right hand side (3
coordinates of the center and the radius), the disk is circular. A fifth expression
defines the radius along Y, leading to an ellipse. Disk is only available with the
OpenCASCADE kernel.

Rectangle ( expression ) = { expression-list };

Create a rectangle. The 3 first expressions define the lower-left corner; the next 2
define the width and height. If a 6th expression is provided, it defines a radius to
round the rectangle corners. Rectangle is only available with the OpenCASCADE
kernel.

Surface Loop ( expression ) = { expression-list } < Using Sewing >;

Create a surface loop (a shell). The expression inside the parentheses is the sur-
face loop’s tag; the expression-list on the right hand side should contain the tags
of all the surfaces that constitute the surface loop. A surface loop must always
represent a closed shell, and the surfaces should be oriented consistently (using neg-
ative tags to specify reverse orientation). (Surface loops are used to create volumes:
see Section 5.2.4 [Volumes], page 105.) With the OpenCASCADE kernel, the op-
tional Using Sewing argument allows to build a shell made of surfaces that share
geometrically identical (but topologically different) curves.
Chapter 5: Gmsh scripting language 105

Physical Surface ( expression | string-expression <, expression > ) <+|->= {

expression-list };
Create a physical surface. The expression inside the parentheses is the physical
surface’s tag; the expression-list on the right hand side should contain the tags of
all the elementary surfaces that need to be grouped inside the physical surface.
If a string-expression is given instead instead of expression inside the parentheses,
a string label is associated with the physical tag, which can be either provided
explicitly (after the comma) or not (in which case a unique tag is automatically
created). In some mesh file formats (e.g. MSH2), specifying negative tags in the
expression-list will reverse the orientation of the mesh elements belonging to the
corresponding elementary surfaces in the saved mesh file.

5.2.4 Volumes
Volume ( expression ) = { expression-list };
Create a volume. The expression inside the parentheses is the volume’s tag; the
expression-list on the right hand side should contain the tags of all the surface loops
defining the volume. The first surface loop defines the exterior boundary of the
volume; all other surface loops define holes in the volume. A surface loop defining
a hole should not have any surfaces in common with the exterior surface loop (in
which case it is not a hole, and the two volumes should be defined separately).
Likewise, a surface loop defining a hole should not have any surfaces in common
with another surface loop defining a hole in the same volume (in which case the two
surface loops should be combined).
Sphere ( expression ) = { expression-list };
Create a sphere, defined by the 3 coordinates of its center and a radius. Additional
expressions define 3 angle limits. The first two optional arguments define the polar
angle opening (from -Pi/2 to Pi/2). The optional ‘angle3’ argument defines the az-
imuthal opening (from 0 to 2*Pi). Sphere is only available with the OpenCASCADE
kernel.
Box ( expression ) = { expression-list };
Create a box, defined by the 3 coordinates of a point and the 3 extents. Box is only
available with the OpenCASCADE kernel.
Cylinder ( expression ) = { expression-list };
Create a cylinder, defined by the 3 coordinates of the center of the first circular
face, the 3 components of the vector defining its axis and its radius. An addi-
tional expression defines the angular opening. Cylinder is only available with the
OpenCASCADE kernel.
Torus ( expression ) = { expression-list };
Create a torus, defined by the 3 coordinates of its center and 2 radii. An additional
expression defines the angular opening. Torus is only available with the OpenCAS-
CADE kernel.
Cone ( expression ) = { expression-list };
Create a cone, defined by the 3 coordinates of the center of the first circular face,
the 3 components of the vector defining its axis and the two radii of the faces (these
radii can be zero). An additional expression defines the angular opening. Cone is
only available with the OpenCASCADE kernel.
Wedge ( expression ) = { expression-list };
Create a right angular wedge, defined by the 3 coordinates of the right-angle point
and the 3 extends. An additional parameter defines the top X extent (zero by
default). Wedge is only available with the OpenCASCADE kernel.
106 Gmsh 4.11.1

ThruSections ( expression ) = { expression-list };

Create a volume defined through curve loops. ThruSections is only available with
the OpenCASCADE kernel.

Ruled ThruSections ( expression ) = { expression-list };

Same as ThruSections, but the surfaces created on the boundary are forced to be
ruled. Ruled ThruSections is only available with the OpenCASCADE kernel.

Physical Volume ( expression | string-expression <, expression > ) <+|->= {

expression-list };
Create a physical volume. The expression inside the parentheses is the physical
volume’s tag; the expression-list on the right hand side should contain the tags of
all the elementary volumes that need to be grouped inside the physical volume.
If a string-expression is given instead instead of expression inside the parentheses,
a string label is associated with the physical tag, which can be either provided
explicitly (after the comma) or not (in which case a unique tag is automatically
created).

5.2.5 Extrusions
Curves, surfaces and volumes can also be created through extrusion of points, curves and sur-
faces, respectively. Here is the syntax of the geometrical extrusion commands (go to Section 5.3.2
[Structured grids], page 111, to see how these commands can be extended in order to also extrude
the mesh):
extrude:

Extrude { expression-list } { extrude-list }

Extrude all elementary entities (points, curves or surfaces) in extrude-list using a
translation. The expression-list should contain three expressions giving the X, Y
and Z components of the translation vector.

Extrude { { expression-list }, { expression-list }, expression } { extrude-list }

Extrude all elementary entities (points, curves or surfaces) in extrude-list using a
rotation. The first expression-list should contain three expressions giving the X,
Y and Z direction of the rotation axis; the second expression-list should contain
three expressions giving the X, Y and Z components of any point on this axis; the
last expression should contain the rotation angle (in radians). With the built-in
geometry kernel the angle should be strictly smaller than Pi.

Extrude { { expression-list }, { expression-list }, { expression-list },

expression } { extrude-list }
Extrude all elementary entities (points, curves or surfaces) in extrude-list using a
translation combined with a rotation (to produce a “twist”). The first expression-
list should contain three expressions giving the X, Y and Z components of the
translation vector; the second expression-list should contain three expressions giving
the X, Y and Z direction of the rotation axis, which should match the direction of
the translation; the third expression-list should contain three expressions giving the
X, Y and Z components of any point on this axis; the last expression should contain
the rotation angle (in radians). With the built-in geometry kernel the angle should
be strictly smaller than Pi.

Extrude { extrude-list }
Extrude entities in extrude-list using a translation along their normal. Only avail-
able with the built-in geometry kernel.
Chapter 5: Gmsh scripting language 107

Extrude { extrude-list } Using Wire { expression-list }

Extrude entities in extrude-list along the give wire. Only available with the Open-
CASCADE geometry kernel.
ThruSections { expression-list }
Create surfaces through the given curve loops or wires. ThruSections is only avail-
able with the OpenCASCADE kernel.
Ruled ThruSections { expression-list }
Create ruled surfaces through the given curve loops or wires. Ruled ThruSections
is only available with the OpenCASCADE kernel.
Fillet { expression-list } { expression-list } { expression-list }
Fillet volumes (first list) on some curves (second list), using the provided radii (third
list). The radius list can either contain a single radius, as many radii as curves, or
twice as many as curves (in which case different radii are provided for the begin and
end points of the curves). Fillet is only available with the OpenCASCADE kernel.
Chamfer { expression-list } { expression-list } { expression-list } {
expression-list }
Chamfer volumes (first list) on some curves (second list), using the provided distance
(fourth list) measured on the given surfaces (third list). The distance list can either
contain a single distance, as many distances as curves, or twice as many as curves
(in which case the first in each pair is measured on the given corresponding surface).
Chamfer is only available with the OpenCASCADE kernel.
with
extrude-list :
<Physical> Point | Curve | Surface { expression-list-or-all }; ...
As explained in Section 5.1.2 [Floating point expressions], page 89, extrude can be used in an
expression, in which case it returns a list of tags. By default, the list contains the “top” of the
extruded entity at index 0 and the extruded entity at index 1, followed by the “sides” of the
extruded entity at indices 2, 3, etc. For example:
Point(1) = {0,0,0};
Point(2) = {1,0,0};
Line(1) = {1, 2};
out[] = Extrude{0,1,0}{ Curve{1}; };
Printf("top curve = %g", out[0]);
Printf("surface = %g", out[1]);
Printf("side curves = %g and %g", out[2], out[3]);
This behaviour can be changed with the Geometry.ExtrudeReturnLateralEntities option
(see Section 7.3 [Geometry options], page 246).

5.2.6 Boolean operations

Boolean operations can be applied on curves, surfaces and volumes. All boolean operation act
on two lists of elementary entities. The first list represents the object; the second represents the
tool. The general syntax for boolean operations is as follows:
boolean:
BooleanIntersection { boolean-list } { boolean-list }
Compute the intersection of the object and the tool.
BooleanUnion { boolean-list } { boolean-list }
Compute the union of the object and the tool.
108 Gmsh 4.11.1

BooleanDifference { boolean-list } { boolean-list }

Subtract the tool from the object.
BooleanFragments { boolean-list } { boolean-list }
Compute all the fragments resulting from the intersection of the entities in the
object and in the tool, making all interfaces conformal. When applied to entities of
different dimensions, the lower dimensional entities will be automatically embedded
in the higher dimensional entities if they are not on their boundary.
with
boolean-list :
<Physical> Curve | Surface | Volume { expression-list-or-all }; ... |
Delete ;
If Delete is specified in the boolean-list, the tool and/or the object is deleted.
As explained in Section 5.1.2 [Floating point expressions], page 89, boolean can be used in an
expression, in which case it returns the list of tags of the highest dimensional entities created
by the boolean operation. See examples/boolean for examples.
An alternative syntax exists for boolean operations, which can be used when it is known before-
hand that the operation will result in a single (highest-dimensional) entity:
boolean-explicit:
BooleanIntersection ( expression ) = { boolean-list } { boolean-list };
Compute the intersection of the object and the tool and assign the result the tag
expression.
BooleanUnion ( expression ) = { boolean-list } { boolean-list };
Compute the union of the object and the tool and assign the result the tag expres-
sion.
BooleanDifference ( expression ) = { boolean-list } { boolean-list };
Subtract the tool from the object and assign the result the tag expression.
Again, see examples/boolean for examples.
Boolean operations are only available with the OpenCASCADE geometry kernel.

5.2.7 Transformations
Geometrical transformations can be applied to elementary entities, or to copies of elementary en-
tities (using the Duplicata command: see below). The syntax of the transformation commands
is:
transform:
Dilate { { expression-list }, expression } { transform-list }
Scale all elementary entities in transform-list by a factor expression. The expression-
list should contain three expressions giving the X, Y, and Z coordinates of the center
of the homothetic transformation.
Dilate { { expression-list }, { expression, expression, expression } } {
transform-list }
Scale all elementary entities in transform-list using different factors along X, Y and Z
(the three expressions). The expression-list should contain three expressions giving
the X, Y, and Z coordinates of the center of the homothetic transformation.
Rotate { { expression-list }, { expression-list }, expression } { transform-list }
Rotate all elementary entities in transform-list by an angle of expression radians.
The first expression-list should contain three expressions giving the X, Y and Z direc-
tion of the rotation axis; the second expression-list should contain three expressions
giving the X, Y and Z components of any point on this axis.
Chapter 5: Gmsh scripting language 109

Symmetry { expression-list } { transform-list }

Transform all elementary entities symmetrically to a plane. The expression-list
should contain four expressions giving the coefficients of the plane’s equation.
Affine { expression-list } { transform-list }
Apply a 4 x 4 affine transformation matrix (16 entries given by row; only 12 can be
provided for convenience) to all elementary entities. Currently only available with
the OpenCASCADE kernel.
Translate { expression-list } { transform-list }
Translate all elementary entities in transform-list. The expression-list should contain
three expressions giving the X, Y and Z components of the translation vector.
Boundary { transform-list }
(Not a transformation per-se.) Return the entities on the boundary of the elemen-
tary entities in transform-list, with signs indicating their orientation in the boundary.
To get unsigned tags (e.g. to reuse the output in other commands), apply the Abs
function on the returned list. This operation triggers a synchronization of the CAD
model with the internal Gmsh model.
CombinedBoundary { transform-list }
(Not a transformation per-se.) Return the boundary of the elementary entities,
combined as if a single entity, in transform-list. Useful to compute the boundary of
a complex part. This operation triggers a synchronization of the CAD model with
the internal Gmsh model.
PointsOf { transform-list }
(Not a transformation per-se.) Return all the geometrical points on the boundary
of the elementary entities. Useful to compute the boundary of a complex part. This
operation triggers a synchronization of the CAD model with the internal Gmsh
model.
Intersect Curve { expression-list } Surface { expression }
(Not a transformation per-se.) Return the intersections of the curves given in
expression-list with the specified surface. Currently only available with the built-in
kernel.
Split Curve { expression } Point { expression-list }
(Not a transformation per-se.) Split the curve expression on the specified control
points. Only available with the built-in kernel, for lines, splines and BSplines.
with
transform-list :
<Physical> Point | Curve | Surface | Volume
{ expression-list-or-all }; ... |
Duplicata { <Physical> Point | Curve | Surface | Volume
{ expression-list-or-all }; ... } |
transform

5.2.8 Other geometry commands

Here is a list of all other geometry commands currently available:
Coherence;
Remove all duplicate elementary entities (e.g., points having identical
coordinates). Note that with the built-in geometry kernel Gmsh executes the
Coherence command automatically after each geometrical transformation, unless
110 Gmsh 4.11.1

Geometry.AutoCoherence is set to zero (see Section 7.3 [Geometry options],

page 246). With the OpenCASCADE geometry kernel, Coherence is simply
a shortcut for a BooleanFragments operation on all entities, with the Delete
operator applied to all operands.
HealShapes;
Apply the shape healing procedure(s), according to Geometry.OCCFixDegenerated,
Geometry.OCCFixSmallEdges, Geometry.OCCFixSmallFaces,
Geometry.OCCSewFaces, Geometry.OCCMakeSolids. Only available with
the OpenCASCADE geometry kernel.
< Recursive > Delete { <Physical> Point | Curve | Surface | Volume {
expression-list-or-all }; ... }
Delete all elementary entities whose tags are given in expression-list-or-all. If an
entity is linked to another entity (for example, if a point is used as a control point
of a curve), Delete has no effect (the curve will have to be deleted before the point
can). The Recursive variant deletes the entities as well as all its sub-entities of
lower dimension. This operation triggers a synchronization of the CAD model with
the internal Gmsh model.
Delete Embedded { <Physical> Point | Curve | Surface | Volume {
expression-list-or-all }; ... }
Delete all the embedded entities in the elementary entities whose tags are given in
expression-list-or-all. This operation triggers a synchronization of the CAD model
with the internal Gmsh model.
SetMaxTag Point | Curve | Surface | Volume ( expression )
Force the maximum tag for a category of entities to a given value, so that subse-
quently created entities in the same category will not have tags smaller than the
given value.
< Recursive > Hide { <Physical> Point | Curve | Surface | Volume {
expression-list-or-all }; ... }
Hide the entities listed in expression-list-or-all.
Hide { : }
Hide all entities.
< Recursive > Show { <Physical> Point | Curve | Surface | Volume {
expression-list-or-all }; ... }
Show the entities listed in expression-list-or-all.
Show { : }
Show all entities.
Sphere | PolarSphere ( expression ) = {expression, expression };
Change the current (surface) geometry used by the built-in geometry kernel to a
(polar) sphere, defined by the two point tags specified on the right hand side. The
expression between parentheses on the left hand side specifies a new unique tag for
this geometry.
Parametric Surface ( expression ) = "string " "string " "string ";
Change the current (surface) geometry used by the built-in geometry kernel to a
parametric surface defined by the three strings expression evaluating to the x, y and
z coordinates. The expression between parentheses on the left hand side specifies a
new unique tag for this geometry.
Chapter 5: Gmsh scripting language 111

Coordinates Surface expression ;

Change the current (surface) geometry used by the built-in geometry kernel to the
geometry identified by the given expression.
Euclidian Coordinates ;
Restore the default planar geometry for the built-in geometry kernel.

5.3 Mesh scripting commands

The mesh module scripting commands allow to modify the mesh element sizes and specify
structured grid parameters. Certain meshing actions (e.g. “mesh all the surfaces”) can also be
specified in the script files, but are usually performed either in the GUI or on the command line
(see Chapter 3 [Gmsh graphical user interface], page 77, and Chapter 4 [Gmsh command-line
interface], page 83).

5.3.1 Mesh element sizes

Here are the mesh commands that are related to the specification of mesh element sizes:
MeshSize { expression-list } = expression ;
Modify the prescribed mesh element size of the points whose tags are listed in
expression-list. The new value is given by expression.
Field[expression ] = string ;
Create a new field (with tag expression), of type string.
Field[expression ].string = string-expression | expression | expression-list ;
Set the option string of the expression-th field.
Background Field = expression ;
Select the expression-th field as the one used to compute element sizes. Only one
background field can be given; if you want to combine several field, use the Min or
Max field (see below).

5.3.2 Structured grids

Extrude { expression-list } { extrude-list layers }
Extrude both the geometry and the mesh using a translation (see Section 5.2.5
[Extrusions], page 106). The layers option determines how the mesh is extruded
and has the following syntax:
layers :
Layers { expression } |
Layers { { expression-list }, { expression-list } } |
Recombine < expression >; ...
QuadTriNoNewVerts <RecombLaterals>; |
QuadTriAddVerts <RecombLaterals>; ...
In the first Layers form, expression gives the number of elements to be created in
the (single) layer. In the second form, the first expression-list defines how many
elements should be created in each extruded layer, and the second expression-list
gives the normalized height of each layer (the list should contain a sequence of n
numbers 0 < h1 < h2 < . . . < hn <= 1). See Section 2.3 [t3], page 21, for an example.
For curve extrusions, the Recombine option will recombine triangles into quadran-
gles when possible. For surface extrusions, the Recombine option will recombine
tetrahedra into prisms, hexahedra or pyramids.
Please note that, starting with Gmsh 2.0, region tags cannot be specified explicitly
anymore in Layers commands. Instead, as with all other geometry commands,
112 Gmsh 4.11.1

you must use the automatically created entity identifier created by the extrusion
command. For example, the following extrusion command will return the tag of the
new “top” surface in num[0] and the tag of the new volume in num[1]:
num[] = Extrude {0,0,1} { Surface{1}; Layers{10}; };
QuadTriNoNewVerts and QuadTriAddVerts allow to connect structured, extruded
volumes containing quadrangle-faced elements to structured or unstructured tetra-
hedral volumes, by subdividing into triangles any quadrangles on boundary surfaces
shared with tetrahedral volumes. (They have no effect for 1D or 2D extrusions.)
QuadTriNoNewVerts subdivides any of the region’s quad-faced 3D elements that
touch these boundary triangles into pyramids, prisms, or tetrahedra as necessary,
all without adding new nodes. QuadTriAddVerts works in a similar way, but subdi-
vides 3D elements touching the boundary triangles by adding a new node inside each
element at the node-based centroid. Either method results in a structured extru-
sion with an outer layer of subdivided elements that interface the inner, unmodified
elements to the triangle-meshed region boundaries.
In some rare cases, due to certain lateral boundary conditions, it may not be possible
make a valid element subdivision with QuadTriNoNewVerts without adding addi-
tional nodes. In this case, an internal node is created at the node-based centroid of
the element. The element is then divided using that node. When an internal node
is created with QuadTriNoNewVerts, the user is alerted by a warning message sent
for each instance; however, the mesh will still be valid and conformal.
Both QuadTriNoNewVerts and QuadTriAddVerts can be used with the optional
RecombLaterals keyword. By default, the QuadTri algorithms will mesh any free
laterals as triangles, if possible. RecombLaterals forces any free laterals to remain
as quadrangles, if possible. Lateral surfaces between two QuadTri regions will always
be meshed as quadrangles.
Note that the QuadTri algorithms will handle all potential meshing conflicts along
the lateral surfaces of the extrusion. In other words, QuadTri will not subdivide a
lateral that must remain as quadrangles, nor will it leave a lateral as quadrangles
if it must be divided. The user should therefore feel free to mix different types of
neighboring regions with a QuadTri meshed region; the mesh should work. However,
be aware that the top surface of the QuadTri extrusion will always be meshed as
triangles, unless it is extruded back onto the original source in a toroidal loop (a
case which also works with QuadTri).
QuadTriNoNewVerts and QuadTriAddVerts may be used interchangeably, but
QuadTriAddVerts often gives better element quality.
If the user wishes to interface a structured extrusion to a tetrahedral volume without
modifying the original structured mesh, the user may create dedicated interface
volumes around the structured geometry and apply a QuadTri algorithm to those
volumes only.
Extrude { { expression-list }, { expression-list }, expression } { extrude-list
layers }
Extrude both the geometry and the mesh using a rotation (see Section 5.2.5 [Extru-
sions], page 106). The layers option is defined as above. With the built-in geometry
kernel the angle should be strictly smaller than Pi. With the OpenCASCADE kernel
the angle should be strictly smaller than 2 Pi.
Extrude { { expression-list }, { expression-list }, { expression-list },
expression } { extrude-list layers }
Extrude both the geometry and the mesh using a combined translation and rotation
(see Section 5.2.5 [Extrusions], page 106). The layers option is defined as above.
Chapter 5: Gmsh scripting language 113

With the built-in geometry kernel the angle should be strictly smaller than Pi. With
the OpenCASCADE kernel the angle should be strictly smaller than 2 Pi.
Extrude { Surface { expression-list }; layers < Using Index[expr ]; > < Using
View[expr ]; > < ScaleLastLayer; > }
Extrude a “topological” boundary layer from the specified surfaces. If no view is
specified, the mesh of the boundary layer entities is created using a gouraud-shaded
(smoothed) normal field. If a scalar view is specified, it locally prescribes the thick-
ness of the layer. If a vector-valued view is specified it locally prescribes both the
extrusion direction and the thickness. Specifying a boundary layer index allows to
extrude several independent boundary layers (with independent normal smoothing).
ScaleLastLayer scales the height of the last (top) layer of each normal’s extrusion
by the average length of the edges in all the source elements that contain the source
node (actually, the average of the averages for each element–edges actually touch-
ing the source node are counted twice). This allows the height of the last layer to
vary along with the size of the source elements in order to achieve better element
quality. For example, in a boundary layer extruded with the Layers definition ’Lay-
ers{ {1,4,2}, {0.5, 0.6, 1.6} },’ a source node adjacent to elements with an overall
average edge length of 5.0 will extrude to have a last layer height = (1.6-0.6) * 5.0
= 5.0. Topological boundary layers are only available with the built-in kernel. See
sphere boundary layer.geo or sphere boundary layer from view.geo for ‘.geo’ file
examples, and aneurysm.py for an API example.
The advantage of this approach is that it provides a topological description of the
boundary layer, which means that it can be connected to other geometrical entities.
The disadvantage is that the mesh is just a “simple” extrusion: no fans, no special
treatments of reentrant corners, etc. Another boundary layer algorithm is currently
available through the BoundaryLayer field (see Section 1.2.2 [Specifying mesh ele-
ment sizes], page 10). It only works in 2D however, and is a meshing constraint:
it works directly at the mesh level, without creating geometrical entities. See e.g.
BL0.geo or naca12 2d.geo.
Transfinite Curve { expression-list-or-all } = expression < Using Progression |
Bump expression >;
Select the curves in expression-list to be meshed with the 1D transfinite algorithm.
The expression on the right hand side gives the number of nodes that will be cre-
ated on the curve (this overrides any other mesh element size prescription—see
Section 1.2.2 [Specifying mesh element sizes], page 10). The optional argument
‘Using Progression expression ’ instructs the transfinite algorithm to distribute
the nodes following a geometric progression (Progression 2 meaning for example
that each line element in the series will be twice as long as the preceding one). The
optional argument ‘Using Bump expression ’ instructs the transfinite algorithm to
distribute the nodes with a refinement at both ends of the curve. This operation
triggers a synchronization of the CAD model with the internal Gmsh model.
Transfinite Surface { expression-list-or-all } < = { expression-list } > < Left |
Right | Alternate | AlternateRight | AlternateLeft > ;
Select surfaces to be meshed with the 2D transfinite algorithm. The expression-
list on the right-hand-side should contain the tags of three or four points on the
boundary of the surface that define the corners of the transfinite interpolation. If
no tags are given, the transfinite algorithm will try to find the corners automatically.
The optional argument specifies the way the triangles are oriented when the mesh
is not recombined. Alternate is a synonym for AlternateRight. For 3-sided
surfaces a specific algorithm can be used to generate structured triangular by setting
114 Gmsh 4.11.1

Mesh.TransfiniteTri to 1. Examples can be found in benchmarks/transfinite.

This operation triggers a synchronization of the CAD model with the internal Gmsh
model.
Transfinite Volume { expression-list } < = { expression-list } > ;
Select five- or six-face volumes to be meshed with the 3D transfinite algorithm. The
expression-list on the right-hand-side should contain the tags of the six or eight
points on the boundary of the volume that define the corners of the transfinite
interpolation. If no tags are given, the transfinite algorithm will try to find the
corners automatically. This operation triggers a synchronization of the CAD model
with the internal Gmsh model.
TransfQuadTri { expression-list } ;
Apply the transfinite QuadTri algorithm on the expression-list list of volumes. A
transfinite volume with any combination of recombined and un-recombined transfi-
nite boundary surfaces is valid when meshed with TransfQuadTri. When applied
to non-Transfinite volumes, TransfQuadTri has no effect on those volumes. This
operation triggers a synchronization of the CAD model with the internal Gmsh
model.

5.3.3 Other mesh commands

Here is a list of all other mesh commands currently available:
Mesh expression ;
Generate expression-D mesh. This operation triggers a synchronization of the CAD
model with the internal Gmsh model.
TransformMesh { expression-list };
Transform all the node coordinates in the current mesh using the 4x4 affine trans-
formation matrix given by row (only 12 entries can be provided for convenience).
TransformMesh { expression-list } { transform-list };
Transform the node coordinates in the current mesh of all the elementary entities
in transform-list using the 4x4 affine transformation matrix given by row (only 12
entries can be provided for convenience).
RefineMesh;
Refine the current mesh by splitting all elements. If Mesh.SecondOrderLinear is
set, the new nodes are inserted by linear interpolation. Otherwise they are snapped
on the actual geometry. This operation triggers a synchronization of the CAD model
with the internal Gmsh model.
OptimizeMesh string-expression ;
Optimize the current mesh with the given algorithm (currently "Gmsh" for de-
fault tetrahedral mesh optimizer, "Netgen" for Netgen optimizer, "HighOrder"
for direct high-order mesh optimizer, "HighOrderElastic" for high-order elastic
smoother, "HighOrderFastCurving" for fast curving algorithm, "Laplace2D" for
Laplace smoothing, "Relocate2D" and "Relocate3D" for node relocation).
AdaptMesh { expression-list } { expression-list } { { expression-list < , ... > } };
Perform adaptive mesh generation. Documentation not yet available.
RelocateMesh Point | Curve | Surface { expression-list-or-all };
Relocate the mesh nodes on the given entities using the parametric coordinates
stored in the nodes. Useful for creating perturbation of meshes e.g. for sensitivity
analyzes. This operation triggers a synchronization of the CAD model with the
internal Gmsh model.
Chapter 5: Gmsh scripting language 115

RecombineMesh;
Recombine the current mesh into quadrangles. This operation triggers a synchro-
nization of the CAD model with the internal Gmsh model.
SetOrder expression ;
Change the order of the elements in the current mesh.
PartitionMesh expression ;
Partition the mesh into expression, using current partitioning options.
Point | Curve { expression-list } In Surface { expression };
Add a meshing constraint to embed the point(s) or curve(s) in the given surface. The
surface mesh will conform to the mesh of the point(s) or curves(s). This operation
triggers a synchronization of the CAD model with the internal Gmsh model.
Point | Curve | Surface { expression-list } In Volume { expression };
Add a meshing constraint to embed the point(s), curve(s) or surface(s) in the given
volume. The volume mesh will conform to the mesh of the corresponding point(s),
curve(s) or surface(s). This is only supported with the 3D Delaunay algorithms.
This operation triggers a synchronization of the CAD model with the internal Gmsh
model.
Periodic Curve { expression-list } = { expression-list } ;
Add a meshing constraint to force the mesh of the curves on the left-hand side to
match the mesh of the curves on the right-hand side (masters). If used after meshing,
generate the periodic node correspondence information assuming the mesh of the
curves on the left-hand side effectively matches the mesh of the curves on the right-
hand side. This operation triggers a synchronization of the CAD model with the
internal Gmsh model.
Periodic Surface expression { expression-list } = expression { expression-list } ;
Add a meshing constraint to force the mesh of the surface on the left-hand side (with
boundary edges specified between braces) to match the mesh of the master surface
on the right-hand side (with boundary edges specified between braces). If used after
meshing, generate the periodic node correspondence information assuming the mesh
of the surface on the left-hand side effectively matches the mesh of the master surface
on the right-hand side (useful for structured and extruded meshes). This operation
triggers a synchronization of the CAD model with the internal Gmsh model.
Periodic Curve | Surface { expression-list } = { expression-list } Affine |
Translate { expression-list } ;
Add a meshing constraint to force mesh of curves or surfaces on the left-hand side
to match the mesh of the curves or surfaces on the right-hand side (masters), using
prescribed geometrical transformations. If used after meshing, generate the peri-
odic node correspondence information assuming the mesh of the curves or surfaces
on the left-hand side effectively matches the mesh of the curves or surfaces on the
right-hand side (useful for structured and extruded meshes). Affine takes a 4 x 4
affine transformation matrix given by row (only 12 entries can be provided for con-
venience); Translate takes the 3 components of the translation as in Section 5.2.7
[Transformations], page 108. This operation triggers a synchronization of the CAD
model with the internal Gmsh model.
Periodic Curve | Surface { expression-list } = { expression-list } Rotate {
expression-list }, { expression-list }, expression } ;
Add a meshing constraint to force the mesh of curves or surfaces on the left-hand side
to match the mesh of the curves on the right-hand side (masters), using a rotation
116 Gmsh 4.11.1

specified as in Section 5.2.7 [Transformations], page 108. If used after meshing,

generate the periodic node correspondence information assuming the mesh of the
curves or surfaces on the left-hand side effectively matches the mesh of the curves or
surfaces on the right-hand side (useful for structured and extruded meshes). This
operation triggers a synchronization of the CAD model with the internal Gmsh
model.

Coherence Mesh;
Remove all duplicate mesh nodes in the current mesh.

CreateTopology < { expression , expression } > ;

Create a boundary representation from the mesh of the current model if the model
does not have one (e.g. when imported from mesh file formats with no BRep rep-
resentation of the underlying model). If the first optional argument is set (or not
given), make all volumes and surfaces simply connected first; if the second optional
argument is set (or not given), clear any built-in CAD kernel entities and export
the discrete entities in the built-in CAD kernel.

CreateGeometry < { <Physical> Point | Curve | Surface | Volume {

expression-list-or-all }; ... } > ;
Create a geometry for discrete entities (represented solely by a mesh, without an
underlying CAD description) in the current model, i.e. create a parametrization for
discrete curves and surfaces, assuming that each can be parametrized with a single
map. If no entities are given, create a geometry for all discrete entities.

ClassifySurfaces { expression , expression , expression < , expression > };

Classify (“color”) the current surface mesh based on an angle threshold (the first
argument, in radians), and create new discrete surfaces, curves and points accord-
ingly. If the second argument is set, also create discrete curves on the boundary if
the surface is open. If the third argument is set, create edges and surfaces than can
be reparametrized with CreateGeometry. The last optional argument sets an angle
threshold to force splitting of the generated curves.

RenumberMeshNodes;
Renumber the node tags in the current mesh in a continuous sequence.

RenumberMeshElements;
Renumber the elements tags in the current mesh in a continuous sequence.

< Recursive > Color color-expression { <Physical> Point | Curve | Surface | Volume {
expression-list-or-all }; ... }
Set the mesh color of the entities in expression-list to color-expression. This opera-
tion triggers a synchronization of the CAD model with the internal Gmsh model.

Recombine Surface { expression-list-or-all } < = expression >;

Recombine the triangular meshes of the surfaces listed in expression-list into mixed
triangular/quadrangular meshes. The optional expression on the right hand side
specifies the maximum difference (in degrees) allowed between the largest angle of
a quadrangle and a right angle (a value of 0 would only accept quadrangles with
right angles; a value of 90 would allow degenerate quadrangles; default value is 45).
This operation triggers a synchronization of the CAD model with the internal Gmsh
model.

MeshAlgorithm Surface { expression-list } = expression ;

Specify the meshing algorithm for the surfaces expression-list.
Chapter 5: Gmsh scripting language 117

MeshSizeFromBoundary Surface { expression-list } = expression ;

Force the mesh size to be extended from the boundary (or not, depending on the
value of expression) for the surfaces expression-list.
Compound Curve | Surface { expression-list-or-all } ;
Treat the given entities as a single entity when meshing, i.e. perform cross-patch
meshing of the entities.
ReverseMesh Curve | Surface { expression-list-or-all } ;
Add a constraint to reverse the orientation of the mesh of the given curve(s) or
surface(s) during meshing. This operation triggers a synchronization of the CAD
model with the internal Gmsh model.
ReorientMesh Volume { expression-list } ;
Add a constraint to reorient the meshes (during mesh generation) of the bounding
surfaces of the given volumes so that the normals point outward to the volumes;
and if a mesh already exists, reorient it. Currently only available with the Open-
CASCADE kernel, as it relies on the STL triangulation. This operation triggers a
synchronization of the CAD model with the internal Gmsh model.
Save string-expression ;
Save the current mesh in a file named string-expression, using the current
Mesh.Format (see Section 7.4 [Mesh options], page 255). If the path in
string-expression is not absolute, string-expression is appended to the path of the
current file. This operation triggers a synchronization of the CAD model with the
internal Gmsh model.
Smoother Surface { expression-list } = expression ;
Set the number of elliptic smoothing steps for the surfaces listed in expression-
list (smoothing only applies to transfinite meshes at the moment). This operation
triggers a synchronization of the CAD model with the internal Gmsh model.
Homology ( { expression-list } ) { { expression-list } , { expression-list } };
Compute a basis representation for homology spaces after a mesh has been gen-
erated. The first expression-list is a list of dimensions whose homology bases are
computed; if empty, all bases are computed. The second expression-list is a list
physical groups that constitute the computation domain; if empty, the whole mesh
is the domain. The third expression-list is a list of physical groups that constitute
the relative subdomain of relative homology computation; if empty, absolute ho-
mology is computed. Resulting basis representation chains are stored as physical
groups in the mesh.
Cohomology ( { expression-list } ) { { expression-list } , { expression-list } };
Similar to command Homology, but computes a basis representation for cohomology
spaces instead.

5.4 Post-processing scripting commands

Here is the list of available post-processing scripting commands.
Alias View[expression ];
Create an alias of the expression-th post-processing view.
Note that Alias creates a logical duplicate of the view without actually duplicating
the data in memory. This is very useful when you want multiple simultaneous
renderings of the same large dataset (usually with different display options), but
you cannot afford to store all copies in memory. If what you really want is multiple
118 Gmsh 4.11.1

physical copies of the data, just merge the file containing the post-processing view
multiple times.
AliasWithOptions View[expression ];
Create an alias of the expression-th post-processing view and copies all the options
of the expression-th view to the new aliased view.
CopyOptions View[expression, expression ];
Copy all the options from the first expression-th post-processing view to the second
one.
Combine ElementsByViewName;
Combine all the post-processing views having the same name into new views. The
combination is done “spatially”, i.e., simply by appending the elements at the end
of the new views.
Combine ElementsFromAllViews | Combine Views;
Combine all the post-processing views into a single new view. The combination is
done “spatially”, i.e., simply by appending the elements at the end of the new view.
Combine ElementsFromVisibleViews;
Combine all the visible post-processing views into a single new view. The combi-
nation is done “spatially”, i.e., simply by appending the elements at the end of the
new view.
Combine TimeStepsByViewName | Combine TimeSteps;
Combine the data from all the post-processing views having the same name into
new multi-time-step views. The combination is done “temporally”, i.e., as if the
data in each view corresponds to a different time instant. The combination will fail
if the meshes in all the views are not identical.
Combine TimeStepsFromAllViews;
Combine the data from all the post-processing views into a new multi-time-step view.
The combination is done “temporally”, i.e., as if the data in each view corresponds
to a different time instant. The combination will fail if the meshes in all the views
are not identical.
Combine TimeStepsFromVisibleViews;
Combine the data from all the visible post-processing views into a new multi-time-
step view. The combination is done “temporally”, i.e., as if the data in each view
corresponds to a different time instant. The combination will fail if the meshes in
all the views are not identical.
Delete View[expression ];
Delete (remove) the expression-th post-processing view. Note that post-processing
view indices start at 0.
Delete Empty Views;
Delete (remove) all the empty post-processing views.
Background Mesh View[expression ];
Apply the expression-th post-processing view as the current background mesh. Note
that post-processing view indices start at 0.
Plugin (string ) . Run;
Execute the plugin string. The list of default plugins is given in Chapter 9 [Gmsh
plugins], page 317.
Chapter 5: Gmsh scripting language 119

Plugin (string ) . string = expression | string-expression ;

Set an option for a given plugin. See Chapter 9 [Gmsh plugins], page 317, for a list
of default plugins and Section 2.9 [t9], page 36, for some examples.
Save View[expression ] string-expression ;
Save the expression-th post-processing view in a file named string-expression. If the
path in string-expression is not absolute, string-expression is appended to the path
of the current file.
SendToServer View[expression ] string-expression ;
Send the expression-th post-processing view to the ONELAB server, with parameter
name string-expression.
View "string " { string < ( expression-list ) > { expression-list }; ... };
Create a new post-processing view, named "string ". This is an easy and quite
powerful way to import post-processing data: all the values are expressions, you
can embed datasets directly into your geometrical descriptions (see, e.g., Section 2.4
[t4], page 23), the data can be easily generated “on-the-fly” (there is no header
containing a priori information on the size of the dataset). The syntax is also very
permissive, which makes it ideal for testing purposes.
However this “parsed format” is read by Gmsh’s script parser, which makes it in-
efficient if there are many elements in the dataset. Also, there is no connectivity
information in parsed views and all the elements are independent (all fields can be
discontinuous), so a lot of information can be duplicated. For large datasets, you
should thus use the mesh-based post-processing file format described in Chapter 10
[Gmsh file formats], page 345, or use one of the standard formats like MED.
More explicitly, the syntax for a parsed View is the following
View "string " {
type ( coordinates ) { values }; ...
< TIME { expression-list }; >
< INTERPOLATION_SCHEME { val-coef-matrix }
{ val-exp-matrix }
< { geo-coef-matrix } { geo-exp-matrix } > ; >
};
where the 47 object types that can be displayed are:
type #coordinates #values
-------------------------------------------------------------
Scalar point SP 3 1 * nb-time-steps
Vector point VP 3 3 * nb-time-steps
Tensor point TP 3 9 * nb-time-steps
Scalar line SL 6 2 * nb-time-steps
Vector line VL 6 6 * nb-time-steps
Tensor line TL 6 18 * nb-time-steps
Scalar triangle ST 9 3 * nb-time-steps
Vector triangle VT 9 9 * nb-time-steps
Tensor triangle TT 9 27 * nb-time-steps
Scalar quadrangle SQ 12 4 * nb-time-steps
Vector quadrangle VQ 12 12 * nb-time-steps
Tensor quadrangle TQ 12 36 * nb-time-steps
Scalar tetrahedron SS 12 4 * nb-time-steps
Vector tetrahedron VS 12 12 * nb-time-steps
Tensor tetrahedron TS 12 36 * nb-time-steps
Scalar hexahedron SH 24 8 * nb-time-steps
120 Gmsh 4.11.1

Vector hexahedron VH 24 24 * nb-time-steps

Tensor hexahedron TH 24 72 * nb-time-steps
Scalar prism SI 18 6 * nb-time-steps
Vector prism VI 18 18 * nb-time-steps
Tensor prism TI 18 54 * nb-time-steps
Scalar pyramid SY 15 5 * nb-time-steps
Vector pyramid VY 15 15 * nb-time-steps
Tensor pyramid TY 15 45 * nb-time-steps
2D text T2 3 arbitrary
3D text T3 4 arbitrary
The coordinates are given ‘by node’, i.e.,
• (coord1, coord2, coord3 ) for a point,
• (coord1-node1, coord2-node1, coord3-node1,
coord1-node2, coord2-node2, coord3-node2 ) for a line,
• (coord1-node1, coord2-node1, coord3-node1,
coord1-node2, coord2-node2, coord3-node2,
coord1-node3, coord2-node3, coord3-node3 ) for a triangle,
• etc.
The ordering of the nodes is given in Section 10.2 [Node ordering], page 352.
The values are given by time step, by node and by component, i.e.:
comp1-node1-time1, comp2-node1-time1, comp3-node1-time1,
comp1-node2-time1, comp2-node2-time1, comp3-node2-time1,
comp1-node3-time1, comp2-node3-time1, comp3-node3-time1,
comp1-node1-time2, comp2-node1-time2, comp3-node1-time2,
comp1-node2-time2, comp2-node2-time2, comp3-node2-time2,
comp1-node3-time2, comp2-node3-time2, comp3-node3-time2,
...
For the 2D text objects, the two first expressions in coordinates give the X-Y po-
sition of the string in screen coordinates, measured from the top-left corner of the
window. If the first (respectively second) expression is negative, the position is
measured from the right (respectively bottom) edge of the window. If the value of
the first (respectively second) expression is larger than 99999, the string is centered
horizontally (respectively vertically). If the third expression is equal to zero, the
text is aligned bottom-left and displayed using the default font and size. Otherwise,
the third expression is converted into an integer whose eight lower bits give the font
size, whose eight next bits select the font (the index corresponds to the position
in the font menu in the GUI), and whose eight next bits define the text align-
ment (0=bottom-left, 1=bottom-center, 2=bottom-right, 3=top-left, 4=top-center,
5=top-right, 6=center-left, 7=center-center, 8=center-right).
For the 3D text objects, the three first expressions in coordinates give the XYZ
position of the string in model (real world) coordinates. The fourth expression has
the same meaning as the third expression in 2D text objects.
For both 2D and 3D text objects, the values can contain an arbitrary number of
string-expressions. If the string-expression starts with file://, the remainder of the
string is interpreted as the name of an image file, and the image is displayed instead
of the string. A format string in the form @wxh or @wxh,wx,wy,wz,hx,hy,hz, where
w and h are the width and height (in model coordinates for T3 or in pixels for T2) of
the image, wx,wy,wz is the direction of the bottom edge of the image and hx,hy,hz
is the direction of the left edge of the image.
Chapter 5: Gmsh scripting language 121

The optional TIME list can contain a list of expressions giving the value of the time
(or any other variable) for which an evolution was saved.
The optional INTERPOLATION_SCHEME lists can contain the interpolation matrices
used for high-order adaptive visualization.
Let us assume that the approximation of the view’s value over an element is written
as a linear combination of d basis functions f [i], i=0, ..., d-1 (the coefficients being
stored in values). Defining f [i] = Sum(j=0, ..., d-1) F[i][j] p[j], with p[j] = u^P[j][0]
v^P[j][1] w^P[j][2] (u, v and w being the coordinates in the element’s parameter
space), then val-coef-matrix denotes the d x d matrix F and val-exp-matrix denotes
the d x 3 matrix P.
In the same way, let us also assume that the coordinates x, y and z of the ele-
ment are obtained through a geometrical mapping from parameter space as a linear
combination of m basis functions g[i], i=0, ..., m-1 (the coefficients being stored in
coordinates). Defining g[i] = Sum(j=0, ..., m-1) G[i][j] q[j], with q[j] = u^Q[j][0]
v^Q[j][1] w^Q[j][2], then geo-coef-matrix denotes the m x m matrix G and geo-exp-
matrix denotes the m x 3 matrix Q.
Here are for example the interpolation matrices for a first order quadrangle:
INTERPOLATION_SCHEME
{
{1/4,-1/4, 1/4,-1/4},
{1/4, 1/4,-1/4,-1/4},
{1/4, 1/4, 1/4, 1/4},
{1/4,-1/4,-1/4, 1/4}
}
{
{0, 0, 0},
{1, 0, 0},
{0, 1, 0},
{1, 1, 0}
};
Chapter 6: Gmsh application programming interface 123

6 Gmsh application programming interface

The Gmsh application programming interface (API) allows to integrate the Gmsh library in
external applications written in C++, C, Python, Julia or Fortran. By design, the Gmsh
API is purely functional, and only uses elementary types from the target languages. See
the tutorials/c++, tutorials/c, tutorials/python, tutorials/julia and tutorials/fortran directories
from the Chapter 2 [Gmsh tutorial], page 15 for examples. For other API examples, see the
examples/api directory.
The different versions of the API are generated automatically from the master API definition
file api/gen.py:
• C++ API: gmsh.h
• C API: gmshc.h
• Python API: gmsh.py
• Julia API: gmsh.jl
• Fortran API: gmsh.f90
The additional gmsh.h cwrap header redefines the C++ API in terms of the C API. This is
provided as a convenience for users of the binary Gmsh Software Development Kit (SDK) whose
C++ compiler Application Binary Interface (ABI) is not compatible with the ABI of the C++
compiler used to create the SDK. To use these C++ bindings of the C API instead of the native
C++ API, simply rename gmsh.h_cwrap as gmsh.h. Note that this will lead to (slightly) reduced
performance compared to using the native Gmsh C++ API, as it entails additional data copies
between the C++ wrapper, the C API and the native C++ code.
The structure of the API reflects the underlying Gmsh data model (see also Section B.1 [Source
code structure], page 373):
• There are two main data containers: models (which hold the geometrical and the mesh
data) and views (which hold post-processing data). These are manipulated by the API
functions in the top-level namespaces gmsh/model and gmsh/view, respectively. The other
top-level namespaces are gmsh/option (which handles all options), gmsh/plugin (which
handles extensions to core Gmsh functionality), gmsh/graphics (which handles drawing),
gmsh/fltk (which handles the graphical user interface), gmsh/parser (which handles the
Gmsh parser), gmsh/onelab (which handles ONELAB parameters and communications
with external codes) and gmsh/logger (which handles information logging).
• Geometrical data is made of model entities, called points (entities of dimension 0), curves
(entities of dimension 1), surfaces (entities of dimension 2) or volumes (entities of dimension
3). Model entities are stored using a boundary representation: a volume is bounded by a
set of surfaces, a surface is bounded by a series of curves, and a curve is bounded by two
end points. Volumes and surfaces can also store embedded entities of lower dimension, to
force a subsequent mesh to be conformal to internal features like a point in the middle of
a surface. Model entities are identified by a pair of integers: their dimension dim (0, 1, 2
or 3) and their tag, a strictly positive identification number. When dealing with multiple
geometrical entities of possibly different dimensions, the API packs them as a vector of (dim,
tag) integer pairs. Physical groups are collections of model entities and are also identified
by their dimension and by a tag. Operations which do not directly reference a model are
performed on the current model.
• Model entities can be either CAD entities (from the built-in geo kernel or from the Open-
CASCADE occ kernel) or discrete entities (defined by a mesh). Operations on CAD entities
are performed directly within their respective CAD kernels (i.e. using functions from the
gmsh/model/geo or gmsh/model/occ namespaces, respectively), as Gmsh does not translate
across CAD formats but rather directly accesses the native representation. CAD entities
 124 Gmsh 4.11.1

must be synchronized with the model in order to be meshed, or, more generally, for func-
tions outside of gmsh/model/geo or gmsh/model/occ to manipulate them. 1D and 2D
meshing algorithms use the parametrization of the underlying geometrical curve or surface
to generate the mesh. Discrete entities can be remeshed provided that a parametrization is
explicitly recomputed for them.
• Mesh data is made of elements (points, lines, triangles, quadrangles, tetrahedra, hexahedra,
prisms, pyramids, ...), defined by an ordered list of their nodes. Elements and nodes are
identified by tags (strictly positive identification numbers), and are stored (classified ) in the
model entity they discretize. Once meshed, a model entity of dimension 0 (a geometrical
point) will thus contain a mesh element of type point (MSH type 15: cf. Section 10.1 [MSH
file format], page 345), as well as a mesh node. A model curve will contain line elements
(e.g. of MSH type 1 or 8 for first order or second order meshes, respectively) as well as its
interior nodes, while its boundary nodes will be stored in the bounding model points. A
model surface will contain triangular and/or quadrangular elements and all the nodes not
classified on its boundary or on its embedded entities (curves and points). A model volume
will contain tetrahedra, hexahedra, etc. and all the nodes not classified on its boundary
or on its embedded entities (surfaces, curves and points). This data model allows to easily
and efficiently handle the creation, modification and destruction of conformal meshes. All
the mesh-related functions are provided in the gmsh/model/mesh namespace.
• Post-processing data is made of views. Each view is identified by a tag, and can also be
accessed by its index (which can change when views are sorted, added or deleted). A view
stores both display options and data, unless the view is an alias of another view (in which
case it only stores display options, and the data points to a reference view). View data
can contain several steps (e.g. to store time series) and can be either linked to one or
more models1 (mesh-based data, as stored in MSH files: cf. Section 10.1 [MSH file format],
page 345) or independent from any model (list-based data, as stored in parsed POS files:
cf. Section 5.4 [Post-processing scripting commands], page 117). Various plugins exist to
modify and create views.
All the functions available in the API are given below. See the relevant header/module file
for the exact definition in each supported language: in C++ gmsh/model/geo/addPoint will
lead to a namespaced function gmsh::model::geo::addPoint, while in Python and Julia it
will lead to gmsh.model.geo.addPoint, in C to gmshModelGeoAddPoint and in Fortran to
gmsh%model%geo%addPoint. In addition to the default “camelCase” function names, the Python
and Julia APIs also define “snake case” aliases, i.e. gmsh.model.geo.add_point, as this is the
recommended style in these languages. Output values are passed by reference in C++, as pointers
in C and directly returned (after the return value, if any) in Python and Julia.

6.1 Namespace gmsh: top-level functions

gmsh/initialize
Initialize the Gmsh API. This must be called before any call to the other functions
in the API. If argc and argv (or just argv in Python or Julia) are provided, they
will be handled in the same way as the command line arguments in the Gmsh app.
If readConfigFiles is set, read system Gmsh configuration files (gmshrc and gmsh-
options). If run is set, run in the same way as the Gmsh app, either interactively or in
batch mode depending on the command line arguments. If run is not set, initializing
the API sets the options "General.AbortOnError" to 2 and "General.Terminal" to
1.
1
Each step can be linked to a different model, which allows to have a single time series based on multiple (e.g.
deforming or moving) meshes.
Chapter 6: Gmsh application programming interface 125

Input: (argc = 0), argv = [] (command line arguments), readConfigFiles =

True (boolean), run = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t4.cpp, t5.cpp, ...), Python (t1.py, t2.py,
t3.py, t4.py, t5.py, ...)
gmsh/isInitialized
Return 1 if the Gmsh API is initialized, and 0 if not.
Input: -
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/finalize
Finalize the Gmsh API. This must be called when you are done using the Gmsh
API.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t4.cpp, t5.cpp, ...), Python (t1.py, t2.py,
t3.py, t4.py, t5.py, ...)
gmsh/open
Open a file. Equivalent to the File->Open menu in the Gmsh app. Handling of
the file depends on its extension and/or its contents: opening a file with model data
will create a new model.
Input: fileName (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py, explore.py, flatten2.py, flatten.py,
heal.py, ...)
gmsh/merge
Merge a file. Equivalent to the File->Merge menu in the Gmsh app. Handling of
the file depends on its extension and/or its contents. Merging a file with model data
will add the data to the current model.
Input: fileName (string)
126 Gmsh 4.11.1

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t7.cpp, t8.cpp, t9.cpp, t13.cpp, t17.cpp), Python (t7.py, t8.py,
t9.py, t13.py, t17.py, ...)
gmsh/write
Write a file. The export format is determined by the file extension.
Input: fileName (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t4.cpp, t5.cpp, ...), Python (t1.py, t2.py,
t3.py, t4.py, t5.py, ...)
gmsh/clear
Clear all loaded models and post-processing data, and add a new empty model.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, x1.cpp), Python (t3.py, t13.py, x1.py, x3d export.py)

6.2 Namespace gmsh/option: option handling functions

gmsh/option/setNumber
Set a numerical option to value. name is of the form "Category.Option" or "Cate-
gory[num].Option". Available categories and options are listed in the Gmsh refer-
ence manual.
Input: name (string), value (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t5.cpp, t6.cpp, t7.cpp, t8.cpp, ...), Python (t3.py, t5.py,
t6.py, t7.py, t8.py, ...)
gmsh/option/getNumber
Get the value of a numerical option. name is of the form "Category.Option" or
"Category[num].Option". Available categories and options are listed in the Gmsh
reference manual.
Input: name (string)
Chapter 6: Gmsh application programming interface 127

Output: value (double)

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t8.cpp), Python (t8.py, test.py)
gmsh/option/setString
Set a string option to value. name is of the form "Category.Option" or "Cate-
gory[num].Option". Available categories and options are listed in the Gmsh refer-
ence manual.
Input: name (string), value (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t4.cpp), Python (t4.py)
gmsh/option/getString
Get the value of a string option. name is of the form "Category.Option" or "Cat-
egory[num].Option". Available categories and options are listed in the Gmsh refer-
ence manual.
Input: name (string)
Output: value (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (test.py)
gmsh/option/setColor
Set a color option to the RGBA value (r, g, b, a), where where r, g, b and a should
be integers between 0 and 255. name is of the form "Category.Color.Option" or
"Category[num].Color.Option". Available categories and options are listed in the
Gmsh reference manual. For conciseness "Color." can be ommitted in name.
Input: name (string), r (integer), g (integer), b (integer), a = 255 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t8.cpp), Python (t3.py, t8.py)
gmsh/option/getColor
Get the r, g, b, a value of a color option. name is of the form "Cate-
gory.Color.Option" or "Category[num].Color.Option". Available categories and
options are listed in the Gmsh reference manual. For conciseness "Color." can be
ommitted in name.
Input: name (string)
128 Gmsh 4.11.1

Output: r (integer), g (integer), b (integer), a (integer)

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp), Python (t3.py)

6.3 Namespace gmsh/model: model functions

gmsh/model/add
Add a new model, with name name, and set it as the current model.
Input: name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t4.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t3.py, t4.py, t5.py, ...)
gmsh/model/remove
Remove the current model.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/list
List the names of all models.
Input: -
Output: names (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getCurrent
Get the name of the current model.
Input: -
Output: name (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py, explore.py)
gmsh/model/setCurrent
Set the current model to the model with name name. If several models have the
same name, select the one that was added first.
Chapter 6: Gmsh application programming interface 129

Input: name (string)

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (copy mesh.py)
gmsh/model/getFileName
Get the file name (if any) associated with the current model. A file name is associ-
ated when a model is read from a file on disk.
Input: -
Output: fileName (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/setFileName
Set the file name associated with the current model.
Input: fileName (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getEntities
Get all the entities in the current model. If dim is >= 0, return only the entities of
the specified dimension (e.g. points if dim == 0). The entities are returned as a
vector of (dim, tag) pairs.
Input: dim = -1 (integer)
Output: dimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t13.cpp, t16.cpp, t18.cpp, t20.cpp, t21.cpp, ...), Python (t13.py,
t16.py, t18.py, t20.py, t21.py, ...)
gmsh/model/setEntityName
Set the name of the entity of dimension dim and tag tag.
Input: dim (integer), tag (integer), name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getEntityName
Get the name of the entity of dimension dim and tag tag.
130 Gmsh 4.11.1

Input: dim (integer), tag (integer)

Output: name (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py, step assembly.py)
gmsh/model/getPhysicalGroups
Get all the physical groups in the current model. If dim is >= 0, return only the
entities of the specified dimension (e.g. physical points if dim == 0). The entities
are returned as a vector of (dim, tag) pairs.
Input: dim = -1 (integer)
Output: dimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (poisson.py)
gmsh/model/getEntitiesForPhysicalGroup
Get the tags of the model entities making up the physical group of dimension dim
and tag tag.
Input: dim (integer), tag (integer)
Output: tags (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (poisson.py, test.py)
gmsh/model/getPhysicalGroupsForEntity
Get the tags of the physical groups (if any) to which the model entity of dimension
dim and tag tag belongs.
Input: dim (integer), tag (integer)
Output: physicalTags (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py)
gmsh/model/addPhysicalGroup
Add a physical group of dimension dim, grouping the model entities with tags tags.
Return the tag of the physical group, equal to tag if tag is positive, or a new tag if
tag < 0. Set the name of the physical group if name is not empty.
Input: dim (integer), tags (vector of integers), tag = -1 (integer), name = ""
(string)
Output: -
Chapter 6: Gmsh application programming interface 131

Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t5.cpp, t14.cpp, ...), Python (t1.py, t2.py,
t3.py, t5.py, t14.py, ...)
gmsh/model/removePhysicalGroups
Remove the physical groups dimTags (given as a vector of (dim, tag) pairs) from
the current model. If dimTags is empty, remove all groups.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/setPhysicalName
Set the name of the physical group of dimension dim and tag tag.
Input: dim (integer), tag (integer), name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (poisson.py, step assembly.py)
gmsh/model/removePhysicalName
Remove the physical name name from the current model.
Input: name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getPhysicalName
Get the name of the physical group of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: name (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py, poisson.py)
gmsh/model/setTag
Set the tag of the entity of dimension dim and tag tag to the new value newTag.
Input: dim (integer), tag (integer), newTag (integer)
Output: -
132 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getBoundary
Get the boundary of the model entities dimTags, given as a vector of (dim, tag)
pairs. Return in outDimTags the boundary of the individual entities (if combined is
false) or the boundary of the combined geometrical shape formed by all input entities
(if combined is true). Return tags multiplied by the sign of the boundary entity if
oriented is true. Apply the boundary operator recursively down to dimension 0
(i.e. to points) if recursive is true.
Input: dimTags (vector of pairs of integers), combined = True (boolean),
oriented = True (boolean), recursive = False (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t14.cpp, t16.cpp, t18.cpp, t19.cpp, t21.cpp), Python (t14.py,
t16.py, t18.py, t19.py, t21.py, ...)
gmsh/model/getAdjacencies
Get the upward and downward adjacencies of the model entity of dimension dim
and tag tag. The upward vector returns the tags of adjacent entities of dimension
dim + 1; the downward vector returns the tags of adjacent entities of dimension dim
- 1.
Input: dim (integer), tag (integer)
Output: upward (vector of integers), downward (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py)
gmsh/model/getEntitiesInBoundingBox
Get the model entities in the bounding box defined by the two points (xmin, ymin,
zmin) and (xmax, ymax, zmax). If dim is >= 0, return only the entities of the specified
dimension (e.g. points if dim == 0).
Input: xmin (double), ymin (double), zmin (double), xmax (double), ymax (dou-
ble), zmax (double), dim = -1 (integer)
Output: dimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp, t18.cpp, t20.cpp), Python (t16.py, t18.py, t20.py,
naca boundary layer 3d.py)
gmsh/model/getBoundingBox
Get the bounding box (xmin, ymin, zmin), (xmax, ymax, zmax) of the model entity
of dimension dim and tag tag. If dim and tag are negative, get the bounding box
of the whole model.
Chapter 6: Gmsh application programming interface 133

Input: dim (integer), tag (integer)

Output: xmin (double), ymin (double), zmin (double), xmax (double), ymax (dou-
ble), zmax (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t18.cpp), Python (t18.py)
gmsh/model/getDimension
Return the geometrical dimension of the current model.
Input: -
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py)
gmsh/model/addDiscreteEntity
Add a discrete model entity (defined by a mesh) of dimension dim in the current
model. Return the tag of the new discrete entity, equal to tag if tag is positive, or
a new tag if tag < 0. boundary specifies the tags of the entities on the boundary
of the discrete entity, if any. Specifying boundary allows Gmsh to construct the
topology of the overall model.
Input: dim (integer), tag = -1 (integer), boundary = [] (vector of integers)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp, x4.cpp, x7.cpp), Python (x2.py, x4.py, x7.py,
copy mesh.py, discrete.py, ...)
gmsh/model/removeEntities
Remove the entities dimTags (given as a vector of (dim, tag) pairs) of the current
model, provided that they are not on the boundary of (or embedded in) higher-
dimensional entities. If recursive is true, remove all the entities on their bound-
aries, down to dimension 0.
Input: dimTags (vector of pairs of integers), recursive = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t18.cpp, t20.cpp), Python (t18.py, t20.py, spherical surf.py)
gmsh/model/removeEntityName
Remove the entity name name from the current model.
134 Gmsh 4.11.1

Input: name (string)

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getType
Get the type of the entity of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: entityType (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t21.cpp, x1.cpp), Python (t21.py, x1.py, explore.py, partition.py)
gmsh/model/getParent
In a partitioned model, get the parent of the entity of dimension dim and tag tag,
i.e. from which the entity is a part of, if any. parentDim and parentTag are set to
-1 if the entity has no parent.
Input: dim (integer), tag (integer)
Output: parentDim (integer), parentTag (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t21.cpp, x1.cpp), Python (t21.py, x1.py, explore.py, partition.py)
gmsh/model/getNumberOfPartitions
Return the number of partitions in the model.
Input: -
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getPartitions
In a partitioned model, return the tags of the partition(s) to which the entity belongs.
Input: dim (integer), tag (integer)
Output: partitions (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t21.cpp, x1.cpp), Python (t21.py, x1.py, explore.py, partition.py)
Chapter 6: Gmsh application programming interface 135

gmsh/model/getValue
Evaluate the parametrization of the entity of dimension dim and tag tag at the
parametric coordinates parametricCoord. Only valid for dim equal to 0 (with empty
parametricCoord), 1 (with parametricCoord containing parametric coordinates on
the curve) or 2 (with parametricCoord containing u, v parametric coordinates on
the surface, concatenated: [p1u, p1v, p2u, ...]). Return x, y, z coordinates in coord,
concatenated: [p1x, p1y, p1z, p2x, ...].
Input: dim (integer), tag (integer), parametricCoord (vector of doubles)
Output: coord (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t2.cpp, x5.cpp), Python (t2.py, x5.py, reparamOnFace.py,
terrain stl.py)
gmsh/model/getDerivative
Evaluate the derivative of the parametrization of the entity of dimension dim and
tag tag at the parametric coordinates parametricCoord. Only valid for dim equal
to 1 (with parametricCoord containing parametric coordinates on the curve) or
2 (with parametricCoord containing u, v parametric coordinates on the surface,
concatenated: [p1u, p1v, p2u, ...]). For dim equal to 1 return the x, y, z components
of the derivative with respect to u [d1ux, d1uy, d1uz, d2ux, ...]; for dim equal to 2
return the x, y, z components of the derivative with respect to u and v: [d1ux, d1uy,
d1uz, d1vx, d1vy, d1vz, d2ux, ...].
Input: dim (integer), tag (integer), parametricCoord (vector of doubles)
Output: derivatives (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getSecondDerivative
Evaluate the second derivative of the parametrization of the entity of dimension dim
and tag tag at the parametric coordinates parametricCoord. Only valid for dim
equal to 1 (with parametricCoord containing parametric coordinates on the curve)
or 2 (with parametricCoord containing u, v parametric coordinates on the surface,
concatenated: [p1u, p1v, p2u, ...]). For dim equal to 1 return the x, y, z components
of the second derivative with respect to u [d1uux, d1uuy, d1uuz, d2uux, ...]; for dim
equal to 2 return the x, y, z components of the second derivative with respect to
u and v, and the mixed derivative with respect to u and v: [d1uux, d1uuy, d1uuz,
d1vvx, d1vvy, d1vvz, d1uvx, d1uvy, d1uvz, d2uux, ...].
Input: dim (integer), tag (integer), parametricCoord (vector of doubles)
Output: derivatives (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getCurvature
Evaluate the (maximum) curvature of the entity of dimension dim and tag tag
at the parametric coordinates parametricCoord. Only valid for dim equal to 1
136 Gmsh 4.11.1

(with parametricCoord containing parametric coordinates on the curve) or 2 (with

parametricCoord containing u, v parametric coordinates on the surface, concate-
nated: [p1u, p1v, p2u, ...]).
Input: dim (integer), tag (integer), parametricCoord (vector of doubles)
Output: curvatures (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x5.cpp), Python (x5.py, normals.py)
gmsh/model/getPrincipalCurvatures
Evaluate the principal curvatures of the surface with tag tag at the parametric coor-
dinates parametricCoord, as well as their respective directions. parametricCoord
are given by pair of u and v coordinates, concatenated: [p1u, p1v, p2u, ...].
Input: tag (integer), parametricCoord (vector of doubles)
Output: curvatureMax (vector of doubles), curvatureMin (vector of doubles),
directionMax (vector of doubles), directionMin (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getNormal
Get the normal to the surface with tag tag at the parametric coordinates
parametricCoord. The parametricCoord vector should contain u and v
coordinates, concatenated: [p1u, p1v, p2u, ...]. normals are returned as a vector of
x, y, z components, concatenated: [n1x, n1y, n1z, n2x, ...].
Input: tag (integer), parametricCoord (vector of doubles)
Output: normals (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x5.cpp), Python (x5.py, normals.py)
gmsh/model/getParametrization
Get the parametric coordinates parametricCoord for the points coord on the entity
of dimension dim and tag tag. coord are given as x, y, z coordinates, concatenated:
[p1x, p1y, p1z, p2x, ...]. parametricCoord returns the parametric coordinates t on
the curve (if dim = 1) or u and v coordinates concatenated on the surface (if dim =
2), i.e. [p1t, p2t, ...] or [p1u, p1v, p2u, ...].
Input: dim (integer), tag (integer), coord (vector of doubles)
Output: parametricCoord (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 137

gmsh/model/getParametrizationBounds
Get the min and max bounds of the parametric coordinates for the entity of dimension
dim and tag tag.
Input: dim (integer), tag (integer)
Output: min (vector of doubles), max (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x5.cpp), Python (x5.py, reparamOnFace.py)
gmsh/model/isInside
Check if the coordinates (or the parametric coordinates if parametric is set) pro-
vided in coord correspond to points inside the entity of dimension dim and tag tag,
and return the number of points inside. This feature is only available for a subset
of entities, depending on the underlying geometrical representation.
Input: dim (integer), tag (integer), coord (vector of doubles), parametric =
False (boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getClosestPoint
Get the points closestCoord on the entity of dimension dim and tag tag to the
points coord, by orthogonal projection. coord and closestCoord are given as x,
y, z coordinates, concatenated: [p1x, p1y, p1z, p2x, ...]. parametricCoord returns
the parametric coordinates t on the curve (if dim = 1) or u and v coordinates
concatenated on the surface (if dim = 2), i.e. [p1t, p2t, ...] or [p1u, p1v, p2u, ...].
Input: dim (integer), tag (integer), coord (vector of doubles)
Output: closestCoord (vector of doubles), parametricCoord (vector of dou-
bles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (closest point.py)
gmsh/model/reparametrizeOnSurface
Reparametrize the boundary entity (point or curve, i.e. with dim == 0 or dim ==
1) of tag tag on the surface surfaceTag. If dim == 1, reparametrize all the points
corresponding to the parametric coordinates parametricCoord. Multiple matches
in case of periodic surfaces can be selected with which. This feature is only available
for a subset of entities, depending on the underlying geometrical representation.
Input: dim (integer), tag (integer), parametricCoord (vector of doubles),
surfaceTag (integer), which = 0 (integer)
Output: surfaceParametricCoord (vector of doubles)
Return: -
138 Gmsh 4.11.1

Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x5.cpp), Python (x5.py, reparamOnFace.py)
gmsh/model/setVisibility
Set the visibility of the model entities dimTags (given as a vector of (dim, tag) pairs)
to value. Apply the visibility setting recursively if recursive is true.
Input: dimTags (vector of pairs of integers), value (integer), recursive =
False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (gui.py, hybrid order.py)
gmsh/model/getVisibility
Get the visibility of the model entity of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: value (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/setVisibilityPerWindow
Set the global visibility of the model per window to value, where windowIndex
identifies the window in the window list.
Input: value (integer), windowIndex = 0 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/setColor
Set the color of the model entities dimTags (given as a vector of (dim, tag) pairs)
to the RGBA value (r, g, b, a), where r, g, b and a should be integers between 0
and 255. Apply the color setting recursively if recursive is true.
Input: dimTags (vector of pairs of integers), r (integer), g (integer), b (integer),
a = 255 (integer), recursive = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t4.cpp), Python (t4.py, gui.py)
gmsh/model/getColor
Get the color of the model entity of dimension dim and tag tag.
Chapter 6: Gmsh application programming interface 139

Input: dim (integer), tag (integer)

Output: r (integer), g (integer), b (integer), a (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (step boundary colors.py)
gmsh/model/setCoordinates
Set the x, y, z coordinates of a geometrical point.
Input: tag (integer), x (double), y (double), z (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp), Python (x2.py, reparamOnFace.py)
gmsh/model/getAttributeNames
Get the names of any optional attributes stored in the model.
Input: -
Output: names (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/getAttribute
Get the values of the attribute with name name.
Input: name (string)
Output: values (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/setAttribute
Set the values of the attribute with name name.
Input: name (string), values (vector of strings)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/removeAttribute
Remove the attribute with name name.
Input: name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
140 Gmsh 4.11.1

6.4 Namespace gmsh/model/mesh: mesh functions

gmsh/model/mesh/generate
Generate a mesh of the current model, up to dimension dim (0, 1, 2 or 3).
Input: dim = 3 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t4.cpp, t5.cpp, ...), Python (t1.py, t2.py,
t3.py, t4.py, t5.py, ...)
gmsh/model/mesh/partition
Partition the mesh of the current model into numPart partitions. Optionally,
elementTags and partitions can be provided to specify the partition of each ele-
ment explicitly.
Input: numPart (integer), elementTags = [] (vector of sizes), partitions =
[] (vector of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t21.cpp), Python (t21.py, partition.py)
gmsh/model/mesh/unpartition
Unpartition the mesh of the current model.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/optimize
Optimize the mesh of the current model using method (empty for default tetrahedral
mesh optimizer, "Netgen" for Netgen optimizer, "HighOrder" for direct high-order
mesh optimizer, "HighOrderElastic" for high-order elastic smoother, "HighOrder-
FastCurving" for fast curving algorithm, "Laplace2D" for Laplace smoothing, "Re-
locate2D" and "Relocate3D" for node relocation, "QuadQuasiStructured" for quad
mesh optimization, "UntangleMeshGeometry" for untangling). If force is set apply
the optimization also to discrete entities. If dimTags (given as a vector of (dim, tag)
pairs) is given, only apply the optimizer to the given entities.
Input: method = "" (string), force = False (boolean), niter = 1 (integer),
dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 141

Examples: Python (naca boundary layer 2d.py, naca boundary layer 3d.py,
opt.py, tube boundary layer.py)
gmsh/model/mesh/recombine
Recombine the mesh of the current model.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (stl to mesh.py)
gmsh/model/mesh/refine
Refine the mesh of the current model by uniformly splitting the elements.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setOrder
Set the order of the elements in the mesh of the current model to order.
Input: order (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x6.cpp), Python (x6.py, hybrid order.py,
naca boundary layer 2d.py, naca boundary layer 3d.py,
tube boundary layer.py)
gmsh/model/mesh/getLastEntityError
Get the last entities dimTags (as a vector of (dim, tag) pairs) where a meshing error
occurred. Currently only populated by the new 3D meshing algorithms.
Input: -
Output: dimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getLastNodeError
Get the last node tags nodeTags where a meshing error occurred. Currently only
populated by the new 3D meshing algorithms.
Input: -
Output: nodeTags (vector of sizes)
142 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/clear
Clear the mesh, i.e. delete all the nodes and elements, for the entities dimTags,
given as a vector of (dim, tag) pairs. If dimTags is empty, clear the whole mesh.
Note that the mesh of an entity can only be cleared if this entity is not on the
boundary of another entity with a non-empty mesh.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (copy mesh.py, flatten.py)
gmsh/model/mesh/reverse
Reverse the orientation of the elements in the entities dimTags, given as a vector of
(dim, tag) pairs. If dimTags is empty, reverse the orientation of the elements in the
whole mesh.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (mirror mesh.py)
gmsh/model/mesh/affineTransform
Apply the affine transformation affineTransform (16 entries of a 4x4 matrix, by
row; only the 12 first can be provided for convenience) to the coordinates of the
nodes classified on the entities dimTags, given as a vector of (dim, tag) pairs. If
dimTags is empty, transform all the nodes in the mesh.
Input: affineTransform (vector of doubles), dimTags = [] (vector of pairs of
integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (flatten2.py)
gmsh/model/mesh/getNodes
Get the nodes classified on the entity of dimension dim and tag tag. If tag < 0, get
the nodes for all entities of dimension dim. If dim and tag are negative, get all the
nodes in the mesh. nodeTags contains the node tags (their unique, strictly positive
identification numbers). coord is a vector of length 3 times the length of nodeTags
that contains the x, y, z coordinates of the nodes, concatenated: [n1x, n1y, n1z, n2x,
...]. If dim >= 0 and returnParamtricCoord is set, parametricCoord contains the
Chapter 6: Gmsh application programming interface 143

parametric coordinates ([u1, u2, ...] or [u1, v1, u2, ...]) of the nodes, if available.
The length of parametricCoord can be 0 or dim times the length of nodeTags. If
includeBoundary is set, also return the nodes classified on the boundary of the
entity (which will be reparametrized on the entity if dim >= 0 in order to compute
their parametric coordinates).
Input: dim = -1 (integer), tag = -1 (integer), includeBoundary = False
(boolean), returnParametricCoord = True (boolean)
Output: nodeTags (vector of sizes), coord (vector of doubles), parametricCoord
(vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp, x4.cpp, x5.cpp), Python (x1.py, x4.py, x5.py,
adapt mesh.py, copy mesh.py, ...)
gmsh/model/mesh/getNodesByElementType
Get the nodes classified on the entity of tag tag, for all the elements of type
elementType. The other arguments are treated as in getNodes.
Input: elementType (integer), tag = -1 (integer), returnParametricCoord =
True (boolean)
Output: nodeTags (vector of sizes), coord (vector of doubles), parametricCoord
(vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (stl to brep.py)
gmsh/model/mesh/getNode
Get the coordinates and the parametric coordinates (if any) of the node with tag
tag, as well as the dimension dim and tag tag of the entity on which the node
is classified. This function relies on an internal cache (a vector in case of dense
node numbering, a map otherwise); for large meshes accessing nodes in bulk is often
preferable.
Input: nodeTag (size)
Output: coord (vector of doubles), parametricCoord (vector of doubles), dim
(integer), tag (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setNode
Set the coordinates and the parametric coordinates (if any) of the node with tag tag.
This function relies on an internal cache (a vector in case of dense node numbering,
a map otherwise); for large meshes accessing nodes in bulk is often preferable.
Input: nodeTag (size), coord (vector of doubles), parametricCoord (vector of
doubles)
Output: -
144 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/rebuildNodeCache
Rebuild the node cache.
Input: onlyIfNecessary = True (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/rebuildElementCache
Rebuild the element cache.
Input: onlyIfNecessary = True (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getNodesForPhysicalGroup
Get the nodes from all the elements belonging to the physical group of dimension
dim and tag tag. nodeTags contains the node tags; coord is a vector of length 3
times the length of nodeTags that contains the x, y, z coordinates of the nodes,
concatenated: [n1x, n1y, n1z, n2x, ...].
Input: dim (integer), tag (integer)
Output: nodeTags (vector of sizes), coord (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getMaxNodeTag
Get the maximum tag maxTag of a node in the mesh.
Input: -
Output: maxTag (size)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/addNodes
Add nodes classified on the model entity of dimension dim and tag tag. nodeTags
contains the node tags (their unique, strictly positive identification numbers). coord
is a vector of length 3 times the length of nodeTags that contains the x, y, z
coordinates of the nodes, concatenated: [n1x, n1y, n1z, n2x, ...]. The optional
parametricCoord vector contains the parametric coordinates of the nodes, if any.
The length of parametricCoord can be 0 or dim times the length of nodeTags. If
the nodeTags vector is empty, new tags are automatically assigned to the nodes.
Chapter 6: Gmsh application programming interface 145

Input: dim (integer), tag (integer), nodeTags (vector of sizes), coord (vector
of doubles), parametricCoord = [] (vector of doubles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp, x4.cpp), Python (x2.py, x4.py, copy mesh.py, discrete.py,
flatten.py, ...)
gmsh/model/mesh/reclassifyNodes
Reclassify all nodes on their associated model entity, based on the elements. Can be
used when importing nodes in bulk (e.g. by associating them all to a single volume),
to reclassify them correctly on model surfaces, curves, etc. after the elements have
been set.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp), Python (x2.py, terrain.py)
gmsh/model/mesh/relocateNodes
Relocate the nodes classified on the entity of dimension dim and tag tag using their
parametric coordinates. If tag < 0, relocate the nodes for all entities of dimension
dim. If dim and tag are negative, relocate all the nodes in the mesh.
Input: dim = -1 (integer), tag = -1 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getElements
Get the elements classified on the entity of dimension dim and tag tag. If tag < 0,
get the elements for all entities of dimension dim. If dim and tag are negative, get
all the elements in the mesh. elementTypes contains the MSH types of the elements
(e.g. 2 for 3-node triangles: see getElementProperties to obtain the properties for
a given element type). elementTags is a vector of the same length as elementTypes;
each entry is a vector containing the tags (unique, strictly positive identifiers) of the
elements of the corresponding type. nodeTags is also a vector of the same length as
elementTypes; each entry is a vector of length equal to the number of elements of
the given type times the number N of nodes for this type of element, that contains
the node tags of all the elements of the given type, concatenated: [e1n1, e1n2, ...,
e1nN, e2n1, ...].
Input: dim = -1 (integer), tag = -1 (integer)
Output: elementTypes (vector of integers), elementTags (vector of vectors of
sizes), nodeTags (vector of vectors of sizes)
Return: -
146 Gmsh 4.11.1

Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py, copy mesh.py, explore.py, flatten.py,
mesh quality.py, ...)
gmsh/model/mesh/getElement
Get the type and node tags of the element with tag tag, as well as the dimension
dim and tag tag of the entity on which the element is classified. This function relies
on an internal cache (a vector in case of dense element numbering, a map otherwise);
for large meshes accessing elements in bulk is often preferable.
Input: elementTag (size)
Output: elementType (integer), nodeTags (vector of sizes), dim (integer), tag
(integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getElementByCoordinates
Search the mesh for an element located at coordinates (x, y, z). This function
performs a search in a spatial octree. If an element is found, return its tag, type
and node tags, as well as the local coordinates (u, v, w) within the reference element
corresponding to search location. If dim is >= 0, only search for elements of the
given dimension. If strict is not set, use a tolerance to find elements near the
search location.
Input: x (double), y (double), z (double), dim = -1 (integer), strict = False
(boolean)
Output: elementTag (size), elementType (integer), nodeTags (vector of sizes),
u (double), v (double), w (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getElementsByCoordinates
Search the mesh for element(s) located at coordinates (x, y, z). This function
performs a search in a spatial octree. Return the tags of all found elements in
elementTags. Additional information about the elements can be accessed through
getElement and getLocalCoordinatesInElement. If dim is >= 0, only search for
elements of the given dimension. If strict is not set, use a tolerance to find elements
near the search location.
Input: x (double), y (double), z (double), dim = -1 (integer), strict = False
(boolean)
Output: elementTags (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getLocalCoordinatesInElement
Return the local coordinates (u, v, w) within the element elementTag corresponding
to the model coordinates (x, y, z). This function relies on an internal cache (a vector
Chapter 6: Gmsh application programming interface 147

in case of dense element numbering, a map otherwise); for large meshes accessing
elements in bulk is often preferable.
Input: elementTag (size), x (double), y (double), z (double)
Output: u (double), v (double), w (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getElementTypes
Get the types of elements in the entity of dimension dim and tag tag. If tag < 0,
get the types for all entities of dimension dim. If dim and tag are negative, get all
the types in the mesh.
Input: dim = -1 (integer), tag = -1 (integer)
Output: elementTypes (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x6.cpp), Python (x6.py, poisson.py)
gmsh/model/mesh/getElementType
Return an element type given its family name familyName ("Point", "Line", "Tri-
angle", "Quadrangle", "Tetrahedron", "Pyramid", "Prism", "Hexahedron") and
polynomial order order. If serendip is true, return the corresponding serendip
element type (element without interior nodes).
Input: familyName (string), order (integer), serendip = False (boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
gmsh/model/mesh/getElementProperties
Get the properties of an element of type elementType: its name (elementName),
dimension (dim), order (order), number of nodes (numNodes), local coordinates of
the nodes in the reference element (localNodeCoord vector, of length dim times
numNodes) and number of primary (first order) nodes (numPrimaryNodes).
Input: elementType (integer)
Output: elementName (string), dim (integer), order (integer), numNodes (inte-
ger), localNodeCoord (vector of doubles), numPrimaryNodes (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x1.cpp), Python (x1.py, x6.py, explore.py, poisson.py)
148 Gmsh 4.11.1

gmsh/model/mesh/getElementsByType
Get the elements of type elementType classified on the entity of tag tag. If tag < 0,
get the elements for all entities. elementTags is a vector containing the tags (unique,
strictly positive identifiers) of the elements of the corresponding type. nodeTags is a
vector of length equal to the number of elements of the given type times the number
N of nodes for this type of element, that contains the node tags of all the elements
of the given type, concatenated: [e1n1, e1n2, ..., e1nN, e2n1, ...]. If numTasks > 1,
only compute and return the part of the data indexed by task.
Input: elementType (integer), tag = -1 (integer), task = 0 (size), numTasks =
1 (size)
Output: elementTags (vector of sizes), nodeTags (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py, adapt mesh.py, neighbors.py, poisson.py,
stl to brep.py)
gmsh/model/mesh/getMaxElementTag
Get the maximum tag maxTag of an element in the mesh.
Input: -
Output: maxTag (size)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
gmsh/model/mesh/preallocateElementsByType
Preallocate data before calling getElementsByType with numTasks > 1. For C and
C++ only.
Input: elementType (integer), elementTag (boolean), nodeTag (boolean), tag
= -1 (integer)
Output: elementTags (vector of sizes), nodeTags (vector of sizes)
Return: -
Language-specific definition:
C++, C
gmsh/model/mesh/getElementQualities
Get the quality elementQualities of the elements with tags elementTags.
qualityType is the requested quality measure: "minSJ" for the minimal
scaled jacobien, "minSICN" for the minimal signed inverted condition number,
"minSIGE" for the signed inverted gradient error, "gamma" for the ratio of the
inscribed to circumcribed sphere radius, "volume" for the volume. If numTasks >
1, only compute and return the part of the data indexed by task.
Input: elementTags (vector of sizes), qualityName = "minSICN" (string), task
= 0 (size), numTasks = 1 (size)
Output: elementsQuality (vector of doubles)
Chapter 6: Gmsh application programming interface 149

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (mesh quality.py)
gmsh/model/mesh/addElements
Add elements classified on the entity of dimension dim and tag tag. types contains
the MSH types of the elements (e.g. 2 for 3-node triangles: see the Gmsh reference
manual). elementTags is a vector of the same length as types; each entry is a
vector containing the tags (unique, strictly positive identifiers) of the elements of
the corresponding type. nodeTags is also a vector of the same length as types; each
entry is a vector of length equal to the number of elements of the given type times
the number N of nodes per element, that contains the node tags of all the elements
of the given type, concatenated: [e1n1, e1n2, ..., e1nN, e2n1, ...].
Input: dim (integer), tag (integer), elementTypes (vector of integers),
elementTags (vector of vectors of integers (size)), nodeTags (vector of
vectors of integers (size))
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (copy mesh.py, discrete.py, flatten.py,
mesh from discrete curve.py, mirror mesh.py, ...)
gmsh/model/mesh/addElementsByType
Add elements of type elementType classified on the entity of tag tag. elementTags
contains the tags (unique, strictly positive identifiers) of the elements of the cor-
responding type. nodeTags is a vector of length equal to the number of elements
times the number N of nodes per element, that contains the node tags of all the
elements, concatenated: [e1n1, e1n2, ..., e1nN, e2n1, ...]. If the elementTag vector
is empty, new tags are automatically assigned to the elements.
Input: tag (integer), elementType (integer), elementTags (vector of sizes),
nodeTags (vector of sizes)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp, x4.cpp, x7.cpp), Python (x2.py, x4.py, x7.py,
import perf.py, raw tetrahedralization.py, ...)
gmsh/model/mesh/getIntegrationPoints
Get the numerical quadrature information for the given element type elementType
and integration rule integrationType, where integrationType concatenates the
integration rule family name with the desired order (e.g. "Gauss4" for a quadrature
suited for integrating 4th order polynomials). The "CompositeGauss" family uses
tensor-product rules based the 1D Gauss-Legendre rule; the "Gauss" family uses an
economic scheme when available (i.e. with a minimal number of points), and falls
back to "CompositeGauss" otherwise. Note that integration points for the "Gauss"
150 Gmsh 4.11.1

family can fall outside of the reference element for high-order rules. localCoord
contains the u, v, w coordinates of the G integration points in the reference element:
[g1u, g1v, g1w, ..., gGu, gGv, gGw]. weights contains the associated weights: [g1q,
..., gGq].
Input: elementType (integer), integrationType (string)
Output: localCoord (vector of doubles), weights (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (x6.py, adapt mesh.py, poisson.py)
gmsh/model/mesh/getJacobians
Get the Jacobians of all the elements of type elementType classified on the entity
of tag tag, at the G evaluation points localCoord given as concatenated u, v, w
coordinates in the reference element [g1u, g1v, g1w, ..., gGu, gGv, gGw]. Data
is returned by element, with elements in the same order as in getElements and
getElementsByType. jacobians contains for each element the 9 entries of the
3x3 Jacobian matrix at each evaluation point. The matrix is returned by column:
[e1g1Jxu, e1g1Jyu, e1g1Jzu, e1g1Jxv, ..., e1g1Jzw, e1g2Jxu, ..., e1gGJzw, e2g1Jxu,
...], with Jxu=dx/du, Jyu=dy/du, etc. determinants contains for each element the
determinant of the Jacobian matrix at each evaluation point: [e1g1, e1g2, ... e1gG,
e2g1, ...]. coord contains for each element the x, y, z coordinates of the evaluation
points. If tag < 0, get the Jacobian data for all entities. If numTasks > 1, only
compute and return the part of the data indexed by task.
Input: elementType (integer), localCoord (vector of doubles), tag = -1 (in-
teger), task = 0 (size), numTasks = 1 (size)
Output: jacobians (vector of doubles), determinants (vector of doubles),
coord (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (x6.py, adapt mesh.py, poisson.py)
gmsh/model/mesh/preallocateJacobians
Preallocate data before calling getJacobians with numTasks > 1. For C and C++
only.
Input: elementType (integer), numEvaluationPoints (integer),
allocateJacobians (boolean), allocateDeterminants (boolean),
allocateCoord (boolean), tag = -1 (integer)
Output: jacobians (vector of doubles), determinants (vector of doubles),
coord (vector of doubles)
Return: -
Language-specific definition:
C++, C
gmsh/model/mesh/getJacobian
Get the Jacobian for a single element elementTag, at the G evaluation points
localCoord given as concatenated u, v, w coordinates in the reference element [g1u,
Chapter 6: Gmsh application programming interface 151

g1v, g1w, ..., gGu, gGv, gGw]. jacobians contains the 9 entries of the 3x3 Jaco-
bian matrix at each evaluation point. The matrix is returned by column: [e1g1Jxu,
e1g1Jyu, e1g1Jzu, e1g1Jxv, ..., e1g1Jzw, e1g2Jxu, ..., e1gGJzw, e2g1Jxu, ...], with
Jxu=dx/du, Jyu=dy/du, etc. determinants contains the determinant of the Ja-
cobian matrix at each evaluation point. coord contains the x, y, z coordinates of
the evaluation points. This function relies on an internal cache (a vector in case of
dense element numbering, a map otherwise); for large meshes accessing Jacobians
in bulk is often preferable.
Input: elementTag (size), localCoord (vector of doubles)
Output: jacobians (vector of doubles), determinants (vector of doubles),
coord (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getBasisFunctions
Get the basis functions of the element of type elementType at the evaluation points
localCoord (given as concatenated u, v, w coordinates in the reference element
[g1u, g1v, g1w, ..., gGu, gGv, gGw]), for the function space functionSpaceType.
Currently supported function spaces include "Lagrange" and "GradLagrange" for
isoparametric Lagrange basis functions and their gradient in the u, v, w coordinates
of the reference element; "LagrangeN" and "GradLagrangeN", with N = 1, 2, ...,
for N-th order Lagrange basis functions; "H1LegendreN" and "GradH1LegendreN",
with N = 1, 2, ..., for N-th order hierarchical H1 Legendre functions; "HcurlLegen-
dreN" and "CurlHcurlLegendreN", with N = 1, 2, ..., for N-th order curl-conforming
basis functions. numComponents returns the number C of components of a basis
function (e.g. 1 for scalar functions and 3 for vector functions). basisFunctions
returns the value of the N basis functions at the evaluation points, i.e. [g1f1, g1f2,
..., g1fN, g2f1, ...] when C == 1 or [g1f1u, g1f1v, g1f1w, g1f2u, ..., g1fNw, g2f1u,
...] when C == 3. For basis functions that depend on the orientation of the ele-
ments, all values for the first orientation are returned first, followed by values for
the second, etc. numOrientations returns the overall number of orientations. If
the wantedOrientations vector is not empty, only return the values for the desired
orientation indices.
Input: elementType (integer), localCoord (vector of doubles),
functionSpaceType (string), wantedOrientations = [] (vector of
integers)
Output: numComponents (integer), basisFunctions (vector of doubles),
numOrientations (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (x6.py, adapt mesh.py, poisson.py)
gmsh/model/mesh/getBasisFunctionsOrientation
Get the orientation index of the elements of type elementType in the entity
of tag tag. The arguments have the same meaning as in getBasisFunctions.
basisFunctionsOrientation is a vector giving for each element the orientation
index in the values returned by getBasisFunctions. For Lagrange basis functions
the call is superfluous as it will return a vector of zeros.
152 Gmsh 4.11.1

Input: elementType (integer), functionSpaceType (string), tag = -1 (inte-

ger), task = 0 (size), numTasks = 1 (size)
Output: basisFunctionsOrientation (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getBasisFunctionsOrientationForElement
Get the orientation of a single element elementTag.
Input: elementTag (size), functionSpaceType (string)
Output: basisFunctionsOrientation (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getNumberOfOrientations
Get the number of possible orientations for elements of type elementType and func-
tion space named functionSpaceType.
Input: elementType (integer), functionSpaceType (string)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/preallocateBasisFunctionsOrientation
Preallocate data before calling getBasisFunctionsOrientation with numTasks >
1. For C and C++ only.
Input: elementType (integer), tag = -1 (integer)
Output: basisFunctionsOrientation (vector of integers)
Return: -
Language-specific definition:
C++, C
gmsh/model/mesh/getEdges
Get the global unique mesh edge identifiers edgeTags and orientations
edgeOrientation for an input list of node tag pairs defining these edges,
concatenated in the vector nodeTags. Mesh edges are created e.g. by
createEdges(), getKeys() or addEdges(). The reference positive orientation is
n1 < n2, where n1 and n2 are the tags of the two edge nodes, which corresponds to
the local orientation of edge-based basis functions as well.
Input: nodeTags (vector of sizes)
Output: edgeTags (vector of sizes), edgeOrientations (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 153

Examples: C++ (x7.cpp), Python (x7.py)

gmsh/model/mesh/getFaces
Get the global unique mesh face identifiers faceTags and orientations
faceOrientations for an input list of a multiple of three (if faceType == 3)
or four (if faceType == 4) node tags defining these faces, concatenated in the
vector nodeTags. Mesh faces are created e.g. by createFaces(), getKeys() or
addFaces().
Input: faceType (integer), nodeTags (vector of sizes)
Output: faceTags (vector of sizes), faceOrientations (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
gmsh/model/mesh/createEdges
Create unique mesh edges for the entities dimTags, given as a vector of (dim, tag)
pairs.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
gmsh/model/mesh/createFaces
Create unique mesh faces for the entities dimTags, given as a vector of (dim, tag)
pairs.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
gmsh/model/mesh/getAllEdges
Get the global unique identifiers edgeTags and the nodes edgeNodes of the edges
in the mesh. Mesh edges are created e.g. by createEdges(), getKeys() or
addEdges().
Input: -
Output: edgeTags (vector of sizes), edgeNodes (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
154 Gmsh 4.11.1

gmsh/model/mesh/getAllFaces
Get the global unique identifiers faceTags and the nodes faceNodes of the faces
of type faceType in the mesh. Mesh faces are created e.g. by createFaces(),
getKeys() or addFaces().
Input: faceType (integer)
Output: faceTags (vector of sizes), faceNodes (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py)
gmsh/model/mesh/addEdges
Add mesh edges defined by their global unique identifiers edgeTags and their nodes
edgeNodes.
Input: edgeTags (vector of sizes), edgeNodes (vector of sizes)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/addFaces
Add mesh faces of type faceType defined by their global unique identifiers faceTags
and their nodes faceNodes.
Input: faceType (integer), faceTags (vector of sizes), faceNodes (vector of
sizes)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getKeys
Generate the pair of keys for the elements of type elementType in the entity of tag
tag, for the functionSpaceType function space. Each pair (typeKey, entityKey)
uniquely identifies a basis function in the function space. If returnCoord is set,
the coord vector contains the x, y, z coordinates locating basis functions for sorting
purposes. Warning: this is an experimental feature and will probably change in a
future release.
Input: elementType (integer), functionSpaceType (string), tag = -1 (inte-
ger), returnCoord = True (boolean)
Output: typeKeys (vector of integers), entityKeys (vector of sizes), coord (vec-
tor of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getKeysForElement
Get the pair of keys for a single element elementTag.
Chapter 6: Gmsh application programming interface 155

Input: elementTag (size), functionSpaceType (string), returnCoord = True

(boolean)
Output: typeKeys (vector of integers), entityKeys (vector of sizes), coord (vec-
tor of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getNumberOfKeys
Get the number of keys by elements of type elementType for function space named
functionSpaceType.
Input: elementType (integer), functionSpaceType (string)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getKeysInformation
Get information about the pair of keys. infoKeys returns information about the
functions associated with the pairs (typeKeys, entityKey). infoKeys[0].first
describes the type of function (0 for vertex function, 1 for edge function, 2 for face
function and 3 for bubble function). infoKeys[0].second gives the order of the
function associated with the key. Warning: this is an experimental feature and will
probably change in a future release.
Input: typeKeys (vector of integers), entityKeys (vector of sizes),
elementType (integer), functionSpaceType (string)
Output: infoKeys (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getBarycenters
Get the barycenters of all elements of type elementType classified on the entity of
tag tag. If primary is set, only the primary nodes of the elements are taken into
account for the barycenter calculation. If fast is set, the function returns the sum
of the primary node coordinates (without normalizing by the number of nodes). If
tag < 0, get the barycenters for all entities. If numTasks > 1, only compute and
return the part of the data indexed by task.
Input: elementType (integer), tag (integer), fast (boolean), primary
(boolean), task = 0 (size), numTasks = 1 (size)
Output: barycenters (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/preallocateBarycenters
Preallocate data before calling getBarycenters with numTasks > 1. For C and C++
only.
156 Gmsh 4.11.1

Input: elementType (integer), tag = -1 (integer)

Output: barycenters (vector of doubles)
Return: -
Language-specific definition:
C++, C
gmsh/model/mesh/getElementEdgeNodes
Get the nodes on the edges of all elements of type elementType classified on the
entity of tag tag. nodeTags contains the node tags of the edges for all the elements:
[e1a1n1, e1a1n2, e1a2n1, ...]. Data is returned by element, with elements in the
same order as in getElements and getElementsByType. If primary is set, only
the primary (begin/end) nodes of the edges are returned. If tag < 0, get the edge
nodes for all entities. If numTasks > 1, only compute and return the part of the data
indexed by task.
Input: elementType (integer), tag = -1 (integer), primary = False (boolean),
task = 0 (size), numTasks = 1 (size)
Output: nodeTags (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py, stl to brep.py)
gmsh/model/mesh/getElementFaceNodes
Get the nodes on the faces of type faceType (3 for triangular faces, 4 for quad-
rangular faces) of all elements of type elementType classified on the entity of tag
tag. nodeTags contains the node tags of the faces for all elements: [e1f1n1, ...,
e1f1nFaceType, e1f2n1, ...]. Data is returned by element, with elements in the same
order as in getElements and getElementsByType. If primary is set, only the pri-
mary (corner) nodes of the faces are returned. If tag < 0, get the face nodes for all
entities. If numTasks > 1, only compute and return the part of the data indexed by
task.
Input: elementType (integer), faceType (integer), tag = -1 (integer), primary
= False (boolean), task = 0 (size), numTasks = 1 (size)
Output: nodeTags (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x7.cpp), Python (x7.py, neighbors.py)
gmsh/model/mesh/getGhostElements
Get the ghost elements elementTags and their associated partitions stored in the
ghost entity of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: elementTags (vector of sizes), partitions (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 157

gmsh/model/mesh/setSize
Set a mesh size constraint on the model entities dimTags, given as a vector of (dim,
tag) pairs. Currently only entities of dimension 0 (points) are handled.
Input: dimTags (vector of pairs of integers), size (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp, t18.cpp, t21.cpp), Python (t16.py, t18.py, t21.py,
adapt mesh.py, extend field.py, ...)
gmsh/model/mesh/getSizes
Get the mesh size constraints (if any) associated with the model entities dimTags,
given as a vector of (dim, tag) pairs. A zero entry in the output sizes vector
indicates that no size constraint is specified on the corresponding entity.
Input: dimTags (vector of pairs of integers)
Output: sizes (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setSizeAtParametricPoints
Set mesh size constraints at the given parametric points parametricCoord on the
model entity of dimension dim and tag tag. Currently only entities of dimension 1
(lines) are handled.
Input: dim (integer), tag (integer), parametricCoord (vector of doubles),
sizes (vector of doubles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setSizeCallback
Set a mesh size callback for the current model. The callback function should take
six arguments as input (dim, tag, x, y, z and lc). The first two integer arguments
correspond to the dimension dim and tag tag of the entity being meshed. The next
four double precision arguments correspond to the coordinates x, y and z around
which to prescribe the mesh size and to the mesh size lc that would be prescribed
if the callback had not been called. The callback function should return a double
precision number specifying the desired mesh size; returning lc is equivalent to a
no-op.
Input: callback ()
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
158 Gmsh 4.11.1

Examples: C++ (t10.cpp), Python (t10.py)

gmsh/model/mesh/removeSizeCallback
Remove the mesh size callback from the current model.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setTransfiniteCurve
Set a transfinite meshing constraint on the curve tag, with numNodes nodes dis-
tributed according to meshType and coef. Currently supported types are "Progres-
sion" (geometrical progression with power coef), "Bump" (refinement toward both
extremities of the curve) and "Beta" (beta law).
Input: tag (integer), numNodes (integer), meshType = "Progression" (string),
coef = 1. (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp), Python (x2.py, terrain.py, terrain bspline.py,
terrain stl.py)
gmsh/model/mesh/setTransfiniteSurface
Set a transfinite meshing constraint on the surface tag. arrangement describes the
arrangement of the triangles when the surface is not flagged as recombined: cur-
rently supported values are "Left", "Right", "AlternateLeft" and "AlternateRight".
cornerTags can be used to specify the (3 or 4) corners of the transfinite interpola-
tion explicitly; specifying the corners explicitly is mandatory if the surface has more
that 3 or 4 points on its boundary.
Input: tag (integer), arrangement = "Left" (string), cornerTags = [] (vector
of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp), Python (x2.py, get data perf.py, terrain.py,
terrain bspline.py, terrain stl.py)
gmsh/model/mesh/setTransfiniteVolume
Set a transfinite meshing constraint on the surface tag. cornerTags can be used to
specify the (6 or 8) corners of the transfinite interpolation explicitly.
Input: tag (integer), cornerTags = [] (vector of integers)
Output: -
Return: -
Chapter 6: Gmsh application programming interface 159

Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp), Python (x2.py, terrain.py, terrain bspline.py,
terrain stl.py)
gmsh/model/mesh/setTransfiniteAutomatic
Set transfinite meshing constraints on the model entities in dimTags, given as a
vector of (dim, tag) pairs. Transfinite meshing constraints are added to the curves
of the quadrangular surfaces and to the faces of 6-sided volumes. Quadragular
faces with a corner angle superior to cornerAngle (in radians) are ignored. The
number of points is automatically determined from the sizing constraints. If dimTag
is empty, the constraints are applied to all entities in the model. If recombine is
true, the recombine flag is automatically set on the transfinite surfaces.
Input: dimTags = [] (vector of pairs of integers), cornerAngle = 2.35 (dou-
ble), recombine = True (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp, x6.cpp), Python (x2.py, x6.py)
gmsh/model/mesh/setRecombine
Set a recombination meshing constraint on the model entity of dimension dim and tag
tag. Currently only entities of dimension 2 (to recombine triangles into quadrangles)
are supported; angle specifies the threshold angle for the simple recombination
algorithm..
Input: dim (integer), tag (integer), angle = 45. (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t11.cpp, x2.cpp), Python (t11.py, x2.py, poisson.py, terrain.py,
terrain bspline.py, ...)
gmsh/model/mesh/setSmoothing
Set a smoothing meshing constraint on the model entity of dimension dim and tag
tag. val iterations of a Laplace smoother are applied.
Input: dim (integer), tag (integer), val (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x2.cpp), Python (x2.py, terrain.py, terrain bspline.py,
terrain stl.py)
gmsh/model/mesh/setReverse
Set a reverse meshing constraint on the model entity of dimension dim and tag tag.
If val is true, the mesh orientation will be reversed with respect to the natural mesh
160 Gmsh 4.11.1

orientation (i.e. the orientation consistent with the orientation of the geometry). If
val is false, the mesh is left as-is.
Input: dim (integer), tag (integer), val = True (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setAlgorithm
Set the meshing algorithm on the model entity of dimension dim and tag tag.
Supported values are those of the Mesh.Algorithm option, as listed in the Gmsh
reference manual. Currently only supported for dim == 2.
Input: dim (integer), tag (integer), val (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t5.cpp), Python (t5.py)
gmsh/model/mesh/setSizeFromBoundary
Force the mesh size to be extended from the boundary, or not, for the model entity
of dimension dim and tag tag. Currently only supported for dim == 2.
Input: dim (integer), tag (integer), val (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setCompound
Set a compound meshing constraint on the model entities of dimension dim and tags
tags. During meshing, compound entities are treated as a single discrete entity,
which is automatically reparametrized.
Input: dim (integer), tags (vector of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t12.cpp), Python (t12.py)
gmsh/model/mesh/setOutwardOrientation
Set meshing constraints on the bounding surfaces of the volume of tag tag so that all
surfaces are oriented with outward pointing normals; and if a mesh already exists,
reorient it. Currently only available with the OpenCASCADE kernel, as it relies on
the STL triangulation.
Input: tag (integer)
Chapter 6: Gmsh application programming interface 161

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/removeConstraints
Remove all meshing constraints from the model entities dimTags, given as a vector
of (dim, tag) pairs. If dimTags is empty, remove all constraings.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (terrain bspline.py)
gmsh/model/mesh/embed
Embed the model entities of dimension dim and tags tags in the (inDim, inTag)
model entity. The dimension dim can 0, 1 or 2 and must be strictly smaller than
inDim, which must be either 2 or 3. The embedded entities should not intersect each
other or be part of the boundary of the entity inTag, whose mesh will conform to the
mesh of the embedded entities. With the OpenCASCADE kernel, if the fragment
operation is applied to entities of different dimensions, the lower dimensional entities
will be automatically embedded in the higher dimensional entities if they are not on
their boundary.
Input: dim (integer), tags (vector of integers), inDim (integer), inTag (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t15.cpp), Python (t15.py)
gmsh/model/mesh/removeEmbedded
Remove embedded entities from the model entities dimTags, given as a vector of
(dim, tag) pairs. if dim is >= 0, only remove embedded entities of the given dimen-
sion (e.g. embedded points if dim == 0).
Input: dimTags (vector of pairs of integers), dim = -1 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getEmbedded
Get the entities (if any) embedded in the model entity of dimension dim and tag
tag.
Input: dim (integer), tag (integer)
Output: dimTags (vector of pairs of integers)
162 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/reorderElements
Reorder the elements of type elementType classified on the entity of tag tag ac-
cording to the ordering vector.
Input: elementType (integer), tag (integer), ordering (vector of sizes)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/renumberNodes
Renumber the node tags in a continuous sequence.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (view renumbering.py)
gmsh/model/mesh/renumberElements
Renumber the element tags in a continuous sequence.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (view renumbering.py)
gmsh/model/mesh/setPeriodic
Set the meshes of the entities of dimension dim and tag tags as periodic copies
of the meshes of entities tagsMaster, using the affine transformation specified in
affineTransformation (16 entries of a 4x4 matrix, by row). If used after meshing,
generate the periodic node correspondence information assuming the meshes of enti-
ties tags effectively match the meshes of entities tagsMaster (useful for structured
and extruded meshes). Currently only available for dim == 1 and dim == 2.
Input: dim (integer), tags (vector of integers), tagsMaster (vector of integers),
affineTransform (vector of doubles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t18.cpp), Python (t18.py, periodic.py)
Chapter 6: Gmsh application programming interface 163

gmsh/model/mesh/getPeriodic
Get master entities tagsMaster for the entities of dimension dim and tags tags.
Input: dim (integer), tags (vector of integers)
Output: tagMaster (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/getPeriodicNodes
Get the master entity tagMaster, the node tags nodeTags and their corresponding
master node tags nodeTagsMaster, and the affine transform affineTransform for
the entity of dimension dim and tag tag. If includeHighOrderNodes is set, include
high-order nodes in the returned data.
Input: dim (integer), tag (integer), includeHighOrderNodes = False
(boolean)
Output: tagMaster (integer), nodeTags (vector of sizes), nodeTagsMaster (vec-
tor of sizes), affineTransform (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (periodic.py)
gmsh/model/mesh/getPeriodicKeys
Get the master entity tagMaster and the key pairs (typeKeyMaster,
entityKeyMaster) corresponding to the entity tag and the key pairs (typeKey,
entityKey) for the elements of type elementType and function space type
functionSpaceType. If returnCoord is set, the coord and coordMaster vectors
contain the x, y, z coordinates locating basis functions for sorting purposes.
Input: elementType (integer), functionSpaceType (string), tag (integer),
returnCoord = True (boolean)
Output: tagMaster (integer), typeKeys (vector of integers), typeKeysMaster
(vector of integers), entityKeys (vector of sizes), entityKeysMaster
(vector of sizes), coord (vector of doubles), coordMaster (vector of
doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (periodic.py)
gmsh/model/mesh/importStl
Import the model STL representation (if available) as the current mesh.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
164 Gmsh 4.11.1

Examples: Python (stl to mesh.py)

gmsh/model/mesh/getDuplicateNodes
Get the tags of any duplicate nodes in the mesh of the entities dimTags, given as
a vector of (dim, tag) pairs. If dimTags is empty, consider the whole mesh.
Input: dimTags = [] (vector of pairs of integers)
Output: tags (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/removeDuplicateNodes
Remove duplicate nodes in the mesh of the entities dimTags, given as a vector of
(dim, tag) pairs. If dimTags is empty, consider the whole mesh.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (glue and remesh stl.py, mirror mesh.py, stl to mesh.py)
gmsh/model/mesh/removeDuplicateElements
Remove duplicate elements (defined by the same nodes, in the same entity) in the
mesh of the entities dimTags, given as a vector of (dim, tag) pairs. If dimTags is
empty, consider the whole mesh.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/splitQuadrangles
Split (into two triangles) all quadrangles in surface tag whose quality is lower than
quality. If tag < 0, split quadrangles in all surfaces.
Input: quality = 1. (double), tag = -1 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/setVisibility
Set the visibility of the elements of tags elementTags to value.
Input: elementTags (vector of sizes), value (integer)
Output: -
Return: -
Chapter 6: Gmsh application programming interface 165

Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/classifySurfaces
Classify ("color") the surface mesh based on the angle threshold angle (in radi-
ans), and create new discrete surfaces, curves and points accordingly. If boundary
is set, also create discrete curves on the boundary if the surface is open. If
forReparametrization is set, create curves and surfaces that can be reparametrized
using a single map. If curveAngle is less than Pi, also force curves to be split ac-
cording to curveAngle. If exportDiscrete is set, clear any built-in CAD kernel
entities and export the discrete entities in the built-in CAD kernel.
Input: angle (double), boundary = True (boolean), forReparametrization =
False (boolean), curveAngle = pi (double), exportDiscrete = True
(boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t13.cpp), Python (t13.py, aneurysm.py, glue and remesh stl.py,
remesh stl.py, terrain stl.py)
gmsh/model/mesh/createGeometry
Create a geometry for the discrete entities dimTags (given as a vector of (dim, tag)
pairs) represented solely by a mesh (without an underlying CAD description), i.e.
create a parametrization for discrete curves and surfaces, assuming that each can
be parametrized with a single map. If dimTags is empty, create a geometry for all
the discrete entities.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t13.cpp, x2.cpp), Python (t13.py, x2.py, aneurysm.py,
glue and remesh stl.py, remesh stl.py, ...)
gmsh/model/mesh/createTopology
Create a boundary representation from the mesh if the model does not have one (e.g.
when imported from mesh file formats with no BRep representation of the underlying
model). If makeSimplyConnected is set, enforce simply connected discrete surfaces
and volumes. If exportDiscrete is set, clear any built-in CAD kernel entities and
export the discrete entities in the built- in CAD kernel.
Input: makeSimplyConnected = True (boolean), exportDiscrete = True
(boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
166 Gmsh 4.11.1

gmsh/model/mesh/addHomologyRequest
Add a request to compute a basis representation for homology spaces (if type ==
"Homology") or cohomology spaces (if type == "Cohomology"). The computation
domain is given in a list of physical group tags domainTags; if empty, the whole
mesh is the domain. The computation subdomain for relative (co)homology com-
putation is given in a list of physical group tags subdomainTags; if empty, absolute
(co)homology is computed. The dimensions of the (co)homology bases to be com-
puted are given in the list dim; if empty, all bases are computed. Resulting basis
representation (co)chains are stored as physical groups in the mesh. If the request
is added before mesh generation, the computation will be performed at the end of
the meshing pipeline.
Input: type = "Homology" (string), domainTags = [] (vector of integers),
subdomainTags = [] (vector of integers), dims = [] (vector of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t14.cpp), Python (t14.py)
gmsh/model/mesh/clearHomologyRequests
Clear all (co)homology computation requests.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/computeHomology
Perform the (co)homology computations requested by addHomologyRequest(). The
newly created physical groups are returned in dimTags as a vector of (dim, tag)
pairs.
Input: -
Output: dimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/computeCrossField
Compute a cross field for the current mesh. The function creates 3 views: the H
function, the Theta function and cross directions. Return the tags of the views.
Input: -
Output: viewTags (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 167

gmsh/model/mesh/triangulate
Triangulate the points given in the coord vector as pairs of u, v coordinates, and
return the node tags (with numbering starting at 1) of the resulting triangles in tri.
Input: coord (vector of doubles)
Output: tri (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (raw triangulation.py)
gmsh/model/mesh/tetrahedralize
Tetrahedralize the points given in the coord vector as x, y, z coordinates, concate-
nated, and return the node tags (with numbering starting at 1) of the resulting
tetrahedra in tetra.
Input: coord (vector of doubles)
Output: tetra (vector of sizes)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (raw tetrahedralization.py)

6.5 Namespace gmsh/model/mesh/field: mesh size field functions

gmsh/model/mesh/field/add
Add a new mesh size field of type fieldType. If tag is positive, assign the tag
explicitly; otherwise a new tag is assigned automatically. Return the field tag.
Input: fieldType (string), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t7.cpp, t10.cpp, t11.cpp, t13.cpp, t17.cpp), Python (t7.py, t10.py,
t13.py, t17.py, adapt mesh.py, ...)
gmsh/model/mesh/field/remove
Remove the field with tag tag.
Input: tag (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/field/list
Get the list of all fields.
Input: -
168 Gmsh 4.11.1

Output: tags (vector of integers)

Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/field/getType
Get the type fieldType of the field with tag tag.
Input: tag (integer)
Output: fileType (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/field/setNumber
Set the numerical option option to value value for field tag.
Input: tag (integer), option (string), value (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t7.cpp, t10.cpp, t17.cpp), Python (t7.py, t10.py, t17.py,
adapt mesh.py, copy mesh.py, ...)
gmsh/model/mesh/field/getNumber
Get the value of the numerical option option for field tag.
Input: tag (integer), option (string)
Output: value (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/mesh/field/setString
Set the string option option to value value for field tag.
Input: tag (integer), option (string), value (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t10.cpp, t11.cpp, t13.cpp), Python (t10.py, t13.py)
gmsh/model/mesh/field/getString
Get the value of the string option option for field tag.
Input: tag (integer), option (string)
Output: value (string)
Return: -
Chapter 6: Gmsh application programming interface 169

Language-specific definition:
C++, C, Python, Julia

gmsh/model/mesh/field/setNumbers
Set the numerical list option option to value values for field tag.

Input: tag (integer), option (string), values (vector of doubles)

Output: -

Return: -

Language-specific definition:
C++, C, Python, Julia

Examples: C++ (t10.cpp), Python (t10.py, extend field.py,

naca boundary layer 2d.py, ocean.py)

gmsh/model/mesh/field/getNumbers
Get the value of the numerical list option option for field tag.

Input: tag (integer), option (string)

Output: values (vector of doubles)

Return: -

Language-specific definition:
C++, C, Python, Julia

gmsh/model/mesh/field/setAsBackgroundMesh
Set the field tag as the background mesh size field.

Input: tag (integer)

Output: -

Return: -

Language-specific definition:
C++, C, Python, Julia

Examples: C++ (t7.cpp, t10.cpp, t11.cpp, t13.cpp, t17.cpp), Python (t7.py, t10.py,
t13.py, t17.py, adapt mesh.py, ...)

gmsh/model/mesh/field/setAsBoundaryLayer
Set the field tag as a boundary layer size field.

Input: tag (integer)

Output: -

Return: -

Language-specific definition:
C++, C, Python, Julia

Examples: Python (naca boundary layer 2d.py)

170 Gmsh 4.11.1

6.6 Namespace gmsh/model/geo: built-in CAD kernel functions

gmsh/model/geo/addPoint
Add a geometrical point in the built-in CAD representation, at coordinates (x, y,
z). If meshSize is > 0, add a meshing constraint at that point. If tag is positive,
set the tag explicitly; otherwise a new tag is selected automatically. Return the tag
of the point. (Note that the point will be added in the current model only after
synchronize is called. This behavior holds for all the entities added in the geo
module.)
Input: x (double), y (double), z (double), meshSize = 0. (double), tag = -1
(integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t5.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t3.py, t5.py, t6.py, ...)
gmsh/model/geo/addLine
Add a straight line segment in the built-in CAD representation, between the two
points with tags startTag and endTag. If tag is positive, set the tag explicitly;
otherwise a new tag is selected automatically. Return the tag of the line.
Input: startTag (integer), endTag (integer), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t5.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t3.py, t5.py, t6.py, ...)
gmsh/model/geo/addCircleArc
Add a circle arc (strictly smaller than Pi) in the built-in CAD representation, be-
tween the two points with tags startTag and endTag, and with center centerTag.
If tag is positive, set the tag explicitly; otherwise a new tag is selected automati-
cally. If (nx, ny, nz) != (0, 0, 0), explicitly set the plane of the circle arc. Return
the tag of the circle arc.
Input: startTag (integer), centerTag (integer), endTag (integer), tag = -1
(integer), nx = 0. (double), ny = 0. (double), nz = 0. (double)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t5.cpp), Python (t5.py)
gmsh/model/geo/addEllipseArc
Add an ellipse arc (strictly smaller than Pi) in the built-in CAD representation,
between the two points startTag and endTag, and with center centerTag and
Chapter 6: Gmsh application programming interface 171

major axis point majorTag. If tag is positive, set the tag explicitly; otherwise a new
tag is selected automatically. If (nx, ny, nz) != (0, 0, 0), explicitly set the plane of
the circle arc. Return the tag of the ellipse arc.
Input: startTag (integer), centerTag (integer), majorTag (integer), endTag
(integer), tag = -1 (integer), nx = 0. (double), ny = 0. (double), nz =
0. (double)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addSpline
Add a spline (Catmull-Rom) curve in the built-in CAD representation, going
through the points pointTags. If tag is positive, set the tag explicitly; other-
wise a new tag is selected automatically. Create a periodic curve if the first and last
points are the same. Return the tag of the spline curve.
Input: pointTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t12.cpp), Python (t12.py)
gmsh/model/geo/addBSpline
Add a cubic b-spline curve in the built-in CAD representation, with pointTags
control points. If tag is positive, set the tag explicitly; otherwise a new tag is
selected automatically. Creates a periodic curve if the first and last points are the
same. Return the tag of the b-spline curve.
Input: pointTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addBezier
Add a Bezier curve in the built-in CAD representation, with pointTags control
points. If tag is positive, set the tag explicitly; otherwise a new tag is selected
automatically. Return the tag of the Bezier curve.
Input: pointTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addPolyline
Add a polyline curve in the built-in CAD representation, going through the points
pointTags. If tag is positive, set the tag explicitly; otherwise a new tag is selected
172 Gmsh 4.11.1

automatically. Create a periodic curve if the first and last points are the same.
Return the tag of the polyline curve.
Input: pointTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addCompoundSpline
Add a spline (Catmull-Rom) curve in the built-in CAD representation, going
through points sampling the curves in curveTags. The density of sampling points
on each curve is governed by numIntervals. If tag is positive, set the tag explicitly;
otherwise a new tag is selected automatically. Return the tag of the spline.
Input: curveTags (vector of integers), numIntervals = 5 (integer), tag = -1
(integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addCompoundBSpline
Add a b-spline curve in the built-in CAD representation, with control points sam-
pling the curves in curveTags. The density of sampling points on each curve is
governed by numIntervals. If tag is positive, set the tag explicitly; otherwise a
new tag is selected automatically. Return the tag of the b-spline.
Input: curveTags (vector of integers), numIntervals = 20 (integer), tag = -1
(integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addCurveLoop
Add a curve loop (a closed wire) in the built-in CAD representation, formed by
the curves curveTags. curveTags should contain (signed) tags of model entities of
dimension 1 forming a closed loop: a negative tag signifies that the underlying curve
is considered with reversed orientation. If tag is positive, set the tag explicitly;
otherwise a new tag is selected automatically. If reorient is set, automatically
reorient the curves if necessary. Return the tag of the curve loop.
Input: curveTags (vector of integers), tag = -1 (integer), reorient = False
(boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t5.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t3.py, t5.py, t6.py, ...)
Chapter 6: Gmsh application programming interface 173

gmsh/model/geo/addCurveLoops
Add curve loops in the built-in CAD representation based on the curves curveTags.
Return the tags of found curve loops, if any.
Input: curveTags (vector of integers)
Output: tags (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (aneurysm.py, tube boundary layer.py)
gmsh/model/geo/addPlaneSurface
Add a plane surface in the built-in CAD representation, defined by one or more
curve loops wireTags. The first curve loop defines the exterior contour; additional
curve loop define holes. If tag is positive, set the tag explicitly; otherwise a new tag
is selected automatically. Return the tag of the surface.
Input: wireTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t5.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t3.py, t5.py, t6.py, ...)
gmsh/model/geo/addSurfaceFilling
Add a surface in the built-in CAD representation, filling the curve loops in wireTags
using transfinite interpolation. Currently only a single curve loop is supported; this
curve loop should be composed by 3 or 4 curves only. If tag is positive, set the
tag explicitly; otherwise a new tag is selected automatically. Return the tag of the
surface.
Input: wireTags (vector of integers), tag = -1 (integer), sphereCenterTag =
-1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t5.cpp, t12.cpp), Python (t5.py, t12.py)
gmsh/model/geo/addSurfaceLoop
Add a surface loop (a closed shell) formed by surfaceTags in the built-in CAD
representation. If tag is positive, set the tag explicitly; otherwise a new tag is
selected automatically. Return the tag of the shell.
Input: surfaceTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
174 Gmsh 4.11.1

Examples: C++ (t2.cpp, t5.cpp, t13.cpp, x2.cpp), Python (t2.py, t5.py, t13.py,
x2.py, aneurysm.py, ...)
gmsh/model/geo/addVolume
Add a volume (a region) in the built-in CAD representation, defined by one or more
shells shellTags. The first surface loop defines the exterior boundary; additional
surface loop define holes. If tag is positive, set the tag explicitly; otherwise a new
tag is selected automatically. Return the tag of the volume.
Input: shellTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t2.cpp, t5.cpp, t13.cpp, x2.cpp), Python (t2.py, t5.py, t13.py,
x2.py, aneurysm.py, ...)
gmsh/model/geo/addGeometry
Add a geometry in the built-in CAD representation. geometry can currently be
one of "Sphere" or "PolarSphere" (where numbers should contain the x, y, z co-
ordinates of the center, followed by the radius), or "Parametric" (where strings
should contains three expression evaluating to the x, y and z coordinates. If tag
is positive, set the tag of the geometry explicitly; otherwise a new tag is selected
automatically. Return the tag of the geometry.
Input: geometry (string), numbers = [] (vector of doubles), strings = []
(vector of strings), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (ocean.py)
gmsh/model/geo/addPointOnGeometry
Add a point in the built-in CAD representation, at coordinates (x, y, z) on the
geometry geometryTag. If meshSize is > 0, add a meshing constraint at that point.
If tag is positive, set the tag explicitly; otherwise a new tag is selected automatically.
Return the tag of the point. For surface geometries, only the x and y coordinates
are used.
Input: geometryTag (integer), x (double), y (double), z = 0. (double),
meshSize = 0. (double), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (ocean.py)
gmsh/model/geo/extrude
Extrude the entities dimTags (given as a vector of (dim, tag) pairs) in the built-
in CAD representation, using a translation along (dx, dy, dz). Return extruded
Chapter 6: Gmsh application programming interface 175

entities in outDimTags. If the numElements vector is not empty, also extrude the
mesh: the entries in numElements give the number of elements in each layer. If
the height vector is not empty, it provides the (cumulative) height of the different
layers, normalized to 1. If recombine is set, recombine the mesh in the layers.
Input: dimTags (vector of pairs of integers), dx (double), dy (double), dz (dou-
ble), numElements = [] (vector of integers), heights = [] (vector of
doubles), recombine = False (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t2.cpp, t3.cpp, t14.cpp, t15.cpp), Python (t2.py, t3.py, t14.py,
t15.py, hex.py)
gmsh/model/geo/revolve
Extrude the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation, using a rotation of angle radians around the axis of revo-
lution defined by the point (x, y, z) and the direction (ax, ay, az). The angle
should be strictly smaller than Pi. Return extruded entities in outDimTags. If the
numElements vector is not empty, also extrude the mesh: the entries in numElements
give the number of elements in each layer. If the height vector is not empty, it pro-
vides the (cumulative) height of the different layers, normalized to 1. If recombine
is set, recombine the mesh in the layers.
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
ax (double), ay (double), az (double), angle (double), numElements =
[] (vector of integers), heights = [] (vector of doubles), recombine =
False (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp), Python (t3.py)
gmsh/model/geo/twist
Extrude the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation, using a combined translation and rotation of angle radians,
along (dx, dy, dz) and around the axis of revolution defined by the point (x, y,
z) and the direction (ax, ay, az). The angle should be strictly smaller than Pi.
Return extruded entities in outDimTags. If the numElements vector is not empty,
also extrude the mesh: the entries in numElements give the number of elements in
each layer. If the height vector is not empty, it provides the (cumulative) height
of the different layers, normalized to 1. If recombine is set, recombine the mesh in
the layers.
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
dx (double), dy (double), dz (double), ax (double), ay (double), az (dou-
ble), angle (double), numElements = [] (vector of integers), heights =
[] (vector of doubles), recombine = False (boolean)
Output: outDimTags (vector of pairs of integers)
176 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp), Python (t3.py)
gmsh/model/geo/extrudeBoundaryLayer
Extrude the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation along the normals of the mesh, creating discrete boundary layer
entities. Return extruded entities in outDimTags. The entries in numElements give
the number of elements in each layer. If the height vector is not empty, it provides
the (cumulative) height of the different layers. If recombine is set, recombine the
mesh in the layers. A second boundary layer can be created from the same entities
if second is set. If viewIndex is >= 0, use the corresponding view to either specify
the normals (if the view contains a vector field) or scale the normals (if the view is
scalar).
Input: dimTags (vector of pairs of integers), numElements = [1] (vector of inte-
gers), heights = [] (vector of doubles), recombine = False (boolean),
second = False (boolean), viewIndex = -1 (integer)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (aneurysm.py, naca boundary layer 2d.py,
naca boundary layer 3d.py, tube boundary layer.py)
gmsh/model/geo/translate
Translate the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation along (dx, dy, dz).
Input: dimTags (vector of pairs of integers), dx (double), dy (double), dz (dou-
ble)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t2.cpp), Python (t2.py)
gmsh/model/geo/rotate
Rotate the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation by angle radians around the axis of revolution defined by the
point (x, y, z) and the direction (ax, ay, az).
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
ax (double), ay (double), az (double), angle (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 177

Examples: C++ (t2.cpp), Python (t2.py)

gmsh/model/geo/dilate
Scale the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in CAD
representation by factors a, b and c along the three coordinate axes; use (x, y, z)
as the center of the homothetic transformation.
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
a (double), b (double), c (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/mirror
Mirror the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation, with respect to the plane of equation a * x + b * y + c * z + d
= 0.
Input: dimTags (vector of pairs of integers), a (double), b (double), c (double),
d (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/symmetrize
Mirror the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in
CAD representation, with respect to the plane of equation a * x + b * y + c * z + d
= 0. (This is a synonym for mirror, which will be deprecated in a future release.)
Input: dimTags (vector of pairs of integers), a (double), b (double), c (double),
d (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/copy
Copy the entities dimTags (given as a vector of (dim, tag) pairs) in the built-in CAD
representation; the new entities are returned in outDimTags.
Input: dimTags (vector of pairs of integers)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t2.cpp), Python (t2.py)
178 Gmsh 4.11.1

gmsh/model/geo/remove
Remove the entities dimTags (given as a vector of (dim, tag) pairs) in the built-
in CAD representation, provided that they are not on the boundary of higher-
dimensional entities. If recursive is true, remove all the entities on their bound-
aries, down to dimension 0.
Input: dimTags (vector of pairs of integers), recursive = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t6.cpp), Python (t6.py)
gmsh/model/geo/removeAllDuplicates
Remove all duplicate entities in the built-in CAD representation (different entities
at the same geometrical location).
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/splitCurve
Split the curve of tag tag in the built-in CAD representation, on the specified control
points pointTags. This feature is only available for lines, splines and b-splines.
Return the tag(s) curveTags of the newly created curve(s).
Input: tag (integer), pointTags (vector of integers)
Output: curveTags (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/getMaxTag
Get the maximum tag of entities of dimension dim in the built-in CAD representa-
tion.
Input: dim (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/setMaxTag
Set the maximum tag maxTag for entities of dimension dim in the built-in CAD
representation.
Input: dim (integer), maxTag (integer)
Output: -
Chapter 6: Gmsh application programming interface 179

Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/addPhysicalGroup
Add a physical group of dimension dim, grouping the entities with tags tags in the
built-in CAD representation. Return the tag of the physical group, equal to tag if
tag is positive, or a new tag if tag < 0. Set the name of the physical group if name
is not empty.
Input: dim (integer), tags (vector of integers), tag = -1 (integer), name = ""
(string)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t5.cpp), Python (t5.py)
gmsh/model/geo/removePhysicalGroups
Remove the physical groups dimTags (given as a vector of (dim, tag) pairs) from
the built-in CAD representation. If dimTags is empty, remove all groups.
Input: dimTags = [] (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/synchronize
Synchronize the built-in CAD representation with the current Gmsh model. This
can be called at any time, but since it involves a non trivial amount of processing,
the number of synchronization points should normally be minimized. Without syn-
chronization the entities in the built-in CAD representation are not available to any
function outside of the built-in CAD kernel functions.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t3.cpp, t5.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t3.py, t5.py, t6.py, ...)

6.7 Namespace gmsh/model/geo/mesh: built-in CAD kernel

meshing constraints
gmsh/model/geo/mesh/setSize
Set a mesh size constraint on the entities dimTags (given as a vector of (dim, tag)
pairs) in the built-in CAD kernel representation. Currently only entities of dimen-
sion 0 (points) are handled.
180 Gmsh 4.11.1

Input: dimTags (vector of pairs of integers), size (double)

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t2.cpp, t15.cpp), Python (t2.py, t15.py)
gmsh/model/geo/mesh/setTransfiniteCurve
Set a transfinite meshing constraint on the curve tag in the built-in CAD kernel
representation, with numNodes nodes distributed according to meshType and coef.
Currently supported types are "Progression" (geometrical progression with power
coef) and "Bump" (refinement toward both extremities of the curve).
Input: tag (integer), nPoints (integer), meshType = "Progression" (string),
coef = 1. (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t6.cpp), Python (t6.py)
gmsh/model/geo/mesh/setTransfiniteSurface
Set a transfinite meshing constraint on the surface tag in the built-in CAD kernel
representation. arrangement describes the arrangement of the triangles when the
surface is not flagged as recombined: currently supported values are "Left", "Right",
"AlternateLeft" and "AlternateRight". cornerTags can be used to specify the (3 or
4) corners of the transfinite interpolation explicitly; specifying the corners explicitly
is mandatory if the surface has more that 3 or 4 points on its boundary.
Input: tag (integer), arrangement = "Left" (string), cornerTags = [] (vector
of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t6.cpp), Python (t6.py)
gmsh/model/geo/mesh/setTransfiniteVolume
Set a transfinite meshing constraint on the surface tag in the built-in CAD kernel
representation. cornerTags can be used to specify the (6 or 8) corners of the
transfinite interpolation explicitly.
Input: tag (integer), cornerTags = [] (vector of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 181

gmsh/model/geo/mesh/setRecombine
Set a recombination meshing constraint on the entity of dimension dim and tag tag
in the built-in CAD kernel representation. Currently only entities of dimension 2 (to
recombine triangles into quadrangles) are supported; angle specifies the threshold
angle for the simple recombination algorithm.
Input: dim (integer), tag (integer), angle = 45. (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t6.cpp), Python (t6.py)
gmsh/model/geo/mesh/setSmoothing
Set a smoothing meshing constraint on the entity of dimension dim and tag tag in
the built-in CAD kernel representation. val iterations of a Laplace smoother are
applied.
Input: dim (integer), tag (integer), val (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/mesh/setReverse
Set a reverse meshing constraint on the entity of dimension dim and tag tag in
the built-in CAD kernel representation. If val is true, the mesh orientation will be
reversed with respect to the natural mesh orientation (i.e. the orientation consistent
with the orientation of the geometry). If val is false, the mesh is left as-is.
Input: dim (integer), tag (integer), val = True (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/mesh/setAlgorithm
Set the meshing algorithm on the entity of dimension dim and tag tag in the built-in
CAD kernel representation. Currently only supported for dim == 2.
Input: dim (integer), tag (integer), val (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/geo/mesh/setSizeFromBoundary
Force the mesh size to be extended from the boundary, or not, for the entity of
dimension dim and tag tag in the built-in CAD kernel representation. Currently
only supported for dim == 2.
182 Gmsh 4.11.1

Input: dim (integer), tag (integer), val (integer)

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia

6.8 Namespace gmsh/model/occ: OpenCASCADE CAD kernel

functions
gmsh/model/occ/addPoint
Add a geometrical point in the OpenCASCADE CAD representation, at coordinates
(x, y, z). If meshSize is > 0, add a meshing constraint at that point. If tag is
positive, set the tag explicitly; otherwise a new tag is selected automatically. Return
the tag of the point. (Note that the point will be added in the current model only
after synchronize is called. This behavior holds for all the entities added in the
occ module.)
Input: x (double), y (double), z (double), meshSize = 0. (double), tag = -1
(integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, bspline bezier patches.py,
bspline bezier trimmed.py, bspline filling.py, closest point.py, ...)
gmsh/model/occ/addLine
Add a straight line segment in the OpenCASCADE CAD representation, between
the two points with tags startTag and endTag. If tag is positive, set the tag
explicitly; otherwise a new tag is selected automatically. Return the tag of the line.
Input: startTag (integer), endTag (integer), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (crack.py, naca boundary layer 2d.py,
naca boundary layer 3d.py, stl to brep.py)
gmsh/model/occ/addCircleArc
Add a circle arc in the OpenCASCADE CAD representation, between the two points
with tags startTag and endTag, with center centerTag. If tag is positive, set the
tag explicitly; otherwise a new tag is selected automatically. Return the tag of the
circle arc.
Input: startTag (integer), centerTag (integer), endTag (integer), tag = -1
(integer)
Output: -
Return: integer
Chapter 6: Gmsh application programming interface 183

Language-specific definition:
C++, C, Python, Julia
Examples: Python (naca boundary layer 2d.py, naca boundary layer 3d.py)
gmsh/model/occ/addCircle
Add a circle of center (x, y, z) and radius r in the OpenCASCADE CAD repre-
sentation. If tag is positive, set the tag explicitly; otherwise a new tag is selected
automatically. If angle1 and angle2 are specified, create a circle arc between the
two angles. If a vector zAxis of size 3 is provided, use it as the normal to the circle
plane (z-axis). If a vector xAxis of size 3 is provided in addition to zAxis, use it to
define the x-axis. Return the tag of the circle.
Input: x (double), y (double), z (double), r (double), tag = -1 (integer),
angle1 = 0. (double), angle2 = 2*pi (double), zAxis = [] (vector of
doubles), xAxis = [] (vector of doubles)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, bspline bezier trimmed.py,
closest point.py, prim axis.py, trimmed.py)
gmsh/model/occ/addEllipseArc
Add an ellipse arc in the OpenCASCADE CAD representation, between the two
points startTag and endTag, and with center centerTag and major axis point
majorTag. If tag is positive, set the tag explicitly; otherwise a new tag is selected
automatically. Return the tag of the ellipse arc. Note that OpenCASCADE does
not allow creating ellipse arcs with the major radius smaller than the minor radius.
Input: startTag (integer), centerTag (integer), majorTag (integer), endTag
(integer), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/addEllipse
Add an ellipse of center (x, y, z) and radii r1 and r2 (with r1 >= r2) along the
x- and y-axes, respectively, in the OpenCASCADE CAD representation. If tag is
positive, set the tag explicitly; otherwise a new tag is selected automatically. If
angle1 and angle2 are specified, create an ellipse arc between the two angles. If a
vector zAxis of size 3 is provided, use it as the normal to the ellipse plane (z-axis).
If a vector xAxis of size 3 is provided in addition to zAxis, use it to define the
x-axis. Return the tag of the ellipse.
Input: x (double), y (double), z (double), r1 (double), r2 (double), tag = -1
(integer), angle1 = 0. (double), angle2 = 2*pi (double), zAxis = []
(vector of doubles), xAxis = [] (vector of doubles)
Output: -
Return: integer
184 Gmsh 4.11.1

Language-specific definition:
C++, C, Python, Julia
Examples: Python (prim axis.py)
gmsh/model/occ/addSpline
Add a spline (C2 b-spline) curve in the OpenCASCADE CAD representation, going
through the points pointTags. If tag is positive, set the tag explicitly; otherwise a
new tag is selected automatically. Create a periodic curve if the first and last points
are the same. Return the tag of the spline curve. If the tangents vector contains 6
entries, use them as concatenated x, y, z components of the initial and final tangents
of the b-spline; if it contains 3 times as many entries as the number of points, use
them as concatenated x, y, z components of the tangents at each point, unless the
norm of the tangent is zero.
Input: pointTags (vector of integers), tag = -1 (integer), tangents = [] (vec-
tor of doubles)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, naca boundary layer 2d.py,
naca boundary layer 3d.py, pipe.py, spline.py, ...)
gmsh/model/occ/addBSpline
Add a b-spline curve of degree degree in the OpenCASCADE CAD representation,
with pointTags control points. If weights, knots or multiplicities are not
provided, default parameters are computed automatically. If tag is positive, set the
tag explicitly; otherwise a new tag is selected automatically. Create a periodic curve
if the first and last points are the same. Return the tag of the b-spline curve.
Input: pointTags (vector of integers), tag = -1 (integer), degree = 3 (inte-
ger), weights = [] (vector of doubles), knots = [] (vector of doubles),
multiplicities = [] (vector of integers)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (bspline filling.py, spline.py)
gmsh/model/occ/addBezier
Add a Bezier curve in the OpenCASCADE CAD representation, with pointTags
control points. If tag is positive, set the tag explicitly; otherwise a new tag is
selected automatically. Return the tag of the Bezier curve.
Input: pointTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (spline.py)
Chapter 6: Gmsh application programming interface 185

gmsh/model/occ/addWire
Add a wire (open or closed) in the OpenCASCADE CAD representation, formed
by the curves curveTags. Note that an OpenCASCADE wire can be made of
curves that share geometrically identical (but topologically different) points. If tag
is positive, set the tag explicitly; otherwise a new tag is selected automatically.
Return the tag of the wire.
Input: curveTags (vector of integers), tag = -1 (integer), checkClosed =
False (boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, bspline bezier trimmed.py,
bspline filling.py, pipe.py, trimmed.py)
gmsh/model/occ/addCurveLoop
Add a curve loop (a closed wire) in the OpenCASCADE CAD representation, formed
by the curves curveTags. curveTags should contain tags of curves forming a closed
loop. Negative tags can be specified for compatibility with the built-in kernel, but
are simply ignored: the wire is oriented according to the orientation of its first
curve. Note that an OpenCASCADE curve loop can be made of curves that share
geometrically identical (but topologically different) points. If tag is positive, set the
tag explicitly; otherwise a new tag is selected automatically. Return the tag of the
curve loop.
Input: curveTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, naca boundary layer 2d.py,
stl to brep.py, surface filling.py)
gmsh/model/occ/addRectangle
Add a rectangle in the OpenCASCADE CAD representation, with lower left corner
at (x, y, z) and upper right corner at (x + dx, y + dy, z). If tag is positive, set the
tag explicitly; otherwise a new tag is selected automatically. Round the corners if
roundedRadius is nonzero. Return the tag of the rectangle.
Input: x (double), y (double), z (double), dx (double), dy (double), tag = -1
(integer), roundedRadius = 0. (double)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t17.cpp, t20.cpp, t21.cpp, x6.cpp), Python (t17.py, t20.py, t21.py,
x6.py, adapt mesh.py, ...)
186 Gmsh 4.11.1

gmsh/model/occ/addDisk
Add a disk in the OpenCASCADE CAD representation, with center (xc, yc, zc) and
radius rx along the x-axis and ry along the y-axis (rx >= ry). If tag is positive, set
the tag explicitly; otherwise a new tag is selected automatically. If a vector zAxis
of size 3 is provided, use it as the normal to the disk (z-axis). If a vector xAxis of
size 3 is provided in addition to zAxis, use it to define the x-axis. Return the tag
of the disk.
Input: xc (double), yc (double), zc (double), rx (double), ry (double), tag
= -1 (integer), zAxis = [] (vector of doubles), xAxis = [] (vector of
doubles)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, pipe.py, poisson.py, prim axis.py)
gmsh/model/occ/addPlaneSurface
Add a plane surface in the OpenCASCADE CAD representation, defined by one
or more curve loops (or closed wires) wireTags. The first curve loop defines the
exterior contour; additional curve loop define holes. If tag is positive, set the tag
explicitly; otherwise a new tag is selected automatically. Return the tag of the
surface.
Input: wireTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (naca boundary layer 2d.py, stl to brep.py)
gmsh/model/occ/addSurfaceFilling
Add a surface in the OpenCASCADE CAD representation, filling the curve loop
wireTag. If tag is positive, set the tag explicitly; otherwise a new tag is selected
automatically. Return the tag of the surface. If pointTags are provided, force the
surface to pass through the given points. The other optional arguments are degree
(the degree of the energy criterion to minimize for computing the deformation of the
surface), numPointsOnCurves (the average number of points for discretisation of the
bounding curves), numIter (the maximum number of iterations of the optimization
process), anisotropic (improve performance when the ratio of the length along
the two parametric coordinates of the surface is high), tol2d (tolerance to the
constraints in the parametric plane of the surface), tol3d (the maximum distance
allowed between the support surface and the constraints), tolAng (the maximum
angle allowed between the normal of the surface and the constraints), tolCurv (the
maximum difference of curvature allowed between the surface and the constraint),
maxDegree (the highest degree which the polynomial defining the filling surface can
have) and, maxSegments (the largest number of segments which the filling surface
can have).
Input: wireTag (integer), tag = -1 (integer), pointTags = [] (vector of
integers), degree = 3 (integer), numPointsOnCurves = 15 (integer),
Chapter 6: Gmsh application programming interface 187

numIter = 2 (integer), anisotropic = False (boolean), tol2d =

0.00001 (double), tol3d = 0.0001 (double), tolAng = 0.01 (double),
tolCurv = 0.1 (double), maxDegree = 8 (integer), maxSegments = 9
(integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (surface filling.py)
gmsh/model/occ/addBSplineFilling
Add a BSpline surface in the OpenCASCADE CAD representation, filling the curve
loop wireTag. The curve loop should be made of 2, 3 or 4 curves. The optional type
argument specifies the type of filling: "Stretch" creates the flattest patch, "Curved"
(the default) creates the most rounded patch, and "Coons" creates a rounded patch
with less depth than "Curved". If tag is positive, set the tag explicitly; otherwise
a new tag is selected automatically. Return the tag of the surface.
Input: wireTag (integer), tag = -1 (integer), type = "" (string)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (bspline filling.py, surface filling.py)
gmsh/model/occ/addBezierFilling
Add a Bezier surface in the OpenCASCADE CAD representation, filling the curve
loop wireTag. The curve loop should be made of 2, 3 or 4 Bezier curves. The
optional type argument specifies the type of filling: "Stretch" creates the flattest
patch, "Curved" (the default) creates the most rounded patch, and "Coons" creates
a rounded patch with less depth than "Curved". If tag is positive, set the tag
explicitly; otherwise a new tag is selected automatically. Return the tag of the
surface.
Input: wireTag (integer), tag = -1 (integer), type = "" (string)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/addBSplineSurface
Add a b-spline surface of degree degreeU x degreeV in the OpenCASCADE CAD
representation, with pointTags control points given as a single vector [Pu1v1, ...
PunumPointsUv1, Pu1v2, ...]. If weights, knotsU, knotsV, multiplicitiesU or
multiplicitiesV are not provided, default parameters are computed automatically.
If tag is positive, set the tag explicitly; otherwise a new tag is selected automatically.
If wireTags is provided, trim the b-spline patch using the provided wires: the first
wire defines the external contour, the others define holes. If wire3D is set, consider
wire curves as 3D curves and project them on the b-spline surface; otherwise consider
the wire curves as defined in the parametric space of the surface. Return the tag of
the b-spline surface.
188 Gmsh 4.11.1

Input: pointTags (vector of integers), numPointsU (integer), tag = -1 (inte-

ger), degreeU = 3 (integer), degreeV = 3 (integer), weights = [] (vec-
tor of doubles), knotsU = [] (vector of doubles), knotsV = [] (vector of
doubles), multiplicitiesU = [] (vector of integers), multiplicitiesV
= [] (vector of integers), wireTags = [] (vector of integers), wire3D =
False (boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (bspline bezier patches.py, bspline bezier trimmed.py,
terrain bspline.py)
gmsh/model/occ/addBezierSurface
Add a Bezier surface in the OpenCASCADE CAD representation, with pointTags
control points given as a single vector [Pu1v1, ... PunumPointsUv1, Pu1v2, ...]. If
tag is positive, set the tag explicitly; otherwise a new tag is selected automatically.
If wireTags is provided, trim the Bezier patch using the provided wires: the first
wire defines the external contour, the others define holes. If wire3D is set, consider
wire curves as 3D curves and project them on the Bezier surface; otherwise consider
the wire curves as defined in the parametric space of the surface. Return the tag of
the Bezier surface.
Input: pointTags (vector of integers), numPointsU (integer), tag = -1 (inte-
ger), wireTags = [] (vector of integers), wire3D = False (boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (bspline bezier patches.py)
gmsh/model/occ/addTrimmedSurface
Trim the surface surfaceTag with the wires wireTags, replacing any existing trim-
ming curves. The first wire defines the external contour, the others define holes. If
wire3D is set, consider wire curves as 3D curves and project them on the surface;
otherwise consider the wire curves as defined in the parametric space of the surface.
If tag is positive, set the tag explicitly; otherwise a new tag is selected automatically.
Return the tag of the trimmed surface.
Input: surfaceTag (integer), wireTags = [] (vector of integers), wire3D =
False (boolean), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (trimmed.py)
gmsh/model/occ/addSurfaceLoop
Add a surface loop (a closed shell) in the OpenCASCADE CAD representation,
formed by surfaceTags. If tag is positive, set the tag explicitly; otherwise a new
Chapter 6: Gmsh application programming interface 189

tag is selected automatically. Return the tag of the surface loop. Setting sewing
allows one to build a shell made of surfaces that share geometrically identical (but
topologically different) curves.
Input: surfaceTags (vector of integers), tag = -1 (integer), sewing = False
(boolean)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (stl to brep.py)
gmsh/model/occ/addVolume
Add a volume (a region) in the OpenCASCADE CAD representation, defined by one
or more surface loops shellTags. The first surface loop defines the exterior bound-
ary; additional surface loop define holes. If tag is positive, set the tag explicitly;
otherwise a new tag is selected automatically. Return the tag of the volume.
Input: shellTags (vector of integers), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (stl to brep.py)
gmsh/model/occ/addSphere
Add a sphere of center (xc, yc, zc) and radius r in the OpenCASCADE CAD
representation. The optional angle1 and angle2 arguments define the polar angle
opening (from -Pi/2 to Pi/2). The optional angle3 argument defines the azimuthal
opening (from 0 to 2*Pi). If tag is positive, set the tag explicitly; otherwise a new
tag is selected automatically. Return the tag of the sphere.
Input: xc (double), yc (double), zc (double), radius (double), tag = -1 (inte-
ger), angle1 = -pi/2 (double), angle2 = pi/2 (double), angle3 = 2*pi
(double)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp, t18.cpp, x5.cpp), Python (t16.py, t18.py, x5.py,
boolean.py, extend field.py, ...)
gmsh/model/occ/addBox
Add a parallelepipedic box in the OpenCASCADE CAD representation, defined by
a point (x, y, z) and the extents along the x-, y- and z-axes. If tag is positive, set
the tag explicitly; otherwise a new tag is selected automatically. Return the tag of
the box.
Input: x (double), y (double), z (double), dx (double), dy (double), dz (double),
tag = -1 (integer)
190 Gmsh 4.11.1

Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp, t18.cpp, x4.cpp, x5.cpp, x7.cpp), Python (t16.py, t18.py,
x4.py, x5.py, x7.py, ...)
gmsh/model/occ/addCylinder
Add a cylinder in the OpenCASCADE CAD representation, defined by the center
(x, y, z) of its first circular face, the 3 components (dx, dy, dz) of the vector defining
its axis and its radius r. The optional angle argument defines the angular opening
(from 0 to 2*Pi). If tag is positive, set the tag explicitly; otherwise a new tag is
selected automatically. Return the tag of the cylinder.
Input: x (double), y (double), z (double), dx (double), dy (double), dz (double),
r (double), tag = -1 (integer), angle = 2*pi (double)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (boolean.py, gui.py, tube boundary layer.py)
gmsh/model/occ/addCone
Add a cone in the OpenCASCADE CAD representation, defined by the center (x,
y, z) of its first circular face, the 3 components of the vector (dx, dy, dz) defining
its axis and the two radii r1 and r2 of the faces (these radii can be zero). If tag is
positive, set the tag explicitly; otherwise a new tag is selected automatically. angle
defines the optional angular opening (from 0 to 2*Pi). Return the tag of the cone.
Input: x (double), y (double), z (double), dx (double), dy (double), dz (double),
r1 (double), r2 (double), tag = -1 (integer), angle = 2*pi (double)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/addWedge
Add a right angular wedge in the OpenCASCADE CAD representation, defined by
the right-angle point (x, y, z) and the 3 extends along the x-, y- and z-axes (dx,
dy, dz). If tag is positive, set the tag explicitly; otherwise a new tag is selected
automatically. The optional argument ltx defines the top extent along the x-axis.
If a vector zAxis of size 3 is provided, use it to define the z-axis. Return the tag of
the wedge.
Input: x (double), y (double), z (double), dx (double), dy (double), dz (double),
tag = -1 (integer), ltx = 0. (double), zAxis = [] (vector of doubles)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 191

Examples: Python (prim axis.py)

gmsh/model/occ/addTorus
Add a torus in the OpenCASCADE CAD representation, defined by its center (x,
y, z) and its 2 radii r and r2. If tag is positive, set the tag explicitly; otherwise a
new tag is selected automatically. The optional argument angle defines the angular
opening (from 0 to 2*Pi). If a vector zAxis of size 3 is provided, use it to define the
z-axis. Return the tag of the torus.
Input: x (double), y (double), z (double), r1 (double), r2 (double), tag = -1
(integer), angle = 2*pi (double), zAxis = [] (vector of doubles)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (prim axis.py)
gmsh/model/occ/addThruSections
Add a volume (if the optional argument makeSolid is set) or surfaces in the Open-
CASCADE CAD representation, defined through the open or closed wires wireTags.
If tag is positive, set the tag explicitly; otherwise a new tag is selected automati-
cally. The new entities are returned in outDimTags as a vector of (dim, tag) pairs.
If the optional argument makeRuled is set, the surfaces created on the boundary are
forced to be ruled surfaces. If maxDegree is positive, set the maximal degree of re-
sulting surface. The optional argument continuity allows to specify the continuity
of the resulting shape ("C0", "G1", "C1", "G2", "C2", "C3", "CN"). The op-
tional argument parametrization sets the parametrization type ("ChordLength",
"Centripetal", "IsoParametric"). The optional argument smoothing determines if
smoothing is applied.
Input: wireTags (vector of integers), tag = -1 (integer), makeSolid = True
(boolean), makeRuled = False (boolean), maxDegree = -1 (integer),
continuity = "" (string), parametrization = "" (string), smoothing
= False (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py)
gmsh/model/occ/addThickSolid
Add a hollowed volume in the OpenCASCADE CAD representation, built from an
initial volume volumeTag and a set of faces from this volume excludeSurfaceTags,
which are to be removed. The remaining faces of the volume become the walls of
the hollowed solid, with thickness offset. If tag is positive, set the tag explicitly;
otherwise a new tag is selected automatically.
Input: volumeTag (integer), excludeSurfaceTags (vector of integers), offset
(double), tag = -1 (integer)
Output: outDimTags (vector of pairs of integers)
Return: -
192 Gmsh 4.11.1

Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/extrude
Extrude the entities dimTags (given as a vector of (dim, tag) pairs) in the Open-
CASCADE CAD representation, using a translation along (dx, dy, dz). Return
extruded entities in outDimTags. If the numElements vector is not empty, also ex-
trude the mesh: the entries in numElements give the number of elements in each
layer. If the height vector is not empty, it provides the (cumulative) height of the
different layers, normalized to 1. If recombine is set, recombine the mesh in the
layers.
Input: dimTags (vector of pairs of integers), dx (double), dy (double), dz (dou-
ble), numElements = [] (vector of integers), heights = [] (vector of
doubles), recombine = False (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (naca boundary layer 3d.py)
gmsh/model/occ/revolve
Extrude the entities dimTags (given as a vector of (dim, tag) pairs) in the Open-
CASCADE CAD representation, using a rotation of angle radians around the axis
of revolution defined by the point (x, y, z) and the direction (ax, ay, az). Return
extruded entities in outDimTags. If the numElements vector is not empty, also ex-
trude the mesh: the entries in numElements give the number of elements in each
layer. If the height vector is not empty, it provides the (cumulative) height of the
different layers, normalized to 1. When the mesh is extruded the angle should be
strictly smaller than 2*Pi. If recombine is set, recombine the mesh in the layers.
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
ax (double), ay (double), az (double), angle (double), numElements =
[] (vector of integers), heights = [] (vector of doubles), recombine =
False (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (naca boundary layer 3d.py)
gmsh/model/occ/addPipe
Add a pipe in the OpenCASCADE CAD representation, by extruding the entities
dimTags (given as a vector of (dim, tag) pairs) along the wire wireTag. The type of
sweep can be specified with trihedron (possible values: "DiscreteTrihedron", "Cor-
rectedFrenet", "Fixed", "Frenet", "ConstantNormal", "Darboux", "GuideAC",
"GuidePlan", "GuideACWithContact", "GuidePlanWithContact"). If trihedron
is not provided, "DiscreteTrihedron" is assumed. Return the pipe in outDimTags.
Input: dimTags (vector of pairs of integers), wireTag (integer), trihedron =
"" (string)
Chapter 6: Gmsh application programming interface 193

Output: outDimTags (vector of pairs of integers)

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py, pipe.py)
gmsh/model/occ/fillet
Fillet the volumes volumeTags on the curves curveTags with radii radii. The
radii vector can either contain a single radius, as many radii as curveTags, or
twice as many as curveTags (in which case different radii are provided for the begin
and end points of the curves). Return the filleted entities in outDimTags as a vector
of (dim, tag) pairs. Remove the original volume if removeVolume is set.
Input: volumeTags (vector of integers), curveTags (vector of integers), radii
(vector of doubles), removeVolume = True (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp), Python (t19.py)
gmsh/model/occ/chamfer
Chamfer the volumes volumeTags on the curves curveTags with distances
distances measured on surfaces surfaceTags. The distances vector can either
contain a single distance, as many distances as curveTags and surfaceTags, or
twice as many as curveTags and surfaceTags (in which case the first in each
pair is measured on the corresponding surface in surfaceTags, the other on the
other adjacent surface). Return the chamfered entities in outDimTags. Remove the
original volume if removeVolume is set.
Input: volumeTags (vector of integers), curveTags (vector of integers),
surfaceTags (vector of integers), distances (vector of doubles),
removeVolume = True (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/fuse
Compute the boolean union (the fusion) of the entities objectDimTags and
toolDimTags (vectors of (dim, tag) pairs) in the OpenCASCADE CAD
representation. Return the resulting entities in outDimTags. If tag is positive,
try to set the tag explicitly (only valid if the boolean operation results in a single
entity). Remove the object if removeObject is set. Remove the tool if removeTool
is set.
Input: objectDimTags (vector of pairs of integers), toolDimTags (vector of
pairs of integers), tag = -1 (integer), removeObject = True (boolean),
removeTool = True (boolean)
Output: outDimTags (vector of pairs of integers), outDimTagsMap (vector of vec-
tors of pairs of integers)
194 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x5.cpp), Python (x5.py, boolean.py, gui.py,
tube boundary layer.py)
gmsh/model/occ/intersect
Compute the boolean intersection (the common parts) of the entities objectDimTags
and toolDimTags (vectors of (dim, tag) pairs) in the OpenCASCADE CAD rep-
resentation. Return the resulting entities in outDimTags. If tag is positive, try to
set the tag explicitly (only valid if the boolean operation results in a single entity).
Remove the object if removeObject is set. Remove the tool if removeTool is set.
Input: objectDimTags (vector of pairs of integers), toolDimTags (vector of
pairs of integers), tag = -1 (integer), removeObject = True (boolean),
removeTool = True (boolean)
Output: outDimTags (vector of pairs of integers), outDimTagsMap (vector of vec-
tors of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (boolean.py, gui.py)
gmsh/model/occ/cut
Compute the boolean difference between the entities objectDimTags and
toolDimTags (given as vectors of (dim, tag) pairs) in the OpenCASCADE CAD
representation. Return the resulting entities in outDimTags. If tag is positive,
try to set the tag explicitly (only valid if the boolean operation results in a single
entity). Remove the object if removeObject is set. Remove the tool if removeTool
is set.
Input: objectDimTags (vector of pairs of integers), toolDimTags (vector of
pairs of integers), tag = -1 (integer), removeObject = True (boolean),
removeTool = True (boolean)
Output: outDimTags (vector of pairs of integers), outDimTagsMap (vector of vec-
tors of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp), Python (t16.py, boolean.py, extend field.py, gui.py,
spherical surf.py)
gmsh/model/occ/fragment
Compute the boolean fragments (general fuse) resulting from the intersection of the
entities objectDimTags and toolDimTags (given as vectors of (dim, tag) pairs) in
the OpenCASCADE CAD representation, making all iterfaces conformal. When
applied to entities of different dimensions, the lower dimensional entities will be
automatically embedded in the higher dimensional entities if they are not on their
boundary. Return the resulting entities in outDimTags. If tag is positive, try to
set the tag explicitly (only valid if the boolean operation results in a single entity).
Remove the object if removeObject is set. Remove the tool if removeTool is set.
Chapter 6: Gmsh application programming interface 195

Input: objectDimTags (vector of pairs of integers), toolDimTags (vector of

pairs of integers), tag = -1 (integer), removeObject = True (boolean),
removeTool = True (boolean)
Output: outDimTags (vector of pairs of integers), outDimTagsMap (vector of vec-
tors of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp, t18.cpp, t20.cpp, t21.cpp), Python (t16.py, t18.py,
t20.py, t21.py, bspline bezier patches.py, ...)
gmsh/model/occ/translate
Translate the entities dimTags (given as a vector of (dim, tag) pairs) in the Open-
CASCADE CAD representation along (dx, dy, dz).
Input: dimTags (vector of pairs of integers), dx (double), dy (double), dz (dou-
ble)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp, t20.cpp), Python (t19.py, t20.py)
gmsh/model/occ/rotate
Rotate the entities dimTags (given as a vector of (dim, tag) pairs) in the OpenCAS-
CADE CAD representation by angle radians around the axis of revolution defined
by the point (x, y, z) and the direction (ax, ay, az).
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
ax (double), ay (double), az (double), angle (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp, t20.cpp), Python (t19.py, t20.py,
naca boundary layer 2d.py, naca boundary layer 3d.py,
pipe.py)
gmsh/model/occ/dilate
Scale the entities dimTags (given as a vector of (dim, tag) pairs) in the OpenCAS-
CADE CAD representation by factors a, b and c along the three coordinate axes;
use (x, y, z) as the center of the homothetic transformation.
Input: dimTags (vector of pairs of integers), x (double), y (double), z (double),
a (double), b (double), c (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
196 Gmsh 4.11.1

gmsh/model/occ/mirror
Mirror the entities dimTags (given as a vector of (dim, tag) pairs) in the OpenCAS-
CADE CAD representation, with respect to the plane of equation a * x + b * y + c
* z + d = 0.
Input: dimTags (vector of pairs of integers), a (double), b (double), c (double),
d (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/symmetrize
Mirror the entities dimTags (given as a vector of (dim, tag) pairs) in the OpenCAS-
CADE CAD representation, with respect to the plane of equation a * x + b * y + c
* z + d = 0. (This is a deprecated synonym for mirror.)
Input: dimTags (vector of pairs of integers), a (double), b (double), c (double),
d (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/affineTransform
Apply a general affine transformation matrix affineTransform (16 entries of a 4x4
matrix, by row; only the 12 first can be provided for convenience) to the entities
dimTags (given as a vector of (dim, tag) pairs) in the OpenCASCADE CAD repre-
sentation.
Input: dimTags (vector of pairs of integers), affineTransform (vector of dou-
bles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/copy
Copy the entities dimTags in the OpenCASCADE CAD representation; the new
entities are returned in outDimTags.
Input: dimTags (vector of pairs of integers)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp, t20.cpp), Python (t19.py, t20.py)
gmsh/model/occ/remove
Remove the entities dimTags (given as a vector of (dim, tag) pairs) in the Open-
CASCADE CAD representation, provided that they are not on the boundary of
Chapter 6: Gmsh application programming interface 197

higher-dimensional entities. If recursive is true, remove all the entities on their

boundaries, down to dimension 0.
Input: dimTags (vector of pairs of integers), recursive = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t19.cpp, t20.cpp), Python (t19.py, t20.py, pipe.py, trimmed.py,
tube boundary layer.py)
gmsh/model/occ/removeAllDuplicates
Remove all duplicate entities in the OpenCASCADE CAD representation (different
entities at the same geometrical location) after intersecting (using boolean frag-
ments) all highest dimensional entities.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (bspline bezier patches.py, hybrid order.py, stl to mesh.py)
gmsh/model/occ/healShapes
Apply various healing procedures to the entities dimTags (given as a vector of (dim,
tag) pairs), or to all the entities in the model if dimTags is empty, in the OpenCAS-
CADE CAD representation. Return the healed entities in outDimTags.
Input: dimTags = [] (vector of pairs of integers), tolerance = 1e-8 (double),
fixDegenerated = True (boolean), fixSmallEdges = True (boolean),
fixSmallFaces = True (boolean), sewFaces = True (boolean),
makeSolids = True (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (bspline bezier patches.py, heal.py)
gmsh/model/occ/convertToNURBS
Convert the entities dimTags to NURBS.
Input: dimTags (vector of pairs of integers)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/importShapes
Import BREP, STEP or IGES shapes from the file fileName in the OpenCASCADE
CAD representation. The imported entities are returned in outDimTags, as a vector
198 Gmsh 4.11.1

of (dim, tag) pairs. If the optional argument highestDimOnly is set, only import
the highest dimensional entities in the file. The optional argument format can be
used to force the format of the file (currently "brep", "step" or "iges").
Input: fileName (string), highestDimOnly = True (boolean), format = ""
(string)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t20.cpp), Python (t20.py)
gmsh/model/occ/importShapesNativePointer
Imports an OpenCASCADE shape by providing a pointer to a native OpenCAS-
CADE TopoDS_Shape object (passed as a pointer to void). The imported entities
are returned in outDimTags as a vector of (dim, tag) pairs. If the optional argu-
ment highestDimOnly is set, only import the highest dimensional entities in shape.
In Python, this function can be used for integration with PythonOCC, in which
the SwigPyObject pointer of TopoDS_Shape must be passed as an int to shape,
i.e., shape = int(pythonocc_shape.this). Warning: this function is unsafe, as
providing an invalid pointer will lead to undefined behavior.
Input: shape (pointer), highestDimOnly = True (boolean)
Output: outDimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/getEntities
Get all the OpenCASCADE entities. If dim is >= 0, return only the entities of the
specified dimension (e.g. points if dim == 0). The entities are returned as a vector
of (dim, tag) pairs.
Input: dim = -1 (integer)
Output: dimTags (vector of pairs of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t20.cpp), Python (t20.py, bspline bezier patches.py,
naca boundary layer 3d.py, tube boundary layer.py)
gmsh/model/occ/getEntitiesInBoundingBox
Get the OpenCASCADE entities in the bounding box defined by the two points
(xmin, ymin, zmin) and (xmax, ymax, zmax). If dim is >= 0, return only the entities
of the specified dimension (e.g. points if dim == 0).
Input: xmin (double), ymin (double), zmin (double), xmax (double), ymax (dou-
ble), zmax (double), dim = -1 (integer)
Output: dimTags (vector of pairs of integers)
Return: -
Chapter 6: Gmsh application programming interface 199

Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/getBoundingBox
Get the bounding box (xmin, ymin, zmin), (xmax, ymax, zmax) of the OpenCAS-
CADE entity of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: xmin (double), ymin (double), zmin (double), xmax (double), ymax (dou-
ble), zmax (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t20.cpp), Python (t20.py, naca boundary layer 3d.py)
gmsh/model/occ/getCurveLoops
Get the tags curveLoopTags of the curve loops making up the surface of tag
surfaceTag, as well as the tags curveTags of the curves making up each curve
loop.
Input: surfaceTag (integer)
Output: curveLoopTags (vector of integers), curveTags (vector of vectors of
integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/getSurfaceLoops
Get the tags surfaceLoopTags of the surface loops making up the volume of tag
volumeTag, as well as the tags surfaceTags of the surfaces making up each surface
loop.
Input: volumeTag (integer)
Output: surfaceLoopTags (vector of integers), surfaceTags (vector of vectors
of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/getMass
Get the mass of the OpenCASCADE entity of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: mass (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (step assembly.py, volume.py)
gmsh/model/occ/getCenterOfMass
Get the center of mass of the OpenCASCADE entity of dimension dim and tag tag.
200 Gmsh 4.11.1

Input: dim (integer), tag (integer)

Output: x (double), y (double), z (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/getMatrixOfInertia
Get the matrix of inertia (by row) of the OpenCASCADE entity of dimension dim
and tag tag.
Input: dim (integer), tag (integer)
Output: mat (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/getMaxTag
Get the maximum tag of entities of dimension dim in the OpenCASCADE CAD
representation.
Input: dim (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/setMaxTag
Set the maximum tag maxTag for entities of dimension dim in the OpenCASCADE
CAD representation.
Input: dim (integer), maxTag (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/model/occ/synchronize
Synchronize the OpenCASCADE CAD representation with the current Gmsh
model. This can be called at any time, but since it involves a non trivial amount
of processing, the number of synchronization points should normally be minimized.
Without synchronization the entities in the OpenCASCADE CAD representation
are not available to any function outside of the OpenCASCADE CAD kernel func-
tions.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp, t17.cpp, t18.cpp, t19.cpp, t20.cpp, ...), Python (t16.py,
t17.py, t18.py, t19.py, t20.py, ...)
Chapter 6: Gmsh application programming interface 201

6.9 Namespace gmsh/model/occ/mesh: OpenCASCADE CAD

kernel meshing constraints
gmsh/model/occ/mesh/setSize
Set a mesh size constraint on the entities dimTags (given as a vector of (dim, tag)
pairs) in the OpenCASCADE CAD representation. Currently only entities of di-
mension 0 (points) are handled.
Input: dimTags (vector of pairs of integers), size (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (naca boundary layer 3d.py)

6.10 Namespace gmsh/view: post-processing view functions

gmsh/view/add
Add a new post-processing view, with name name. If tag is positive use it (and
remove the view with that tag if it already exists), otherwise associate a new tag.
Return the view tag.
Input: name (string), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t4.cpp, x3.cpp, x4.cpp, x5.cpp), Python (t4.py, x3.py, x4.py,
x5.py, adapt mesh.py, ...)
gmsh/view/remove
Remove the view with tag tag.
Input: tag (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (plugin.py)
gmsh/view/getIndex
Get the index of the view with tag tag in the list of currently loaded views. This
dynamic index (it can change when views are removed) is used to access view options.
Input: tag (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (adapt mesh.py)
202 Gmsh 4.11.1

gmsh/view/getTags
Get the tags of all views.
Input: -
Output: tags (vector of integers)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t8.cpp, t9.cpp), Python (t8.py, t9.py, plugin.py)
gmsh/view/addModelData
Add model-based post-processing data to the view with tag tag. modelName iden-
tifies the model the data is attached to. dataType specifies the type of data, cur-
rently either "NodeData", "ElementData" or "ElementNodeData". step specifies
the identifier (>= 0) of the data in a sequence. tags gives the tags of the nodes or
elements in the mesh to which the data is associated. data is a vector of the same
length as tags: each entry is the vector of double precision numbers representing the
data associated with the corresponding tag. The optional time argument associate
a time value with the data. numComponents gives the number of data components
(1 for scalar data, 3 for vector data, etc.) per entity; if negative, it is automatically
inferred (when possible) from the input data. partition allows one to specify data
in several sub-sets.
Input: tag (integer), step (integer), modelName (string), dataType (string),
tags (vector of sizes), data (vector of vectors of doubles), time = 0.
(double), numComponents = -1 (integer), partition = 0 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (adapt mesh.py, plugin.py, poisson.py, view.py)
gmsh/view/addHomogeneousModelData
Add homogeneous model-based post-processing data to the view with tag tag. The
arguments have the same meaning as in addModelData, except that data is supposed
to be homogeneous and is thus flattened in a single vector. For data types that can
lead to different data sizes per tag (like "ElementNodeData"), the data should be
padded.
Input: tag (integer), step (integer), modelName (string), dataType (string),
tags (vector of sizes), data (vector of doubles), time = 0. (double),
numComponents = -1 (integer), partition = 0 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x4.cpp), Python (x4.py, copy mesh.py, view renumbering.py)
gmsh/view/getModelData
Get model-based post-processing data from the view with tag tag at step step.
Return the data associated to the nodes or the elements with tags tags, as well as
the dataType and the number of components numComponents.
Chapter 6: Gmsh application programming interface 203

Input: tag (integer), step (integer)

Output: dataType (string), tags (vector of sizes), data (vector of vectors of
doubles), time (double), numComponents (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (get data perf.py, mesh quality.py, plugin.py)
gmsh/view/getHomogeneousModelData
Get homogeneous model-based post-processing data from the view with tag tag
at step step. The arguments have the same meaning as in getModelData, except
that data is returned flattened in a single vector, with the appropriate padding if
necessary.
Input: tag (integer), step (integer)
Output: dataType (string), tags (vector of sizes), data (vector of doubles), time
(double), numComponents (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (get data perf.py)
gmsh/view/addListData
Add list-based post-processing data to the view with tag tag. List-based datasets
are independent from any model and any mesh. dataType identifies the data by
concatenating the field type ("S" for scalar, "V" for vector, "T" for tensor) and the
element type ("P" for point, "L" for line, "T" for triangle, "S" for tetrahedron, "I"
for prism, "H" for hexaHedron, "Y" for pyramid). For example dataType should
be "ST" for a scalar field on triangles. numEle gives the number of elements in
the data. data contains the data for the numEle elements, concatenated, with node
coordinates followed by values per node, repeated for each step: [e1x1, ..., e1xn,
e1y1, ..., e1yn, e1z1, ..., e1zn, e1v1..., e1vN, e2x1, ...].
Input: tag (integer), dataType (string), numEle (integer), data (vector of dou-
bles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x3.cpp, x5.cpp), Python (x3.py, x5.py, normals.py,
view combine.py, viewlist.py)
gmsh/view/getListData
Get list-based post-processing data from the view with tag tag. Return the types
dataTypes, the number of elements numElements for each data type and the data
for each data type.
Input: tag (integer)
Output: dataType (vector of strings), numElements (vector of integers), data
(vector of vectors of doubles)
204 Gmsh 4.11.1

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (plugin.py, volume.py)
gmsh/view/addListDataString
Add a string to a list-based post-processing view with tag tag. If coord contains
3 coordinates the string is positioned in the 3D model space ("3D string");
if it contains 2 coordinates it is positioned in the 2D graphics viewport ("2D
string"). data contains one or more (for multistep views) strings. style
contains key-value pairs of styling parameters, concatenated. Available keys
are "Font" (possible values: "Times-Roman", "Times- Bold", "Times-Italic",
"Times-BoldItalic", "Helvetica", "Helvetica-Bold", "Helvetica-Oblique",
"Helvetica-BoldOblique", "Courier", "Courier-Bold", "Courier-Oblique",
"Courier-BoldOblique", "Symbol", "ZapfDingbats", "Screen"), "FontSize" and
"Align" (possible values: "Left" or "BottomLeft", "Center" or "BottomCenter",
"Right" or "BottomRight", "TopLeft", "TopCenter", "TopRight", "CenterLeft",
"CenterCenter", "CenterRight").
Input: tag (integer), coord (vector of doubles), data (vector of strings), style
= [] (vector of strings)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t4.cpp, x3.cpp), Python (t4.py, x3.py)
gmsh/view/getListDataStrings
Get list-based post-processing data strings (2D strings if dim = 2, 3D strings if dim
= 3) from the view with tag tag. Return the coordinates in coord, the strings in
data and the styles in style.
Input: tag (integer), dim (integer)
Output: coord (vector of doubles), data (vector of strings), style (vector of
strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/view/setInterpolationMatrices
Set interpolation matrices for the element family type ("Line", "Triangle", "Quad-
rangle", "Tetrahedron", "Hexahedron", "Prism", "Pyramid") in the view tag. The
approximation of the values over an element is written as a linear combination of d
basis functions f i(u, v, w) = sum (j = 0, ..., d - 1) coef[i][j] u^exp[j][0] v^exp[j][1]
w^exp[j][2], i = 0, ..., d-1, with u, v, w the coordinates in the reference element. The
coef matrix (of size d x d) and the exp matrix (of size d x 3) are stored as vectors,
by row. If dGeo is positive, use coefGeo and expGeo to define the interpolation of
the x, y, z coordinates of the element in terms of the u, v, w coordinates, in exactly
the same way. If d < 0, remove the interpolation matrices.
Chapter 6: Gmsh application programming interface 205

Input: tag (integer), type (string), d (integer), coef (vector of doubles), exp
(vector of doubles), dGeo = 0 (integer), coefGeo = [] (vector of dou-
bles), expGeo = [] (vector of doubles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x3.cpp), Python (x3.py)
gmsh/view/addAlias
Add a post-processing view as an alias of the reference view with tag refTag. If
copyOptions is set, copy the options of the reference view. If tag is positive use it
(and remove the view with that tag if it already exists), otherwise associate a new
tag. Return the view tag.
Input: refTag (integer), copyOptions = False (boolean), tag = -1 (integer)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (view combine.py)
gmsh/view/combine
Combine elements (if what == "elements") or steps (if what == "steps") of all
views (how == "all"), all visible views (how == "visible") or all views having the
same name (how == "name"). Remove original views if remove is set.
Input: what (string), how (string), remove = True (boolean), copyOptions =
True (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (view combine.py)
gmsh/view/probe
Probe the view tag for its values at point (x, y, z). If no match is found, value
is returned empty. Return only the value at step step is step is positive. Re-
turn only values with numComp if numComp is positive. Return the gradient of the
values if gradient is set. If distanceMax is zero, only return a result if an ex-
act match inside an element in the view is found; if distanceMax is positive and
an exact match is not found, return the value at the closest node if it is closer
than distanceMax; if distanceMax is negative and an exact match is not found,
always return the value at the closest node. The distance to the match is returned
in distance. Return the result from the element described by its coordinates if
xElementCoord, yElementCoord and zElementCoord are provided. If dim is >= 0,
return only matches from elements of the specified dimension.
Input: tag (integer), x (double), y (double), z (double), step = -1 (integer),
numComp = -1 (integer), gradient = False (boolean), distanceMax =
206 Gmsh 4.11.1

0. (double), xElemCoord = [] (vector of doubles), yElemCoord = []

(vector of doubles), zElemCoord = [] (vector of doubles), dim = -1 (in-
teger)
Output: values (vector of doubles), distance (double)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x3.cpp), Python (x3.py)
gmsh/view/write
Write the view to a file fileName. The export format is determined by the file
extension. Append to the file if append is set.
Input: tag (integer), fileName (string), append = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (x3.cpp, x4.cpp), Python (x3.py, x4.py, adapt mesh.py,
normals.py, plugin.py, ...)
gmsh/view/setVisibilityPerWindow
Set the global visibility of the view tag per window to value, where windowIndex
identifies the window in the window list.
Input: tag (integer), value (integer), windowIndex = 0 (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia

6.11 Namespace gmsh/view/option: view option handling

functions
gmsh/view/option/setNumber
Set the numerical option name to value value for the view with tag tag.
Input: tag (integer), name (string), value (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t8.cpp, t9.cpp, x3.cpp, x5.cpp), Python (t8.py, t9.py, x3.py, x5.py)
gmsh/view/option/getNumber
Get the value of the numerical option name for the view with tag tag.
Input: tag (integer), name (string)
Output: value (double)
Chapter 6: Gmsh application programming interface 207

Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t8.cpp, x3.cpp), Python (t8.py, x3.py)
gmsh/view/option/setString
Set the string option name to value value for the view with tag tag.
Input: tag (integer), name (string), value (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t4.cpp, t8.cpp), Python (t4.py, t8.py)
gmsh/view/option/getString
Get the value of the string option name for the view with tag tag.
Input: tag (integer), name (string)
Output: value (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/view/option/setColor
Set the color option name to the RGBA value (r, g, b, a) for the view with tag tag,
where where r, g, b and a should be integers between 0 and 255.
Input: tag (integer), name (string), r (integer), g (integer), b (integer), a = 255
(integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/view/option/getColor
Get the r, g, b, a value of the color option name for the view with tag tag.
Input: tag (integer), name (string)
Output: r (integer), g (integer), b (integer), a (integer)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/view/option/copy
Copy the options from the view with tag refTag to the view with tag tag.
Input: refTag (integer), tag (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
208 Gmsh 4.11.1

6.12 Namespace gmsh/plugin: plugin functions

gmsh/plugin/setNumber
Set the numerical option option to the value value for plugin name.
Input: name (string), option (string), value (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t9.cpp, t21.cpp), Python (t9.py, t21.py, adapt mesh.py,
crack3d.py, crack.py, ...)
gmsh/plugin/setString
Set the string option option to the value value for plugin name.
Input: name (string), option (string), value (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t9.cpp), Python (t9.py)
gmsh/plugin/run
Run the plugin name. Return the tag of the created view (if any).
Input: name (string)
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t9.cpp, t21.cpp), Python (t9.py, t21.py, adapt mesh.py,
crack3d.py, crack.py, ...)

6.13 Namespace gmsh/graphics: graphics functions

gmsh/graphics/draw
Draw all the OpenGL scenes.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t8.cpp, t13.cpp, t21.cpp), Python (t3.py, t8.py, t13.py,
t21.py, split window.py)
Chapter 6: Gmsh application programming interface 209

6.14 Namespace gmsh/fltk: FLTK graphical user interface

functions
gmsh/fltk/initialize
Create the FLTK graphical user interface. Can only be called in the main thread.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t8.cpp, t13.cpp, t21.cpp), Python (t3.py, t8.py, t13.py,
t21.py, custom gui.py, ...)
gmsh/fltk/finalize
Close the FLTK graphical user interface. Can only be called in the main thread.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/fltk/wait
Wait at most time seconds for user interface events and return. If time < 0, wait
indefinitely. First automatically create the user interface if it has not yet been
initialized. Can only be called in the main thread.
Input: time = -1. (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t13.cpp, t21.cpp), Python (t3.py, t13.py, t21.py,
custom gui.py, prepro.py, ...)
gmsh/fltk/update
Update the user interface (potentially creating new widgets and windows). First
automatically create the user interface if it has not yet been initialized. Can only
be called in the main thread: use awake("update") to trigger an update of the user
interface from another thread.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (custom gui.py, prepro.py)
gmsh/fltk/awake
Awake the main user interface thread and process pending events, and optionally
perform an action (currently the only action allowed is "update").
210 Gmsh 4.11.1

Input: action = "" (string)

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (custom gui.py)
gmsh/fltk/lock
Block the current thread until it can safely modify the user interface.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (custom gui.py)
gmsh/fltk/unlock
Release the lock that was set using lock.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (custom gui.py)
gmsh/fltk/run
Run the event loop of the graphical user interface, i.e. repeatedly call wait(). First
automatically create the user interface if it has not yet been initialized. Can only
be called in the main thread.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t1.cpp, t2.cpp, t4.cpp, t5.cpp, t6.cpp, ...), Python (t1.py, t2.py,
t4.py, t5.py, t6.py, ...)
gmsh/fltk/isAvailable
Check if the user interface is available (e.g. to detect if it has been closed).
Input: -
Output: -
Return: integer
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 211

Examples: C++ (t3.cpp, t13.cpp, t21.cpp), Python (t3.py, t13.py, t21.py,

custom gui.py, prepro.py, ...)
gmsh/fltk/selectEntities
Select entities in the user interface. Return the selected entities as a vector of (dim,
tag) pairs. If dim is >= 0, return only the entities of the specified dimension (e.g.
points if dim == 0).
Input: dim = -1 (integer)
Output: dimTags (vector of pairs of integers)
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (prepro.py)
gmsh/fltk/selectElements
Select elements in the user interface.
Input: -
Output: elementTags (vector of sizes)
Return: integer
Language-specific definition:
C++, C, Python, Julia
Examples: Python (select elements.py)
gmsh/fltk/selectViews
Select views in the user interface.
Input: -
Output: viewTags (vector of integers)
Return: integer
Language-specific definition:
C++, C, Python, Julia
gmsh/fltk/splitCurrentWindow
Split the current window horizontally (if how = "h") or vertically (if how = "v"),
using ratio ratio. If how = "u", restore a single window.
Input: how = "v" (string), ratio = 0.5 (double)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (split window.py)
gmsh/fltk/setCurrentWindow
Set the current window by speficying its index (starting at 0) in the list of all
windows. When new windows are created by splits, new windows are appended at
the end of the list.
Input: windowIndex = 0 (integer)
212 Gmsh 4.11.1

Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (split window.py)
gmsh/fltk/setStatusMessage
Set a status message in the current window. If graphics is set, display the message
inside the graphic window instead of the status bar.
Input: message (string), graphics = False (boolean)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (prepro.py, select elements.py)
gmsh/fltk/showContextWindow
Show context window for the entity of dimension dim and tag tag.
Input: dim (integer), tag (integer)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (prepro.py)
gmsh/fltk/openTreeItem
Open the name item in the menu tree.
Input: name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (prepro.py)
gmsh/fltk/closeTreeItem
Close the name item in the menu tree.
Input: name (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 6: Gmsh application programming interface 213

6.15 Namespace gmsh/parser: parser functions

gmsh/parser/getNames
Get the names of the variables in the Gmsh parser matching the search regular
expression. If search is empty, return all the names.
Input: search = "" (string)
Output: names (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/parser/setNumber
Set the value of the number variable name in the Gmsh parser. Create the variable
if it does not exist; update the value if the variable exists.
Input: name (string), value (vector of doubles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/parser/setString
Set the value of the string variable name in the Gmsh parser. Create the variable if
it does not exist; update the value if the variable exists.
Input: name (string), value (vector of strings)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/parser/getNumber
Get the value of the number variable name from the Gmsh parser. Return an empty
vector if the variable does not exist.
Input: name (string)
Output: value (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/parser/getString
Get the value of the string variable name from the Gmsh parser. Return an empty
vector if the variable does not exist.
Input: name (string)
Output: value (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
214 Gmsh 4.11.1

gmsh/parser/clear
Clear all the Gmsh parser variables, or remove a single variable if name is given.
Input: name = "" (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
gmsh/parser/parse
Parse the file fileName with the Gmsh parser.
Input: fileName (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia

6.16 Namespace gmsh/onelab: ONELAB server functions

gmsh/onelab/set
Set one or more parameters in the ONELAB database, encoded in format.
Input: data (string), format = "json" (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t13.cpp, t21.cpp), Python (t3.py, t13.py, t21.py,
custom gui.py, onelab test.py, ...)
gmsh/onelab/get
Get all the parameters (or a single one if name is specified) from the ONELAB
database, encoded in format.
Input: name = "" (string), format = "json" (string)
Output: data (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (onelab run auto.py, onelab test.py, prepro.py)
gmsh/onelab/getNames
Get the names of the parameters in the ONELAB database matching the search
regular expression. If search is empty, return all the names.
Input: search = "" (string)
Output: names (vector of strings)
Return: -
Chapter 6: Gmsh application programming interface 215

Language-specific definition:
C++, C, Python, Julia
Examples: Python (prepro.py)
gmsh/onelab/setNumber
Set the value of the number parameter name in the ONELAB database. Create the
parameter if it does not exist; update the value if the parameter exists.
Input: name (string), value (vector of doubles)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: Python (custom gui.py, onelab run.py, onelab test.py)
gmsh/onelab/setString
Set the value of the string parameter name in the ONELAB database. Create the
parameter if it does not exist; update the value if the parameter exists.
Input: name (string), value (vector of strings)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t13.cpp, t21.cpp), Python (t3.py, t13.py, t21.py,
custom gui.py, onelab test.py, ...)
gmsh/onelab/getNumber
Get the value of the number parameter name from the ONELAB database. Return
an empty vector if the parameter does not exist.
Input: name (string)
Output: value (vector of doubles)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t3.cpp, t13.cpp, t21.cpp), Python (t3.py, t13.py, t21.py,
custom gui.py, prepro.py, ...)
gmsh/onelab/getString
Get the value of the string parameter name from the ONELAB database. Return
an empty vector if the parameter does not exist.
Input: name (string)
Output: value (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
216 Gmsh 4.11.1

Examples: C++ (t3.cpp, t13.cpp, t21.cpp), Python (t3.py, t13.py, t21.py,

custom gui.py, prepro.py, ...)

gmsh/onelab/getChanged
Check if any parameters in the ONELAB database used by the client name have
been changed.

Input: name (string)

Output: -

Return: integer

Language-specific definition:
C++, C, Python, Julia

gmsh/onelab/setChanged
Set the changed flag to value value for all the parameters in the ONELAB database
used by the client name.

Input: name (string), value (integer)

Output: -

Return: -

Language-specific definition:
C++, C, Python, Julia

gmsh/onelab/clear
Clear the ONELAB database, or remove a single parameter if name is given.

Input: name = "" (string)

Output: -

Return: -

Language-specific definition:
C++, C, Python, Julia

Examples: Python (onelab test.py)

gmsh/onelab/run
Run a ONELAB client. If name is provided, create a new ONELAB client with
name name and executes command. If not, try to run a client that might be linked
to the processed input files.

Input: name = "" (string), command = "" (string)

Output: -

Return: -

Language-specific definition:
C++, C, Python, Julia

Examples: Python (onelab run.py, onelab run auto.py)

Chapter 6: Gmsh application programming interface 217

6.17 Namespace gmsh/logger: information logging functions

gmsh/logger/write
Write a message. level can be "info", "warning" or "error".
Input: message (string), level = "info" (string)
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t7.cpp, t8.cpp, t9.cpp, t13.cpp, t16.cpp, ...), Python (t8.py, t9.py,
x5.py, custom gui.py, terrain stl.py)
gmsh/logger/start
Start logging messages.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp), Python (t16.py)
gmsh/logger/get
Get logged messages.
Input: -
Output: log (vector of strings)
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp), Python (t16.py)
gmsh/logger/stop
Stop logging messages.
Input: -
Output: -
Return: -
Language-specific definition:
C++, C, Python, Julia
Examples: C++ (t16.cpp), Python (t16.py)
gmsh/logger/getWallTime
Return wall clock time.
Input: -
Output: -
Return: double
218 Gmsh 4.11.1

Language-specific definition:
C++, C, Python, Julia
Examples: Python (import perf.py)
gmsh/logger/getCpuTime
Return CPU time.
Input: -
Output: -
Return: double
Language-specific definition:
C++, C, Python, Julia
gmsh/logger/getLastError
Return last error message, if any.
Input: -
Output: error (string)
Return: -
Language-specific definition:
C++, C, Python, Julia
Chapter 7: Gmsh options 219

7 Gmsh options
This chapter lists all the Gmsh options. Options can be specified in script files (see
Section 5.1 [General scripting commands], page 89) or using the API (see Section 6.2 [Names-
pace gmsh/option], page 126): see Section 2.3 [t3], page 21 for an example. They can also be
specified on the command line using the -setnumber and -setstring switches: see Chapter 4
[Gmsh command-line interface], page 83. Many options can also be changed interactively in the
GUI (see Chapter 3 [Gmsh graphical user interface], page 77): to see which option corresponds
to which widget in the GUI, leave your mouse on the widget and a tooltip with the option
name will appear. Note that some options can affect the GUI in real time: loading a script file
that sets General.GraphicsWidth for example (see Section 7.1 [General options], page 219) will
change the width of the graphic window at runtime.
Gmsh’s default behavior is to save some of these options in a per-user “session resource” file (cf.
“Saved in: General.SessionFileName” in the option descriptions below) every time Gmsh is
shut down. This permits for example to automatically remember the size and location of the
windows or which fonts to use. A second set of options can be saved (automatically or manually
with the ‘File->Save Options As Default’ menu) in a per-user “option” file (cf. “Saved in:
General.OptionsFileName” in the descriptions below), automatically loaded by Gmsh every
time it starts up. Finally, other options are only saved to disk manually, either by explicitly
saving an option file with ‘File->Export’, or when saving per-model options with ‘File->Save
Model Options’ (cf. “Saved in: -” in the lists below). Per-model options are saved in a file
name matching the model file, but with an extra ‘.opt’ extension appended: the option file will
be automatically opened after Gmsh opens the model file.
Gmsh will attempt to save and load the session and option files first in the $GMSH_HOME directory,
then in $APPDATA (on Windows) or $HOME (on other OSes), then in $TMP, and finally in $TEMP,
in that order. If none of these variables are defined, Gmsh will try to save and load the files
from the current working directory.
To reset all options to their default values, either delete the General.SessionFileName and
General.OptionsFileName files by hand, use ‘Help->Restore All Options to Default Settings’,
or click on ‘Restore all options to default settings’ button in the ‘Tools->Options->General-
>Advanced’ window.

7.1 General options

General.AxesFormatX
Number format for X-axis (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
General.AxesFormatY
Number format for Y-axis (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
General.AxesFormatZ
Number format for Z-axis (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
General.AxesLabelX
X-axis label
Default value: ""
Saved in: General.OptionsFileName
220 Gmsh 4.11.1

General.AxesLabelY
Y-axis label
Default value: ""
Saved in: General.OptionsFileName

General.AxesLabelZ
Z-axis label
Default value: ""
Saved in: General.OptionsFileName

General.BackgroundImageFileName
Background image file in JPEG, PNG or PDF format
Default value: ""
Saved in: General.OptionsFileName

General.BuildInfo
Gmsh build information (read-only)
Default value: "Version: 4.11.1-git-516d090cd; License: GNU General
Public License; Build OS: MacOSX-sdk; Build date: 20221205; Build host:
MacBook-Pro-Christophe.local; Build options: 64Bit ALGLIB[contrib]
ANN[contrib] Bamg Blas[petsc] Blossom Cairo Cgns DIntegration
Dlopen DomHex Eigen[contrib] Fltk GMP Gmm[contrib] Hxt Jpeg Kbipack
Lapack[petsc] MathEx[contrib] Med Mesh Metis[contrib] Mmg Mpeg
Netgen ONELAB ONELABMetamodel OpenCASCADE OpenCASCADE-CAF OpenGL
OpenMP OptHom PETSc Parasolid ParasolidSTEP Parser Plugins Png Post
QuadMeshingTools QuadTri Solver TetGen/BR TouchBar Voro++[contrib]
WinslowUntangler Zlib; FLTK version: 1.4.0; PETSc version: 3.14.4
(complex arithmtic); OCC version: 7.8.0; MED version: 4.1.0;
Packaged by: geuzaine; Web site: https://gmsh.info; Issue tracker:
https://gitlab.onelab.info/gmsh/gmsh/issues"
Saved in: -

General.BuildOptions
Gmsh build options (read-only)
Default value: "64Bit ALGLIB[contrib] ANN[contrib] Bamg Blas[petsc]
Blossom Cairo Cgns DIntegration Dlopen DomHex Eigen[contrib] Fltk GMP
Gmm[contrib] Hxt Jpeg Kbipack Lapack[petsc] MathEx[contrib] Med Mesh
Metis[contrib] Mmg Mpeg Netgen ONELAB ONELABMetamodel OpenCASCADE
OpenCASCADE-CAF OpenGL OpenMP OptHom PETSc Parasolid ParasolidSTEP
Parser Plugins Png Post QuadMeshingTools QuadTri Solver TetGen/BR
TouchBar Voro++[contrib] WinslowUntangler Zlib"
Saved in: -

General.DefaultFileName
Default project file name
Default value: "untitled.geo"
Saved in: General.OptionsFileName

General.Display
X server to use (only for Unix versions)
Default value: ""
Saved in: -
Chapter 7: Gmsh options 221

General.ErrorFileName
File into which the log is saved if a fatal error occurs
Default value: ".gmsh-errors"
Saved in: General.OptionsFileName
General.ExecutableFileName
File name of the Gmsh executable (read-only)
Default value: ""
Saved in: General.SessionFileName
General.FileName
Current project file name (read-only)
Default value: ""
Saved in: -
General.FltkTheme
FLTK user interface theme (try e.g. plastic or gtk+)
Default value: ""
Saved in: General.SessionFileName
General.GraphicsFont
Font used in the graphic window
Default value: "Helvetica"
Saved in: General.OptionsFileName
General.GraphicsFontEngine
Set graphics font engine (Native, StringTexture, Cairo)
Default value: "Native"
Saved in: General.OptionsFileName
General.GraphicsFontTitle
Font used in the graphic window for titles
Default value: "Helvetica"
Saved in: General.OptionsFileName
General.OptionsFileName
Option file created with ‘Tools->Options->Save’; automatically read on startup
Default value: ".gmsh-options"
Saved in: General.SessionFileName
General.RecentFile0
Most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName
General.RecentFile1
2nd most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName
General.RecentFile2
3rd most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName
General.RecentFile3
4th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName
222 Gmsh 4.11.1

General.RecentFile4
5th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName

General.RecentFile5
6th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName

General.RecentFile6
7th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName

General.RecentFile7
8th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName

General.RecentFile8
9th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName

General.RecentFile9
10th most recent opened file
Default value: "untitled.geo"
Saved in: General.SessionFileName

General.SessionFileName
Option file into which session specific information is saved; automatically read on
startup
Default value: ".gmshrc"
Saved in: -

General.ScriptingLanguages
Language(s) in which scripting commands generated by the GUI are written
Default value: "geo"
Saved in: General.OptionsFileName

General.TextEditor
System command to launch a text editor
Default value: "open -t ’%s’"
Saved in: General.OptionsFileName

General.TmpFileName
Temporary file used by the geometry module
Default value: ".gmsh-tmp"
Saved in: General.SessionFileName

General.Version
Gmsh version (read-only)
Default value: "4.11.1-git-516d090cd"
Saved in: -
Chapter 7: Gmsh options 223

General.WatchFilePattern
Pattern of files to merge as they become available
Default value: ""
Saved in: -

General.AbortOnError
Abort on error? (0: no, 1: abort meshing, 2: throw an exception unless in interactive
mode, 3: throw an exception always, 4: exit)
Default value: 0
Saved in: General.OptionsFileName

General.AlphaBlending
Enable alpha blending (transparency) in post-processing views
Default value: 1
Saved in: General.OptionsFileName

General.Antialiasing
Use multisample antialiasing (will slow down rendering)
Default value: 0
Saved in: General.OptionsFileName

General.ArrowHeadRadius
Relative radius of arrow head
Default value: 0.12
Saved in: General.OptionsFileName

General.ArrowStemLength
Relative length of arrow stem
Default value: 0.56
Saved in: General.OptionsFileName

General.ArrowStemRadius
Relative radius of arrow stem
Default value: 0.02
Saved in: General.OptionsFileName

General.Axes
Axes (0: none, 1: simple axes, 2: box, 3: full grid, 4: open grid, 5: ruler)
Default value: 0
Saved in: General.OptionsFileName

General.AxesMikado
Mikado axes style
Default value: 0
Saved in: General.OptionsFileName

General.AxesAutoPosition
Position the axes automatically
Default value: 1
Saved in: General.OptionsFileName

General.AxesForceValue
Force values on axes (otherwise use natural coordinates)
Default value: 0
Saved in: General.OptionsFileName
224 Gmsh 4.11.1

General.AxesMaxX
Maximum X-axis coordinate
Default value: 1
Saved in: General.OptionsFileName
General.AxesMaxY
Maximum Y-axis coordinate
Default value: 1
Saved in: General.OptionsFileName
General.AxesMaxZ
Maximum Z-axis coordinate
Default value: 1
Saved in: General.OptionsFileName
General.AxesMinX
Minimum X-axis coordinate
Default value: 0
Saved in: General.OptionsFileName
General.AxesMinY
Minimum Y-axis coordinate
Default value: 0
Saved in: General.OptionsFileName
General.AxesMinZ
Minimum Z-axis coordinate
Default value: 0
Saved in: General.OptionsFileName
General.AxesTicsX
Number of tics on the X-axis
Default value: 5
Saved in: General.OptionsFileName
General.AxesTicsY
Number of tics on the Y-axis
Default value: 5
Saved in: General.OptionsFileName
General.AxesTicsZ
Number of tics on the Z-axis
Default value: 5
Saved in: General.OptionsFileName
General.AxesValueMaxX
Maximum X-axis forced value
Default value: 1
Saved in: General.OptionsFileName
General.AxesValueMaxY
Maximum Y-axis forced value
Default value: 1
Saved in: General.OptionsFileName
General.AxesValueMaxZ
Maximum Z-axis forced value
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 225

General.AxesValueMinX
Minimum X-axis forced value
Default value: 0
Saved in: General.OptionsFileName

General.AxesValueMinY
Minimum Y-axis forced value
Default value: 0
Saved in: General.OptionsFileName

General.AxesValueMinZ
Minimum Z-axis forced value
Default value: 0
Saved in: General.OptionsFileName

General.BackgroundGradient
Draw background gradient (0: none, 1: vertical, 2: horizontal, 3: radial)
Default value: 1
Saved in: General.OptionsFileName

General.BackgroundImage3D
Create background image in the 3D model (units = model units) or as 2D back-
ground (units = pixels)
Default value: 0
Saved in: General.OptionsFileName

General.BackgroundImagePage
Page to render in the background image (for multi-page PDFs)
Default value: 0
Saved in: General.OptionsFileName

General.BackgroundImagePositionX
X position of background image (for 2D background: < 0: measure from right
window edge; >= 1e5: centered)
Default value: 0
Saved in: General.OptionsFileName

General.BackgroundImagePositionY
Y position of background image (for 2D background: < 0: measure from bottom
window edge; >= 1e5: centered)
Default value: 0
Saved in: General.OptionsFileName

General.BackgroundImageWidth
Width of background image (0: actual width if height = 0, natural scaling if not;
-1: graphic window width)
Default value: -1
Saved in: General.OptionsFileName

General.BackgroundImageHeight
Height of background image (0: actual height if width = 0, natural scaling if not;
-1: graphic window height)
Default value: -1
Saved in: General.OptionsFileName
226 Gmsh 4.11.1

General.BoundingBoxSize
Overall bounding box size (read-only)
Default value: 1
Saved in: General.OptionsFileName
General.Camera
Enable camera view mode
Default value: 0
Saved in: General.OptionsFileName
General.CameraAperture
Camera aperture in degrees
Default value: 40
Saved in: General.OptionsFileName
General.CameraEyeSeparationRatio
Eye separation ratio in % for stereo rendering
Default value: 1.5
Saved in: General.OptionsFileName
General.CameraFocalLengthRatio
Camera Focal length ratio
Default value: 1
Saved in: General.OptionsFileName
General.Clip0A
First coefficient in equation for clipping plane 0 (‘A’ in ‘AX+BY+CZ+D=0’)
Default value: 1
Saved in: -
General.Clip0B
Second coefficient in equation for clipping plane 0 (‘B’ in ‘AX+BY+CZ+D=0’)
Default value: 0
Saved in: -
General.Clip0C
Third coefficient in equation for clipping plane 0 (‘C’ in ‘AX+BY+CZ+D=0’)
Default value: 0
Saved in: -
General.Clip0D
Fourth coefficient in equation for clipping plane 0 (‘D’ in ‘AX+BY+CZ+D=0’)
Default value: 0
Saved in: -
General.Clip1A
First coefficient in equation for clipping plane 1
Default value: 0
Saved in: -
General.Clip1B
Second coefficient in equation for clipping plane 1
Default value: 1
Saved in: -
General.Clip1C
Third coefficient in equation for clipping plane 1
Default value: 0
Saved in: -
Chapter 7: Gmsh options 227

General.Clip1D
Fourth coefficient in equation for clipping plane 1
Default value: 0
Saved in: -
General.Clip2A
First coefficient in equation for clipping plane 2
Default value: 0
Saved in: -
General.Clip2B
Second coefficient in equation for clipping plane 2
Default value: 0
Saved in: -
General.Clip2C
Third coefficient in equation for clipping plane 2
Default value: 1
Saved in: -
General.Clip2D
Fourth coefficient in equation for clipping plane 2
Default value: 0
Saved in: -
General.Clip3A
First coefficient in equation for clipping plane 3
Default value: -1
Saved in: -
General.Clip3B
Second coefficient in equation for clipping plane 3
Default value: 0
Saved in: -
General.Clip3C
Third coefficient in equation for clipping plane 3
Default value: 0
Saved in: -
General.Clip3D
Fourth coefficient in equation for clipping plane 3
Default value: 1
Saved in: -
General.Clip4A
First coefficient in equation for clipping plane 4
Default value: 0
Saved in: -
General.Clip4B
Second coefficient in equation for clipping plane 4
Default value: -1
Saved in: -
General.Clip4C
Third coefficient in equation for clipping plane 4
Default value: 0
Saved in: -
228 Gmsh 4.11.1

General.Clip4D
Fourth coefficient in equation for clipping plane 4
Default value: 1
Saved in: -

General.Clip5A
First coefficient in equation for clipping plane 5
Default value: 0
Saved in: -

General.Clip5B
Second coefficient in equation for clipping plane 5
Default value: 0
Saved in: -

General.Clip5C
Third coefficient in equation for clipping plane 5
Default value: -1
Saved in: -

General.Clip5D
Fourth coefficient in equation for clipping plane 5
Default value: 1
Saved in: -

General.ClipFactor
Near and far clipping plane distance factor (decrease value for better z-buffer reso-
lution)
Default value: 5
Saved in: -

General.ClipOnlyDrawIntersectingVolume
Only draw layer of elements that intersect the clipping plane
Default value: 0
Saved in: General.OptionsFileName

General.ClipOnlyVolume
Only clip volume elements
Default value: 0
Saved in: General.OptionsFileName

General.ClipPositionX
Horizontal position (in pixels) of the upper left corner of the clipping planes window
Default value: 650
Saved in: General.SessionFileName

General.ClipPositionY
Vertical position (in pixels) of the upper left corner of the clipping planes window
Default value: 150
Saved in: General.SessionFileName

General.ClipWholeElements
Clip whole elements
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 229

General.ColorScheme
Default color scheme for graphics (0: light, 1: default, 2: grayscale, 3: dark)
Default value: 1
Saved in: General.SessionFileName

General.ConfirmOverwrite
Ask confirmation before overwriting files?
Default value: 1
Saved in: General.OptionsFileName

General.ContextPositionX
Horizontal position (in pixels) of the upper left corner of the contextual windows
Default value: 650
Saved in: General.SessionFileName

General.ContextPositionY
Vertical position (in pixels) of the upper left corner of the contextual windows
Default value: 150
Saved in: General.SessionFileName

General.DetachedMenu
Should the menu window be detached from the graphic window?
Default value: 0
Saved in: General.SessionFileName

General.DetachedProcess
On Windows, should processes created by Gmsh be detached?
Default value: 1
Saved in: General.OptionsFileName

General.DisplayBorderFactor
Border factor for model display (0: model fits window size exactly)
Default value: 0.2
Saved in: General.OptionsFileName

General.DoubleBuffer
Use a double buffered graphic window (on Unix, should be set to 0 when working
on a remote host without GLX)
Default value: 1
Saved in: General.OptionsFileName

General.DrawBoundingBoxes
Draw bounding boxes
Default value: 0
Saved in: General.OptionsFileName

General.ExpertMode
Enable expert mode (to disable all the messages meant for inexperienced users)
Default value: 0
Saved in: General.OptionsFileName

General.ExtraPositionX
Horizontal position (in pixels) of the upper left corner of the generic extra window
Default value: 650
Saved in: General.SessionFileName
230 Gmsh 4.11.1

General.ExtraPositionY
Vertical position (in pixels) of the upper left corner of the generic extra window
Default value: 350
Saved in: General.SessionFileName
General.ExtraHeight
Height (in pixels) of the generic extra window
Default value: 100
Saved in: General.SessionFileName
General.ExtraWidth
Width (in pixels) of the generic extra window
Default value: 100
Saved in: General.SessionFileName
General.FastRedraw
Draw simplified model while rotating, panning and zooming
Default value: 0
Saved in: General.OptionsFileName
General.FieldPositionX
Horizontal position (in pixels) of the upper left corner of the field window
Default value: 650
Saved in: General.SessionFileName
General.FieldPositionY
Vertical position (in pixels) of the upper left corner of the field window
Default value: 550
Saved in: General.SessionFileName
General.FieldHeight
Height (in pixels) of the field window
Default value: 320
Saved in: General.SessionFileName
General.FieldWidth
Width (in pixels) of the field window
Default value: 420
Saved in: General.SessionFileName
General.FileChooserPositionX
Horizontal position (in pixels) of the upper left corner of the file chooser windows
Default value: 200
Saved in: General.SessionFileName
General.FileChooserPositionY
Vertical position (in pixels) of the upper left corner of the file chooser windows
Default value: 200
Saved in: General.SessionFileName
General.FltkColorScheme
FLTK user interface color theme (0: standard, 1:dark)
Default value: 0
Saved in: General.SessionFileName
General.FltkRefreshRate
FLTK user interface maximum refresh rate, per second (0: no limit)
Default value: 5
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 231

General.FontSize
Size of the font in the user interface, in pixels (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
General.GraphicsFontSize
Size of the font in the graphic window, in pixels
Default value: 15
Saved in: General.OptionsFileName
General.GraphicsFontSizeTitle
Size of the font in the graphic window for titles, in pixels
Default value: 18
Saved in: General.OptionsFileName
General.GraphicsHeight
Height (in pixels) of the graphic window
Default value: 600
Saved in: General.SessionFileName
General.GraphicsPositionX
Horizontal position (in pixels) of the upper left corner of the graphic window
Default value: 50
Saved in: General.SessionFileName
General.GraphicsPositionY
Vertical position (in pixels) of the upper left corner of the graphic window
Default value: 50
Saved in: General.SessionFileName
General.GraphicsWidth
Width (in pixels) of the graphic window
Default value: 800
Saved in: General.SessionFileName
General.HighOrderToolsPositionX
Horizontal position (in pixels) of the upper left corner of the high-order tools window
Default value: 650
Saved in: General.SessionFileName
General.HighOrderToolsPositionY
Vertical position (in pixels) of the upper left corner of the high-order tools window
Default value: 150
Saved in: General.SessionFileName
General.HighResolutionGraphics
Use high-resolution OpenGL graphics (e.g. for Macs with retina displays)
Default value: 1
Saved in: General.OptionsFileName
General.InitialModule
Module launched on startup (0: automatic, 1: geometry, 2: mesh, 3: solver, 4:
post-processing)
Default value: 0
Saved in: General.OptionsFileName
General.InputScrolling
Enable numerical input scrolling in user interface (moving the mouse to change
numbers)
232 Gmsh 4.11.1

Default value: 1
Saved in: General.OptionsFileName
General.Light0
Enable light source 0
Default value: 1
Saved in: General.OptionsFileName
General.Light0X
X position of light source 0
Default value: 0.65
Saved in: General.OptionsFileName
General.Light0Y
Y position of light source 0
Default value: 0.65
Saved in: General.OptionsFileName
General.Light0Z
Z position of light source 0
Default value: 1
Saved in: General.OptionsFileName
General.Light0W
Divisor of the X, Y and Z coordinates of light source 0 (W=0 means infinitely far
source)
Default value: 0
Saved in: General.OptionsFileName
General.Light1
Enable light source 1
Default value: 0
Saved in: General.OptionsFileName
General.Light1X
X position of light source 1
Default value: 0.5
Saved in: General.OptionsFileName
General.Light1Y
Y position of light source 1
Default value: 0.3
Saved in: General.OptionsFileName
General.Light1Z
Z position of light source 1
Default value: 1
Saved in: General.OptionsFileName
General.Light1W
Divisor of the X, Y and Z coordinates of light source 1 (W=0 means infinitely far
source)
Default value: 0
Saved in: General.OptionsFileName
General.Light2
Enable light source 2
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 233

General.Light2X
X position of light source 2
Default value: 0.5
Saved in: General.OptionsFileName
General.Light2Y
Y position of light source 2
Default value: 0.3
Saved in: General.OptionsFileName
General.Light2Z
Z position of light source 2
Default value: 1
Saved in: General.OptionsFileName
General.Light2W
Divisor of the X, Y and Z coordinates of light source 2 (W=0 means infinitely far
source)
Default value: 0
Saved in: General.OptionsFileName
General.Light3
Enable light source 3
Default value: 0
Saved in: General.OptionsFileName
General.Light3X
X position of light source 3
Default value: 0.5
Saved in: General.OptionsFileName
General.Light3Y
Y position of light source 3
Default value: 0.3
Saved in: General.OptionsFileName
General.Light3Z
Z position of light source 3
Default value: 1
Saved in: General.OptionsFileName
General.Light3W
Divisor of the X, Y and Z coordinates of light source 3 (W=0 means infinitely far
source)
Default value: 0
Saved in: General.OptionsFileName
General.Light4
Enable light source 4
Default value: 0
Saved in: General.OptionsFileName
General.Light4X
X position of light source 4
Default value: 0.5
Saved in: General.OptionsFileName
234 Gmsh 4.11.1

General.Light4Y
Y position of light source 4
Default value: 0.3
Saved in: General.OptionsFileName
General.Light4Z
Z position of light source 4
Default value: 1
Saved in: General.OptionsFileName
General.Light4W
Divisor of the X, Y and Z coordinates of light source 4 (W=0 means infinitely far
source)
Default value: 0
Saved in: General.OptionsFileName
General.Light5
Enable light source 5
Default value: 0
Saved in: General.OptionsFileName
General.Light5X
X position of light source 5
Default value: 0.5
Saved in: General.OptionsFileName
General.Light5Y
Y position of light source 5
Default value: 0.3
Saved in: General.OptionsFileName
General.Light5Z
Z position of light source 5
Default value: 1
Saved in: General.OptionsFileName
General.Light5W
Divisor of the X, Y and Z coordinates of light source 5 (W=0 means infinitely far
source)
Default value: 0
Saved in: General.OptionsFileName
General.LineWidth
Display width of lines (in pixels)
Default value: 1
Saved in: General.OptionsFileName
General.ManipulatorPositionX
Horizontal position (in pixels) of the upper left corner of the manipulator window
Default value: 650
Saved in: General.SessionFileName
General.ManipulatorPositionY
Vertical position (in pixels) of the upper left corner of the manipulator window
Default value: 150
Saved in: General.SessionFileName
Chapter 7: Gmsh options 235

General.MaxX
Maximum model coordinate along the X-axis (read-only)
Default value: 0
Saved in: -
General.MaxY
Maximum model coordinate along the Y-axis (read-only)
Default value: 0
Saved in: -
General.MaxZ
Maximum model coordinate along the Z-axis (read-only)
Default value: 0
Saved in: -
General.MenuWidth
Width (in pixels) of the menu tree
Default value: 200
Saved in: General.SessionFileName
General.MenuHeight
Height (in pixels) of the (detached) menu tree
Default value: 200
Saved in: General.SessionFileName
General.MenuPositionX
Horizontal position (in pixels) of the (detached) menu tree
Default value: 400
Saved in: General.SessionFileName
General.MenuPositionY
Vertical position (in pixels) of the (detached) menu tree
Default value: 400
Saved in: General.SessionFileName
General.MessageFontSize
Size of the font in the message window, in pixels (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
General.MessageHeight
Height (in pixels) of the message console when it is visible (should be > 0)
Default value: 300
Saved in: General.SessionFileName
General.MinX
Minimum model coordinate along the X-axis (read-only)
Default value: 0
Saved in: -
General.MinY
Minimum model coordinate along the Y-axis (read-only)
Default value: 0
Saved in: -
General.MinZ
Minimum model coordinate along the Z-axis (read-only)
Default value: 0
Saved in: -
236 Gmsh 4.11.1

General.MouseHoverMeshes
Enable mouse hover on meshes
Default value: 0
Saved in: General.OptionsFileName

General.MouseSelection
Enable mouse selection
Default value: 1
Saved in: General.OptionsFileName

General.MouseInvertZoom
Invert mouse wheel zoom direction
Default value: 0
Saved in: General.OptionsFileName

General.NativeFileChooser
Use the native file chooser?
Default value: 1
Saved in: General.SessionFileName

General.NonModalWindows
Force all control windows to be on top of the graphic window ("non-modal")
Default value: 1
Saved in: General.SessionFileName

General.NoPopup
Disable interactive dialog windows in scripts (and use default values instead)
Default value: 0
Saved in: General.OptionsFileName

General.NumThreads
Maximum number of threads used by Gmsh when compiled with OpenMP support
(0: use system default, i.e. OMP NUM THREADS)
Default value: 1
Saved in: General.OptionsFileName

General.OptionsPositionX
Horizontal position (in pixels) of the upper left corner of the option window
Default value: 650
Saved in: General.SessionFileName

General.OptionsPositionY
Vertical position (in pixels) of the upper left corner of the option window
Default value: 150
Saved in: General.SessionFileName

General.Orthographic
Orthographic projection mode (0: perspective projection)
Default value: 1
Saved in: General.OptionsFileName

General.PluginPositionX
Horizontal position (in pixels) of the upper left corner of the plugin window
Default value: 650
Saved in: General.SessionFileName
Chapter 7: Gmsh options 237

General.PluginPositionY
Vertical position (in pixels) of the upper left corner of the plugin window
Default value: 550
Saved in: General.SessionFileName
General.PluginHeight
Height (in pixels) of the plugin window
Default value: 320
Saved in: General.SessionFileName
General.PluginWidth
Width (in pixels) of the plugin window
Default value: 420
Saved in: General.SessionFileName
General.PointSize
Display size of points (in pixels)
Default value: 3
Saved in: General.OptionsFileName
General.PolygonOffsetAlwaysOn
Always apply polygon offset, instead of trying to detect when it is required
Default value: 0
Saved in: General.OptionsFileName
General.PolygonOffsetFactor
Polygon offset factor (offset = factor * DZ + r * units)
Default value: 0.5
Saved in: General.OptionsFileName
General.PolygonOffsetUnits
Polygon offset units (offset = factor * DZ + r * units)
Default value: 1
Saved in: General.OptionsFileName
General.ProgressMeterStep
Increment (in percent) of the progress meter bar
Default value: 10
Saved in: General.OptionsFileName
General.QuadricSubdivisions
Number of subdivisions used to draw points or lines as spheres or cylinders
Default value: 6
Saved in: General.OptionsFileName
General.RotationX
First Euler angle (used if Trackball=0)
Default value: 0
Saved in: -
General.RotationY
Second Euler angle (used if Trackball=0)
Default value: 0
Saved in: -
General.RotationZ
Third Euler angle (used if Trackball=0)
Default value: 0
Saved in: -
238 Gmsh 4.11.1

General.RotationCenterGravity
Rotate around the (pseudo) center of mass instead of (RotationCenterX, Rotation-
CenterY, RotationCenterZ)
Default value: 1
Saved in: General.OptionsFileName
General.RotationCenterX
X coordinate of the center of rotation
Default value: 0
Saved in: -
General.RotationCenterY
Y coordinate of the center of rotation
Default value: 0
Saved in: -
General.RotationCenterZ
Z coordinate of the center of rotation
Default value: 0
Saved in: -
General.SaveOptions
Automatically save current options in General.OptionsFileName (1) or per model
(2)when the graphical user interface is closed?
Default value: 0
Saved in: General.SessionFileName
General.SaveSession
Automatically save session specific information in General.SessionFileName when
the graphical user interface is closed?
Default value: 1
Saved in: General.SessionFileName
General.ScaleX
X-axis scale factor
Default value: 1
Saved in: -
General.ScaleY
Y-axis scale factor
Default value: 1
Saved in: -
General.ScaleZ
Z-axis scale factor
Default value: 1
Saved in: -
General.Shininess
Material shininess
Default value: 0.4
Saved in: General.OptionsFileName
General.ShininessExponent
Material shininess exponent (between 0 and 128)
Default value: 40
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 239

General.ShowModuleMenu
Show the standard Gmsh menu in the tree
Default value: 1
Saved in: General.OptionsFileName
General.ShowOptionsOnStartup
Show option window on startup
Default value: 0
Saved in: General.OptionsFileName
General.ShowMessagesOnStartup
Show message window on startup
Default value: 0
Saved in: General.OptionsFileName
General.SmallAxes
Display the small axes
Default value: 1
Saved in: General.OptionsFileName
General.SmallAxesPositionX
X position (in pixels) of small axes (< 0: measure from right window edge; >= 1e5:
centered)
Default value: -60
Saved in: General.OptionsFileName
General.SmallAxesPositionY
Y position (in pixels) of small axes (< 0: measure from bottom window edge; >=
1e5: centered)
Default value: -40
Saved in: General.OptionsFileName
General.SmallAxesSize
Size (in pixels) of small axes
Default value: 30
Saved in: General.OptionsFileName
General.StatisticsPositionX
Horizontal position (in pixels) of the upper left corner of the statistic window
Default value: 650
Saved in: General.SessionFileName
General.StatisticsPositionY
Vertical position (in pixels) of the upper left corner of the statistic window
Default value: 150
Saved in: General.SessionFileName
General.Stereo
Use stereo rendering
Default value: 0
Saved in: General.OptionsFileName
General.SystemMenuBar
Use the system menu bar on macOS?
Default value: 1
Saved in: General.SessionFileName
240 Gmsh 4.11.1

General.Terminal
Should information be printed on the terminal (if available)?
Default value: 0
Saved in: General.OptionsFileName
General.Tooltips
Show tooltips in the user interface
Default value: 1
Saved in: General.OptionsFileName
General.Trackball
Use trackball rotation mode
Default value: 1
Saved in: General.OptionsFileName
General.TrackballHyperbolicSheet
Use hyperbolic sheet away from trackball center for z-rotations
Default value: 1
Saved in: General.OptionsFileName
General.TrackballQuaternion0
First trackball quaternion component (used if General.Trackball=1)
Default value: 0
Saved in: -
General.TrackballQuaternion1
Second trackball quaternion component (used if General.Trackball=1)
Default value: 0
Saved in: -
General.TrackballQuaternion2
Third trackball quaternion component (used if General.Trackball=1)
Default value: 0
Saved in: -
General.TrackballQuaternion3
Fourth trackball quaternion component (used if General.Trackball=1)
Default value: 1
Saved in: -
General.TranslationX
X-axis translation (in model units)
Default value: 0
Saved in: -
General.TranslationY
Y-axis translation (in model units)
Default value: 0
Saved in: -
General.TranslationZ
Z-axis translation (in model units)
Default value: 0
Saved in: -
General.VectorType
Default vector display type (for normals, etc.)
Default value: 4
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 241

General.Verbosity
Level of information printed on the terminal and the message console (0: silent
except for fatal errors, 1: +errors, 2: +warnings, 3: +direct, 4: +information, 5:
+status, 99: +debug)
Default value: 5
Saved in: General.OptionsFileName
General.VisibilityPositionX
Horizontal position (in pixels) of the upper left corner of the visibility window
Default value: 650
Saved in: General.SessionFileName
General.VisibilityPositionY
Vertical position (in pixels) of the upper left corner of the visibility window
Default value: 150
Saved in: General.SessionFileName
General.ZoomFactor
Middle mouse button zoom acceleration factor
Default value: 4
Saved in: General.OptionsFileName
General.Color.Background
Background color
Default value: {255,255,255}
Saved in: General.OptionsFileName
General.Color.BackgroundGradient
Background gradient color
Default value: {208,215,255}
Saved in: General.OptionsFileName
General.Color.Foreground
Foreground color
Default value: {85,85,85}
Saved in: General.OptionsFileName
General.Color.Text
Text color
Default value: {0,0,0}
Saved in: General.OptionsFileName
General.Color.Axes
Axes color
Default value: {0,0,0}
Saved in: General.OptionsFileName
General.Color.SmallAxes
Small axes color
Default value: {0,0,0}
Saved in: General.OptionsFileName
General.Color.AmbientLight
Ambient light color
Default value: {25,25,25}
Saved in: General.OptionsFileName
242 Gmsh 4.11.1

General.Color.DiffuseLight
Diffuse light color
Default value: {255,255,255}
Saved in: General.OptionsFileName
General.Color.SpecularLight
Specular light color
Default value: {255,255,255}
Saved in: General.OptionsFileName

7.2 Print options

Print.ParameterCommand
Command parsed when the print parameter is changed
Default value: "Mesh.Clip=1; View.Clip=1; General.ClipWholeElements=1;
General.Clip0D=Print.Parameter; SetChanged;"
Saved in: General.OptionsFileName
Print.Parameter
Current value of the print parameter
Default value: 0
Saved in: General.OptionsFileName
Print.ParameterFirst
First value of print parameter in loop
Default value: -1
Saved in: General.OptionsFileName
Print.ParameterLast
Last value of print parameter in loop
Default value: 1
Saved in: General.OptionsFileName
Print.ParameterSteps
Number of steps in loop over print parameter
Default value: 10
Saved in: General.OptionsFileName
Print.Background
Print background (gradient and image)?
Default value: 0
Saved in: General.OptionsFileName
Print.CompositeWindows
Composite all window tiles in the same output image (for bitmap output only)
Default value: 0
Saved in: General.OptionsFileName
Print.DeleteTemporaryFiles
Delete temporary files used during printing
Default value: 1
Saved in: General.OptionsFileName
Print.EpsBestRoot
Try to minimize primitive splitting in BSP tree sorted PostScript/PDF output
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 243

Print.EpsCompress
Compress PostScript/PDF output using zlib
Default value: 0
Saved in: General.OptionsFileName

Print.EpsLineWidthFactor
Width factor for lines in PostScript/PDF output
Default value: 1
Saved in: General.OptionsFileName

Print.EpsOcclusionCulling
Cull occluded primitives (to reduce PostScript/PDF file size)
Default value: 1
Saved in: General.OptionsFileName

Print.EpsPointSizeFactor
Size factor for points in PostScript/PDF output
Default value: 1
Saved in: General.OptionsFileName

Print.EpsPS3Shading
Enable PostScript Level 3 shading
Default value: 0
Saved in: General.OptionsFileName

Print.EpsQuality
PostScript/PDF quality (0: bitmap, 1: vector (simple sort), 2: vector (accurate
sort), 3: vector (unsorted)
Default value: 1
Saved in: General.OptionsFileName

Print.Format
File format (10: automatic)
Default value: 10
Saved in: General.OptionsFileName

Print.GeoLabels
Save labels in unrolled Gmsh geometries
Default value: 1
Saved in: General.OptionsFileName

Print.GeoOnlyPhysicals
Only save entities that belong to physical groups
Default value: 0
Saved in: General.OptionsFileName

Print.GifDither
Apply dithering to GIF output
Default value: 0
Saved in: General.OptionsFileName

Print.GifInterlace
Interlace GIF output
Default value: 0
Saved in: General.OptionsFileName
244 Gmsh 4.11.1

Print.GifSort
Sort the colormap in GIF output
Default value: 1
Saved in: General.OptionsFileName

Print.GifTransparent
Output transparent GIF image
Default value: 0
Saved in: General.OptionsFileName

Print.Height
Height of printed image; use (possibly scaled) current height if < 0
Default value: -1
Saved in: General.OptionsFileName

Print.JpegQuality
JPEG quality (between 1 and 100)
Default value: 100
Saved in: General.OptionsFileName

Print.JpegSmoothing
JPEG smoothing (between 0 and 100)
Default value: 0
Saved in: General.OptionsFileName

Print.PgfTwoDim
Output PGF format for two dimensions. Mostly irrelevant if ‘PgfExportAxis=0‘.
Default ‘1‘ (yes).
Default value: 1
Saved in: General.OptionsFileName

Print.PgfExportAxis
Include axis in export pgf code (not in the png). Default ‘0‘ (no).
Default value: 0
Saved in: General.OptionsFileName

Print.PgfHorizontalBar
Use a horizontal color bar in the pgf output. Default ‘0‘ (no).
Default value: 0
Saved in: General.OptionsFileName

Print.PostElementary
Save elementary region tags in mesh statistics exported as post-processing views
Default value: 1
Saved in: General.OptionsFileName

Print.PostElement
Save element tags in mesh statistics exported as post-processing views
Default value: 0
Saved in: General.OptionsFileName

Print.PostGamma
Save Gamma quality measure in mesh statistics exported as post-processing views
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 245

Print.PostEta
Save Eta quality measure in mesh statistics exported as post-processing views
Default value: 0
Saved in: General.OptionsFileName
Print.PostSICN
Save SICN (signed inverse condition number) quality measure in mesh statistics
exported as post-processing views
Default value: 0
Saved in: General.OptionsFileName
Print.PostSIGE
Save SIGE (signed inverse gradient error) quality measure in mesh statistics ex-
ported as post-processing views
Default value: 0
Saved in: General.OptionsFileName
Print.PostDisto
Save Disto quality measure in mesh statistics exported as post-processing views
Default value: 0
Saved in: General.OptionsFileName
Print.TexAsEquation
Print all TeX strings as equations
Default value: 0
Saved in: General.OptionsFileName
Print.TexForceFontSize
Force font size of TeX strings to fontsize in the graphic window
Default value: 0
Saved in: General.OptionsFileName
Print.TexWidthInMm
Width of tex graphics in mm (use 0 for the natural width inferred from the image
width in pixels)
Default value: 150
Saved in: General.OptionsFileName
Print.Text
Print text strings?
Default value: 1
Saved in: General.OptionsFileName
Print.X3dCompatibility
Produce highly compatible X3D output (no scale bar)
Default value: 0
Saved in: General.OptionsFileName
Print.X3dPrecision
Precision of X3D output
Default value: 1e-09
Saved in: General.OptionsFileName
Print.X3dRemoveInnerBorders
Remove inner borders in X3D output
Default value: 0
Saved in: General.OptionsFileName
246 Gmsh 4.11.1

Print.X3dTransparency
Transparency for X3D output
Default value: 0
Saved in: General.OptionsFileName
Print.X3dSurfaces
Save surfaces in CAD X3D output (0: no, 1: yes in a single X3D object,2: one X3D
object per geometrical surface, 3: one X3D object perphysical surface)
Default value: 1
Saved in: General.OptionsFileName
Print.X3dEdges
Save edges in CAD X3D output (0: no, 1: yes in a single X3D object,2: one X3D
object per geometrical edge, 3: one X3D object perphysical edge)
Default value: 0
Saved in: General.OptionsFileName
Print.X3dVertices
Save vertices in CAD X3D output (0: no, 1: yes)
Default value: 0
Saved in: General.OptionsFileName
Print.X3dVolumes
Save separate volumes in CAD X3D output (0: no, 1: yes)
Default value: 0
Saved in: General.OptionsFileName
Print.X3dColorize
Apply colors to faces (0: no, 1: yes)
Default value: 0
Saved in: General.OptionsFileName
Print.Width
Width of printed image; use (possibly scaled) current width if < 0)
Default value: -1
Saved in: General.OptionsFileName

7.3 Geometry options

Geometry.DoubleClickedPointCommand
Command parsed when double-clicking on a point, or ’ONELAB’ to edit associated
ONELAB parameters
Default value: "ONELAB"
Saved in: General.OptionsFileName
Geometry.DoubleClickedCurveCommand
Command parsed when double-clicking on a curve, or ’ONELAB’ to edit associated
ONELAB parameters
Default value: "ONELAB"
Saved in: General.OptionsFileName
Geometry.DoubleClickedSurfaceCommand
Command parsed when double-clicking on a surface, or ’ONELAB’ to edit associated
ONELAB parameters
Default value: "ONELAB"
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 247

Geometry.DoubleClickedVolumeCommand
Command parsed when double-clicking on a volume, or ’ONELAB’ to edit associated
ONELAB parameters
Default value: "ONELAB"
Saved in: General.OptionsFileName
Geometry.OCCTargetUnit
Length unit to which coordinates from STEP and IGES files are converted to when
imported by OpenCASCADE, e.g. ’M’ for meters (leave empty to use the default
OpenCASCADE behavior); the option should be set before importing the STEP or
IGES file
Default value: ""
Saved in: General.OptionsFileName
Geometry.PipeDefaultTrihedron
Default trihedron type when creating pipes
Default value: "DiscreteTrihedron"
Saved in: General.OptionsFileName
Geometry.AutoCoherence
Should all duplicate entities be automatically removed with the built-in geometry
kernel? If Geometry.AutoCoherence = 2, also remove degenerate entities. The
option has no effect with the OpenCASCADE kernel
Default value: 1
Saved in: General.OptionsFileName
Geometry.Clip
Enable clipping planes? (Plane[i]=2^i, i=0,...,5)
Default value: 0
Saved in: -
Geometry.CopyMeshingMethod
Copy meshing method (unstructured or transfinite) when duplicating geometrical
entities with built-in geometry kernel?
Default value: 0
Saved in: General.OptionsFileName
Geometry.Curves
Display geometry curves?
Default value: 1
Saved in: General.OptionsFileName
Geometry.CurveLabels
Display curve labels?
Default value: 0
Saved in: General.OptionsFileName
Geometry.CurveSelectWidth
Display width of selected curves (in pixels)
Default value: 3
Saved in: General.OptionsFileName
Geometry.CurveType
Display curves as solid color segments (0), 3D cylinders (1) or tapered cylinders (2)
Default value: 0
Saved in: General.OptionsFileName
248 Gmsh 4.11.1

Geometry.CurveWidth
Display width of lines (in pixels)
Default value: 2
Saved in: General.OptionsFileName
Geometry.DoubleClickedEntityTag
Tag of last double-clicked geometrical entity
Default value: 0
Saved in: -
Geometry.ExactExtrusion
Use exact extrusion formula in interpolations (set to 0 to allow geometrical trans-
formations of extruded entities)
Default value: 1
Saved in: General.OptionsFileName
Geometry.ExtrudeReturnLateralEntities
Add lateral entities in lists returned by extrusion commands?
Default value: 1
Saved in: General.OptionsFileName
Geometry.ExtrudeSplinePoints
Number of control points for splines created during extrusion
Default value: 5
Saved in: General.OptionsFileName
Geometry.HighlightOrphans
Highlight orphan and boundary entities?
Default value: 0
Saved in: General.OptionsFileName
Geometry.LabelType
Type of entity label (0: description, 1: elementary entity tag, 2: physical group tag,
3: elementary name, 4: physical name)
Default value: 0
Saved in: General.OptionsFileName
Geometry.Light
Enable lighting for the geometry
Default value: 1
Saved in: General.OptionsFileName
Geometry.LightTwoSide
Light both sides of surfaces (leads to slower rendering)
Default value: 1
Saved in: General.OptionsFileName
Geometry.MatchGeomAndMesh
Matches geometries and meshes
Default value: 0
Saved in: General.OptionsFileName
Geometry.MatchMeshScaleFactor
Rescaling factor for the mesh to correspond to size of the geometry
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 249

Geometry.MatchMeshTolerance
Tolerance for matching mesh and geometry
Default value: 1e-06
Saved in: General.OptionsFileName

Geometry.Normals
Display size of normal vectors (in pixels)
Default value: 0
Saved in: General.OptionsFileName

Geometry.NumSubEdges
Number of subdivisions (per control point or pole) used to draw curves
Default value: 40
Saved in: General.OptionsFileName

Geometry.OCCAutoEmbed
Automatically embed points, curves and faces in higher dimensional entities if they
are marked as ’internal’ by OpenCASCADE
Default value: 1
Saved in: General.OptionsFileName

Geometry.OCCAutoFix
Automatically fix orientation of wires, faces, shells and volumes when creating new
entities with the OpenCASCADE kernel
Default value: 1
Saved in: General.OptionsFileName

Geometry.OCCBooleanPreserveNumbering
Try to preserve the numbering of entities through OpenCASCADE boolean opera-
tions
Default value: 1
Saved in: General.OptionsFileName

Geometry.OCCBoundsUseStl
Use STL mesh for computing bounds of OpenCASCADE shapes (more accurate,
but slower)
Default value: 0
Saved in: General.OptionsFileName

Geometry.OCCDisableStl
Disable STL creation in OpenCASCADE kernel
Default value: 0
Saved in: General.OptionsFileName

Geometry.OCCFixDegenerated
Fix degenerated edges/faces when importing STEP, IGES and BRep models with
the OpenCASCADE kernel
Default value: 0
Saved in: General.OptionsFileName

Geometry.OCCFixSmallEdges
Fix small edges when importing STEP, IGES and BRep models with the OpenCAS-
CADE kernel
Default value: 0
Saved in: General.OptionsFileName
250 Gmsh 4.11.1

Geometry.OCCFixSmallFaces
Fix small faces when importing STEP, IGES and BRep models with the OpenCAS-
CADE kernel
Default value: 0
Saved in: General.OptionsFileName
Geometry.OCCExportOnlyVisible
Only consider visible shapes when exporting STEP or BREP models with the Open-
CASCADE kernel
Default value: 0
Saved in: General.OptionsFileName
Geometry.OCCImportLabels
Import labels and colors when importing STEP models with the OpenCASCADE
kernel
Default value: 1
Saved in: General.OptionsFileName
Geometry.OCCMakeSolids
Fix shells and make solids when importing STEP, IGES and BRep models with the
OpenCASCADE kernel
Default value: 0
Saved in: General.OptionsFileName
Geometry.OCCParallel
Use multi-threaded OpenCASCADE boolean operators
Default value: 0
Saved in: General.OptionsFileName
Geometry.OCCSafeUnbind
Revert to safe (i.e. with recursive checks on boundaries) unbinding of entities in
boolean operations and geometrical transformations
Default value: 0
Saved in: General.OptionsFileName
Geometry.OCCScaling
Scale STEP, IGES and BRep models by the given factor when importing them with
the OpenCASCADE kernel
Default value: 1
Saved in: General.OptionsFileName
Geometry.OCCSewFaces
Sew faces when importing STEP, IGES and BRep models with the OpenCASCADE
kernel
Default value: 0
Saved in: General.OptionsFileName
Geometry.OCCThruSectionsDegree
Maximum degree of surfaces generated by thrusections with the OpenCASCADE
kernel, if not explicitly specified (default OCC value if negative)
Default value: -1
Saved in: General.OptionsFileName
Geometry.OCCUnionUnify
Try to unify faces and edges (remove internal seams) which lie on the same geometry
after performing a boolean union with the OpenCASCADE kernel
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 251

Geometry.OCCUseGenericClosestPoint
Use generic algrithm to compute point projections in the OpenCASCADE kernel
(less robust, but significally faster in some configurations)
Default value: 0
Saved in: General.OptionsFileName
Geometry.OffsetX
Model display offset along X-axis (in model coordinates)
Default value: 0
Saved in: -
Geometry.OffsetY
Model display offset along Y-axis (in model coordinates)
Default value: 0
Saved in: -
Geometry.OffsetZ
Model display offset along Z-axis (in model coordinates)
Default value: 0
Saved in: -
Geometry.OldCircle
Use old circle description (compatibility option for old Gmsh geometries)
Default value: 0
Saved in: General.OptionsFileName
Geometry.OldRuledSurface
Use old 3-sided ruled surface interpolation (compatibility option for old Gmsh ge-
ometries)
Default value: 0
Saved in: General.OptionsFileName
Geometry.OldNewReg
Use old newreg definition for geometrical transformations (compatibility option for
old Gmsh geometries)
Default value: 1
Saved in: General.OptionsFileName
Geometry.OrientedPhysicals
Use sign of elementary entity in physical definition as orientation indicator
Default value: 1
Saved in: General.OptionsFileName
Geometry.Points
Display geometry points?
Default value: 1
Saved in: General.OptionsFileName
Geometry.PointLabels
Display points labels?
Default value: 0
Saved in: General.OptionsFileName
Geometry.PointSelectSize
Display size of selected points (in pixels)
Default value: 6
Saved in: General.OptionsFileName
252 Gmsh 4.11.1

Geometry.PointSize
Display size of points (in pixels)
Default value: 4
Saved in: General.OptionsFileName
Geometry.PointType
Display points as solid color dots (0) or 3D spheres (1)
Default value: 0
Saved in: General.OptionsFileName
Geometry.ReparamOnFaceRobust
Use projection for reparametrization of a point classified on GEdge on a GFace
Default value: 0
Saved in: General.OptionsFileName
Geometry.ScalingFactor
Global geometry scaling factor
Default value: 1
Saved in: General.OptionsFileName
Geometry.SnapPoints
Snap points on curves if their evaluation using the parametrization is larger than
the geometrical tolerance (currently only with the OpenCASCADE kernel)
Default value: 1
Saved in: General.OptionsFileName
Geometry.SnapX
Snapping grid spacing along the X-axis
Default value: 0.1
Saved in: General.OptionsFileName
Geometry.SnapY
Snapping grid spacing along the Y-axis
Default value: 0.1
Saved in: General.OptionsFileName
Geometry.SnapZ
Snapping grid spacing along the Z-axis
Default value: 0.1
Saved in: General.OptionsFileName
Geometry.Surfaces
Display geometry surfaces?
Default value: 0
Saved in: General.OptionsFileName
Geometry.SurfaceLabels
Display surface labels?
Default value: 0
Saved in: General.OptionsFileName
Geometry.SurfaceType
Surface display type (0: cross, 1: wireframe, 2: solid). Wireframe and solid are not
available with the built-in geometry kernel.
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 253

Geometry.Tangents
Display size of tangent vectors (in pixels)
Default value: 0
Saved in: General.OptionsFileName
Geometry.Tolerance
Geometrical tolerance
Default value: 1e-08
Saved in: General.OptionsFileName
Geometry.ToleranceBoolean
Geometrical tolerance for boolean operations
Default value: 0
Saved in: General.OptionsFileName
Geometry.Transform
Transform model display coordinates (0: no, 1: scale)
Default value: 0
Saved in: -
Geometry.TransformXX
Element (1,1) of the 3x3 model display transformation matrix
Default value: 1
Saved in: -
Geometry.TransformXY
Element (1,2) of the 3x3 model display transformation matrix
Default value: 0
Saved in: -
Geometry.TransformXZ
Element (1,3) of the 3x3 model display transformation matrix
Default value: 0
Saved in: -
Geometry.TransformYX
Element (2,1) of the 3x3 model display transformation matrix
Default value: 0
Saved in: -
Geometry.TransformYY
Element (2,2) of the 3x3 model display transformation matrix
Default value: 1
Saved in: -
Geometry.TransformYZ
Element (2,3) of the 3x3 model display transformation matrix
Default value: 0
Saved in: -
Geometry.TransformZX
Element (3,1) of the 3x3 model display transformation matrix
Default value: 0
Saved in: -
Geometry.TransformZY
Element (3,2) of the 3x3 model display transformation matrix
Default value: 0
Saved in: -
254 Gmsh 4.11.1

Geometry.TransformZZ
Element (3,3) of the 3x3 model display transformation matrix
Default value: 1
Saved in: -
Geometry.Volumes
Display geometry volumes?
Default value: 0
Saved in: General.OptionsFileName
Geometry.VolumeLabels
Display volume labels?
Default value: 0
Saved in: General.OptionsFileName
Geometry.Color.Points
Normal geometry point color
Default value: {90,90,90}
Saved in: General.OptionsFileName
Geometry.Color.Curves
Normal geometry curve color
Default value: {0,0,255}
Saved in: General.OptionsFileName
Geometry.Color.Surfaces
Normal geometry surface color
Default value: {128,128,128}
Saved in: General.OptionsFileName
Geometry.Color.Volumes
Normal geometry volume color
Default value: {255,255,0}
Saved in: General.OptionsFileName
Geometry.Color.Selection
Selected geometry color
Default value: {255,0,0}
Saved in: General.OptionsFileName
Geometry.Color.HighlightZero
Highlight 0 color
Default value: {255,0,0}
Saved in: General.OptionsFileName
Geometry.Color.HighlightOne
Highlight 1 color
Default value: {255,150,0}
Saved in: General.OptionsFileName
Geometry.Color.HighlightTwo
Highlight 2 color
Default value: {255,255,0}
Saved in: General.OptionsFileName
Geometry.Color.Tangents
Tangent geometry vectors color
Default value: {255,255,0}
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 255

Geometry.Color.Normals
Normal geometry vectors color
Default value: {255,0,0}
Saved in: General.OptionsFileName
Geometry.Color.Projection
Projection surface color
Default value: {0,255,0}
Saved in: General.OptionsFileName

7.4 Mesh options

Mesh.Algorithm
2D mesh algorithm (1: MeshAdapt, 2: Automatic, 3: Initial mesh only, 5: Delaunay,
6: Frontal-Delaunay, 7: BAMG, 8: Frontal-Delaunay for Quads, 9: Packing of
Parallelograms, 11: Quasi-structured Quad)
Default value: 6
Saved in: General.OptionsFileName
Mesh.Algorithm3D
3D mesh algorithm (1: Delaunay, 3: Initial mesh only, 4: Frontal, 7: MMG3D, 9:
R-tree, 10: HXT)
Default value: 1
Saved in: General.OptionsFileName
Mesh.AlgorithmSwitchOnFailure
Switch meshing algorithm on failure? (Currently only for 2D Delaunay-based algo-
rithms, switching to MeshAdapt)
Default value: 1
Saved in: General.OptionsFileName
Mesh.AngleSmoothNormals
Threshold angle below which normals are not smoothed
Default value: 30
Saved in: General.OptionsFileName
Mesh.AngleToleranceFacetOverlap
Consider connected facets as overlapping when the dihedral angle between the facets
is smaller than the user’s defined tolerance (in degrees)
Default value: 0.1
Saved in: General.OptionsFileName
Mesh.AnisoMax
Maximum anisotropy of the mesh
Default value: 1e+33
Saved in: General.OptionsFileName
Mesh.AllowSwapAngle
Threshold angle (in degrees) between faces normals under which we allow an edge
swap
Default value: 10
Saved in: General.OptionsFileName
Mesh.BdfFieldFormat
Field format for Nastran BDF files (0: free, 1: small, 2: large)
Default value: 1
Saved in: General.OptionsFileName
256 Gmsh 4.11.1

Mesh.Binary
Write mesh files in binary format (if possible)
Default value: 0
Saved in: General.OptionsFileName
Mesh.BoundaryLayerFanElements
Number of elements (per Pi radians) for 2D boundary layer fans
Default value: 5
Saved in: General.OptionsFileName
Mesh.CgnsImportOrder
Order of the mesh to be created by coarsening CGNS structured zones (1 to 4)
Default value: 1
Saved in: General.OptionsFileName
Mesh.CgnsImportIgnoreBC
Ignore information in ZoneBC structures when reading a CGNS file
Default value: 0
Saved in: General.OptionsFileName
Mesh.CgnsImportIgnoreSolution
Ignore solution when reading a CGNS file
Default value: 0
Saved in: General.OptionsFileName
Mesh.CgnsConstructTopology
Reconstruct the model topology (BREP) after reading a CGNS file
Default value: 0
Saved in: General.OptionsFileName
Mesh.CgnsExportCPEX0045
Use the CPEX0045 convention when exporting a high-order mesh to CGNS
Default value: 0
Saved in: General.OptionsFileName
Mesh.CgnsExportStructured
Export transfinite meshes as structured CGNS grids
Default value: 0
Saved in: General.OptionsFileName
Mesh.Clip
Enable clipping planes? (Plane[i]=2^i, i=0,...,5)
Default value: 0
Saved in: -
Mesh.ColorCarousel
Mesh coloring (0: by element type, 1: by elementary entity, 2: by physical group,
3: by mesh partition)
Default value: 1
Saved in: General.OptionsFileName
Mesh.CompoundClassify
How are surface mesh elements classified on compounds? (0: on the new discrete
surface, 1: on the original geometrical surfaces - incompatible with e.g. high-order
meshing)
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 257

Mesh.CompoundMeshSizeFactor
Mesh size factor applied to compound parts
Default value: 0.5
Saved in: General.OptionsFileName
Mesh.CpuTime
CPU time (in seconds) for the generation of the current mesh (read-only)
Default value: 0
Saved in: -
Mesh.CreateTopologyMsh2
Attempt to (re)create the model topology when reading MSH2 files
Default value: 0
Saved in: General.OptionsFileName
Mesh.DrawSkinOnly
Draw only the skin of 3D meshes?
Default value: 0
Saved in: General.OptionsFileName
Mesh.Dual
Display the dual mesh obtained by barycentric subdivision
Default value: 0
Saved in: General.OptionsFileName
Mesh.ElementOrder
Element order (1: first order elements)
Default value: 1
Saved in: General.OptionsFileName
Mesh.Explode
Element shrinking factor (between 0 and 1)
Default value: 1
Saved in: General.OptionsFileName
Mesh.FirstElementTag
First tag (>= 1) of mesh elements when generating or renumbering a mesh
Default value: 1
Saved in: General.OptionsFileName
Mesh.FirstNodeTag
First tag (>= 1) of mesh nodes when generating or renumbering a mesh
Default value: 1
Saved in: General.OptionsFileName
Mesh.FlexibleTransfinite
Allow transfinite constraints to be modified for recombination (e.g. Blossom) or by
global mesh size factor
Default value: 0
Saved in: General.OptionsFileName
Mesh.Format
Mesh output format (1: msh, 2: unv, 10: auto, 16: vtk, 19: vrml, 21: mail, 26: pos
stat, 27: stl, 28: p3d, 30: mesh, 31: bdf, 32: cgns, 33: med, 34: diff, 38: ir3, 39:
inp, 40: ply2, 41: celum, 42: su2, 47: tochnog, 49: neu, 50: matlab)
Default value: 10
Saved in: General.OptionsFileName
258 Gmsh 4.11.1

Mesh.Hexahedra
Display mesh hexahedra?
Default value: 1
Saved in: General.OptionsFileName

Mesh.HighOrderDistCAD
Try to optimize distance to CAD in high-order optimizer?
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderFixBoundaryNodes
Fix boundary nodes during high-order optimization?
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderIterMax
Maximum number of iterations in high-order optimization pass
Default value: 100
Saved in: General.OptionsFileName

Mesh.HighOrderNumLayers
Number of layers around a problematic element to consider for high-order opti-
mization, or number of element layers to consider in the boundary layer mesh for
high-order fast curving
Default value: 6
Saved in: General.OptionsFileName

Mesh.HighOrderOptimize
Optimize high-order meshes? (0: none, 1: optimization, 2: elastic+optimization, 3:
elastic, 4: fast curving)
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderPassMax
Maximum number of high-order optimization passes (moving barrier)
Default value: 25
Saved in: General.OptionsFileName

Mesh.HighOrderPeriodic
Force location of nodes for periodic meshes using periodicity transform (0: assume
identical parametrisations, 1: invert parametrisations, 2: compute closest point
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderPoissonRatio
Poisson ratio of the material used in the elastic smoother for high-order meshes
(between -1.0 and 0.5, excluded)
Default value: 0.33
Saved in: General.OptionsFileName

Mesh.HighOrderSavePeriodic
Save high-order nodes in periodic section of MSH files?
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 259

Mesh.HighOrderPrimSurfMesh
Try to fix flipped surface mesh elements in high-order optimizer?
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderThresholdMin
Minimum threshold for high-order element optimization
Default value: 0.1
Saved in: General.OptionsFileName

Mesh.HighOrderThresholdMax
Maximum threshold for high-order element optimization
Default value: 2
Saved in: General.OptionsFileName

Mesh.HighOrderFastCurvingNewAlgo
Curve boundary layer with new "fast curving" algorithm (experimental)
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderCurveOuterBL
Curve also the outer surface of the boundary layer in the fast curving algorithm (0
= do not curve, 1 = curve according to boundary, 2 = curve without breaking outer
elements)
Default value: 0
Saved in: General.OptionsFileName

Mesh.HighOrderMaxRho
Maximum min/max ratio of edge/face size for the detection of BL element columns
in the fast curving algorithm
Default value: 0.3
Saved in: General.OptionsFileName

Mesh.HighOrderMaxAngle
Maximum angle between layers of BL elements for the detection of columns in the
fast curving algorithm
Default value: 0.174533
Saved in: General.OptionsFileName

Mesh.HighOrderMaxInnerAngle
Maximum angle between edges/faces within layers of BL triangles/tets for the de-
tection of columns in the fast curving algorithm
Default value: 0.523599
Saved in: General.OptionsFileName

Mesh.IgnoreParametrization
Skip parametrization section when reading meshes in the MSH4 format
Default value: 0
Saved in: General.OptionsFileName

Mesh.IgnorePeriodicity
Skip periodic node section and skip periodic boundary alignment step when reading
meshes in the MSH2 format
Default value: 1
Saved in: General.OptionsFileName
260 Gmsh 4.11.1

Mesh.LabelSampling
Label sampling rate (display one label every ‘LabelSampling’ elements)
Default value: 1
Saved in: General.OptionsFileName
Mesh.LabelType
Type of element label (0: node/element tag, 1: elementary entity tag, 2: physical
entity tag, 3: partition, 4: coordinates)
Default value: 0
Saved in: General.OptionsFileName
Mesh.LcIntegrationPrecision
Accuracy of evaluation of the LC field for 1D mesh generation
Default value: 1e-09
Saved in: General.OptionsFileName
Mesh.Light
Enable lighting for the mesh
Default value: 1
Saved in: General.OptionsFileName
Mesh.LightLines
Enable lighting for mesh edges (0: no, 1: surfaces, 2: surfaces+volumes
Default value: 2
Saved in: General.OptionsFileName
Mesh.LightTwoSide
Light both sides of surfaces (leads to slower rendering)
Default value: 1
Saved in: General.OptionsFileName
Mesh.Lines
Display mesh lines (1D elements)?
Default value: 0
Saved in: General.OptionsFileName
Mesh.LineLabels
Display mesh line labels?
Default value: 0
Saved in: General.OptionsFileName
Mesh.LineWidth
Display width of mesh lines (in pixels)
Default value: 1
Saved in: General.OptionsFileName
Mesh.MaxIterDelaunay3D
Maximum number of point insertion iterations in 3D Delaunay mesher (0: unlim-
ited)
Default value: 0
Saved in: General.OptionsFileName
Mesh.MaxNumThreads1D
Maximum number of threads for 1D meshing (0: use General.NumThreads)
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 261

Mesh.MaxNumThreads2D
Maximum number of threads for 2D meshing (0: use General.NumThreads)
Default value: 0
Saved in: General.OptionsFileName

Mesh.MaxNumThreads3D
Maximum number of threads for 3D meshing (0: use General.NumThreads)
Default value: 0
Saved in: General.OptionsFileName

Mesh.MaxRetries
Maximum number of times meshing is retried on curves and surfaces with a pending
mesh
Default value: 10
Saved in: General.OptionsFileName

Mesh.MeshOnlyVisible
Mesh only visible entities (experimental)
Default value: 0
Saved in: General.OptionsFileName

Mesh.MeshOnlyEmpty
Mesh only entities that have no existing mesh
Default value: 0
Saved in: General.OptionsFileName

Mesh.MeshSizeExtendFromBoundary
Extend computation of mesh element sizes from the boundaries into the interior (0:
never; 1: for surfaces and volumes; 2: for surfaces and volumes, but use smallest
surface element edge length instead of longest length in 3D Delaunay; -2: only for
surfaces; -3: only for volumes)
Default value: 1
Saved in: General.OptionsFileName

Mesh.MeshSizeFactor
Factor applied to all mesh element sizes
Default value: 1
Saved in: General.OptionsFileName

Mesh.MeshSizeMin
Minimum mesh element size
Default value: 0
Saved in: General.OptionsFileName

Mesh.MeshSizeMax
Maximum mesh element size
Default value: 1e+22
Saved in: General.OptionsFileName

Mesh.MeshSizeFromCurvature
Automatically compute mesh element sizes from curvature, using the value as the
target number of elements per 2 * Pi radians
Default value: 0
Saved in: General.OptionsFileName
262 Gmsh 4.11.1

Mesh.MeshSizeFromCurvatureIsotropic
Force isotropic curvature estimation when the mesh size is computed from curvature
Default value: 0
Saved in: General.OptionsFileName
Mesh.MeshSizeFromPoints
Compute mesh element sizes from values given at geometry points
Default value: 1
Saved in: General.OptionsFileName
Mesh.MeshSizeFromParametricPoints
Compute mesh element sizes from values given at geometry points defining para-
metric curves
Default value: 0
Saved in: General.OptionsFileName
Mesh.MetisAlgorithm
METIS partitioning algorithm ’ptype’ (1: Recursive, 2: K-way)
Default value: 1
Saved in: General.OptionsFileName
Mesh.MetisEdgeMatching
METIS edge matching type ’ctype’ (1: Random, 2: Sorted Heavy-Edge)
Default value: 2
Saved in: General.OptionsFileName
Mesh.MetisMaxLoadImbalance
METIS maximum load imbalance ’ufactor’ (-1: default, i.e. 30 for K-way and 1 for
Recursive)
Default value: -1
Saved in: General.OptionsFileName
Mesh.MetisObjective
METIS objective type ’objtype’ (1: min. edge-cut, 2: min. communication volume)
Default value: 1
Saved in: General.OptionsFileName
Mesh.MetisMinConn
METIS minimize maximum connectivity of partitions ’minconn’ (-1: default)
Default value: -1
Saved in: General.OptionsFileName
Mesh.MetisRefinementAlgorithm
METIS algorithm for k-way refinement ’rtype’ (1: FM-based cut, 2: Greedy, 3:
Two-sided node FM, 4: One-sided node FM)
Default value: 2
Saved in: General.OptionsFileName
Mesh.MinimumLineNodes
Minimum number of nodes used to mesh (straight) lines
Default value: 2
Saved in: General.OptionsFileName
Mesh.MinimumCircleNodes
Minimum number of nodes used to mesh circles and ellipses
Default value: 7
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 263

Mesh.MinimumCurveNodes
Minimum number of nodes used to mesh curves other than lines, circles and ellipses
Default value: 3
Saved in: General.OptionsFileName

Mesh.MinimumElementsPerTwoPi
[Deprecated]
Default value: 0
Saved in: General.OptionsFileName

Mesh.MshFileVersion
Version of the MSH file format to use
Default value: 4.1
Saved in: General.OptionsFileName

Mesh.MedFileMinorVersion
Minor version of the MED file format to use (-1: use minor version of the MED
library)
Default value: -1
Saved in: General.OptionsFileName

Mesh.MedImportGroupsOfNodes
Import groups of nodes (0: no; 1: create geometrical point for each node)?
Default value: 0
Saved in: General.OptionsFileName

Mesh.MedSingleModel
Import MED meshes in the current model, even if several MED mesh names exist
Default value: 0
Saved in: General.OptionsFileName

Mesh.NbHexahedra
Number of hexahedra in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NbNodes
Number of nodes in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NbPartitions
Number of partitions
Default value: 0
Saved in: General.OptionsFileName

Mesh.NbPrisms
Number of prisms in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NbPyramids
Number of pyramids in the current mesh (read-only)
Default value: 0
Saved in: -
264 Gmsh 4.11.1

Mesh.NbTrihedra
Number of trihedra in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NbQuadrangles
Number of quadrangles in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NbTetrahedra
Number of tetrahedra in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NbTriangles
Number of triangles in the current mesh (read-only)
Default value: 0
Saved in: -

Mesh.NewtonConvergenceTestXYZ
Force inverse surface mapping algorithm (Newton-Raphson) to converge in real co-
ordinates (experimental)
Default value: 0
Saved in: General.OptionsFileName

Mesh.Nodes
Display mesh nodes?
Default value: 0
Saved in: General.OptionsFileName

Mesh.NodeLabels
Display mesh node labels?
Default value: 0
Saved in: General.OptionsFileName

Mesh.NodeSize
Display size of mesh nodes (in pixels)
Default value: 4
Saved in: General.OptionsFileName

Mesh.NodeType
Display mesh nodes as solid color dots (0) or 3D spheres (1)
Default value: 0
Saved in: General.OptionsFileName

Mesh.Normals
Display size of normal vectors (in pixels)
Default value: 0
Saved in: General.OptionsFileName

Mesh.NumSubEdges
Number of edge subdivisions used to draw high-order mesh elements
Default value: 2
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 265

Mesh.OldInitialDelaunay2D
Use old initial 2D Delaunay code
Default value: 0
Saved in: General.OptionsFileName
Mesh.Optimize
Optimize the mesh to improve the quality of tetrahedral elements
Default value: 1
Saved in: General.OptionsFileName
Mesh.OptimizeThreshold
Optimize tetrahedra that have a quality below ...
Default value: 0.3
Saved in: General.OptionsFileName
Mesh.OptimizeNetgen
Optimize the mesh using Netgen to improve the quality of tetrahedral elements
Default value: 0
Saved in: General.OptionsFileName
Mesh.PartitionHexWeight
Weight of hexahedral element for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
Mesh.PartitionLineWeight
Weight of line element for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
Mesh.PartitionPrismWeight
Weight of prismatic element (wedge) for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
Mesh.PartitionPyramidWeight
Weight of pyramidal element for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
Mesh.PartitionQuadWeight
Weight of quadrangle for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
Mesh.PartitionTrihedronWeight
Weight of trihedron element for METIS load balancing (-1: automatic)
Default value: 0
Saved in: General.OptionsFileName
Mesh.PartitionTetWeight
Weight of tetrahedral element for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
Mesh.PartitionTriWeight
Weight of triangle element for METIS load balancing (-1: automatic)
Default value: -1
Saved in: General.OptionsFileName
266 Gmsh 4.11.1

Mesh.PartitionCreateTopology
Create boundary representation of partitions
Default value: 1
Saved in: General.OptionsFileName
Mesh.PartitionCreatePhysicals
Create physical groups for partitions, based on existing physical groups
Default value: 1
Saved in: General.OptionsFileName
Mesh.PartitionCreateGhostCells
Create ghost cells, i.e. create for each partition a ghost entity containing elements
connected to neighboring partitions by at least one node.
Default value: 0
Saved in: General.OptionsFileName
Mesh.PartitionSplitMeshFiles
Write one file for each mesh partition
Default value: 0
Saved in: General.OptionsFileName
Mesh.PartitionTopologyFile
Write a .pro file with the partition topology
Default value: 0
Saved in: General.OptionsFileName
Mesh.PartitionOldStyleMsh2
Write partitioned meshes in MSH2 format using old style (i.e. by not referencing new
partitioned entities, except on partition boundaries), for backward compatibility
Default value: 1
Saved in: General.OptionsFileName
Mesh.PartitionConvertMsh2
When reading partitioned meshes in MSH2 format, create new partition entities
Default value: 1
Saved in: General.OptionsFileName
Mesh.PreserveNumberingMsh2
Preserve element numbering in MSH2 format (will break meshes with multiple phys-
ical groups for a single elementary entity)
Default value: 0
Saved in: General.OptionsFileName
Mesh.Prisms
Display mesh prisms?
Default value: 1
Saved in: General.OptionsFileName
Mesh.Pyramids
Display mesh pyramids?
Default value: 1
Saved in: General.OptionsFileName
Mesh.QuadqsSizemapMethod
Size map method in QuadQuasiStructured. 0: default, 1: cross-field,2: cross-field +
CAD small features adaptation,3: from background mesh (e.g. sizes in current tri-
angulation),4: cross-field + CAD small features adaptation (clamped by background
Chapter 7: Gmsh options 267

mesh)
Default value: 3
Saved in: General.OptionsFileName
Mesh.QuadqsTopologyOptimizationMethods
Topology optimization methods in QuadQuasiStructured. 0: default (all),100:
pattern-based CAD faces,010: disk quadrangulation remeshing,001: cavity remesh-
ing,xxx: combination of multiple methods (e.g. 111 for all)
Default value: 0
Saved in: General.OptionsFileName
Mesh.QuadqsRemeshingBoldness
Controls how much cavity remeshing is allowed to distort the quad mesh. From 0 (no
quality decrease during remeshing) to 1 (quality can tend to 0 during remeshing).
Default value: 0.66
Saved in: General.OptionsFileName
Mesh.QuadqsScalingOnTriangulation
Ratio on the edge length between the triangulation and the quadrangulation. Use
a small ratio (e.g. 0.5) to get a background triangulation finer than the quad mesh.
Useful to get a more accurate cross-field.
Default value: 0.75
Saved in: General.OptionsFileName
Mesh.Quadrangles
Display mesh quadrangles?
Default value: 1
Saved in: General.OptionsFileName
Mesh.QualityInf
Only display elements whose quality measure is greater than QualityInf
Default value: 0
Saved in: General.OptionsFileName
Mesh.QualitySup
Only display elements whose quality measure is smaller than QualitySup
Default value: 0
Saved in: General.OptionsFileName
Mesh.QualityType
Type of quality measure (0: SICN~signed inverse condition number, 1: SIGE~signed
inverse gradient error, 2: gamma~vol/sum face/max edge, 3: Disto~minJ/maxJ
Default value: 2
Saved in: General.OptionsFileName
Mesh.RadiusInf
Only display elements whose longest edge is greater than RadiusInf
Default value: 0
Saved in: General.OptionsFileName
Mesh.RadiusSup
Only display elements whose longest edge is smaller than RadiusSup
Default value: 0
Saved in: General.OptionsFileName
Mesh.RandomFactor
Random factor used in the 2D meshing algorithm (should be increased if Random-
Factor * size(triangle)/size(model) approaches machine accuracy)
268 Gmsh 4.11.1

Default value: 1e-09

Saved in: General.OptionsFileName
Mesh.RandomFactor3D
Random factor used in the 3D meshing algorithm
Default value: 1e-12
Saved in: General.OptionsFileName
Mesh.RandomSeed
Seed of pseudo-random number generator
Default value: 1
Saved in: General.OptionsFileName
Mesh.ReadGroupsOfElements
Read groups of elements in UNV meshes (this will discard the elementary entity
tags inferred from the element section)
Default value: 1
Saved in: General.OptionsFileName
Mesh.RecombinationAlgorithm
Mesh recombination algorithm (0: simple, 1: blossom, 2: simple full-quad, 3: blos-
som full-quad)
Default value: 1
Saved in: General.OptionsFileName
Mesh.RecombineAll
Apply recombination algorithm to all surfaces, ignoring per-surface spec
Default value: 0
Saved in: General.OptionsFileName
Mesh.RecombineOptimizeTopology
Number of topological optimization passes (removal of diamonds, ...) of recombined
surface meshes
Default value: 5
Saved in: General.OptionsFileName
Mesh.RecombineNodeRepositioning
Allow repositioning of nodes during recombination of surface meshes
Default value: 1
Saved in: General.OptionsFileName
Mesh.RecombineMinimumQuality
Minimum quality for quadrangle generated by recombination
Default value: 0.01
Saved in: General.OptionsFileName
Mesh.Recombine3DAll
Apply recombination3D algorithm to all volumes, ignoring per-volume spec (exper-
imental)
Default value: 0
Saved in: General.OptionsFileName
Mesh.Recombine3DLevel
3d recombination level (0: hex, 1: hex+prisms, 2: hex+prism+pyramids) (experi-
mental)
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 269

Mesh.Recombine3DConformity
3d recombination conformity type (0: nonconforming, 1: trihedra, 2: pyra-
mids+trihedra, 3:pyramids+hexSplit+trihedra, 4:hexSplit+trihedra)(experimental)
Default value: 0
Saved in: General.OptionsFileName
Mesh.RefineSteps
Number of refinement steps in the MeshAdapt-based 2D algorithms
Default value: 10
Saved in: General.OptionsFileName
Mesh.Renumber
Renumber nodes and elements in a continuous sequence after mesh generation
Default value: 1
Saved in: General.OptionsFileName
Mesh.ReparamMaxTriangles
Maximum number of triangles in a single parametrization patch
Default value: 250000
Saved in: General.OptionsFileName
Mesh.SaveAll
Save all elements, even if they don’t belong to physical groups (for some mesh
formats, this removes physical groups altogether)
Default value: 0
Saved in: -
Mesh.SaveElementTagType
Type of the element tag saved in mesh formats that don’t support saving physical
or partition ids (1: elementary, 2: physical, 3: partition)
Default value: 1
Saved in: General.OptionsFileName
Mesh.SaveGroupsOfElements
Save groups of elements for each physical group (for UNV and INP mesh format) if
value is positive; if negative, save groups of elements for physical groups of dimension
dim if the (dim+1)^th least significant digit of -Mesh.SaveGroupsOfElements is 1
(for example: -100 will only savesurfaces, while -1010 will save volumes and curves),
and for INP skip saving elements of dimension dim altogether if the (dim+1)^th
least significant digit of -Mesh.SaveGroupsOfElements is 0
Default value: 1
Saved in: General.OptionsFileName
Mesh.SaveGroupsOfNodes
Save groups of nodes for each physical group (for UNV, INP and Tochnog mesh
formats) if value is positive; if negative, save groups of nodes for physical groups of
dimension dim if the (dim+1)^th least significant digit of -Mesh.SaveGroupsOfNodes
is 1 (for example: -100 will only save surfaces, while -1010 will save volumes and
curves); for INP, save groups of nodes for all entities of dimension dim if the
(dim+1)^th least significant digit of -Mesh.SaveGroupsOfNodes is 2
Default value: 0
Saved in: General.OptionsFileName
Mesh.SaveParametric
Save parametric coordinates of nodes
Default value: 0
Saved in: General.OptionsFileName
270 Gmsh 4.11.1

Mesh.SaveWithoutOrphans
Don’t save orphan entities (not connected to any highest dimensional entity in the
model) in MSH4 files
Default value: 0
Saved in: General.OptionsFileName
Mesh.SaveTopology
Save model topology in MSH2 output files (this is always saved in MSH3 and above)
Default value: 0
Saved in: General.OptionsFileName
Mesh.ScalingFactor
Global scaling factor applied to the saved mesh
Default value: 1
Saved in: General.OptionsFileName
Mesh.SecondOrderIncomplete
Create incomplete second order elements? (8-node quads, 20-node hexas, etc.)
Default value: 0
Saved in: General.OptionsFileName
Mesh.SecondOrderLinear
Should second order nodes (as well as nodes generated with subdivision algorithms)
simply be created by linear interpolation?
Default value: 0
Saved in: General.OptionsFileName
Mesh.Smoothing
Number of smoothing steps applied to the final mesh
Default value: 1
Saved in: General.OptionsFileName
Mesh.SmoothCrossField
Apply n barycentric smoothing passes to the 3D cross field
Default value: 0
Saved in: General.OptionsFileName
Mesh.CrossFieldClosestPoint
Use closest point to compute 2D crossfield
Default value: 1
Saved in: General.OptionsFileName
Mesh.SmoothNormals
Smooth the mesh normals?
Default value: 0
Saved in: General.OptionsFileName
Mesh.SmoothRatio
Ratio between mesh sizes at nodes of a same edge (used in BAMG)
Default value: 1.8
Saved in: General.OptionsFileName
Mesh.StlAngularDeflection
Maximum angular deflection when creating STL representations of entities (cur-
rently only used with the OpenCASCADE kernel)
Default value: 0.3
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 271

Mesh.StlLinearDeflection
Maximum relative linear deflection when creating STL representation of entities
(currently only used with the OpenCASCADE kernel)
Default value: 0.001
Saved in: General.OptionsFileName
Mesh.StlLinearDeflectionRelative
Compute the linear deflection for STL representations relative to the length of curves
(currently only used with the OpenCASCADE kernel)
Default value: 1
Saved in: General.OptionsFileName
Mesh.StlOneSolidPerSurface
Create one solid per surface when exporting STL files? (0: single solid, 1: one solid
per face, 2: one solid per physical surface)
Default value: 0
Saved in: General.OptionsFileName
Mesh.StlRemoveDuplicateTriangles
Remove duplicate triangles when importing STL files?
Default value: 0
Saved in: General.OptionsFileName
Mesh.SubdivisionAlgorithm
Mesh subdivision algorithm (0: none, 1: all quadrangles, 2: all hexahedra, 3:
barycentric)
Default value: 0
Saved in: General.OptionsFileName
Mesh.SurfaceEdges
Display edges of surface mesh?
Default value: 1
Saved in: General.OptionsFileName
Mesh.SurfaceFaces
Display faces of surface mesh?
Default value: 0
Saved in: General.OptionsFileName
Mesh.SurfaceLabels
Display surface mesh element labels?
Default value: 0
Saved in: General.OptionsFileName
Mesh.SwitchElementTags
Invert elementary and physical tags when reading the mesh
Default value: 0
Saved in: General.OptionsFileName
Mesh.Tangents
Display size of tangent vectors (in pixels)
Default value: 0
Saved in: General.OptionsFileName
Mesh.Tetrahedra
Display mesh tetrahedra?
Default value: 1
Saved in: General.OptionsFileName
272 Gmsh 4.11.1

Mesh.ToleranceEdgeLength
Skip a model edge in mesh generation if its length is less than user’s defined tolerance
Default value: 0
Saved in: General.OptionsFileName

Mesh.ToleranceInitialDelaunay
Tolerance for initial 3D Delaunay mesher
Default value: 1e-12
Saved in: General.OptionsFileName

Mesh.ToleranceReferenceElement
Tolerance for classifying a point inside a reference element (of size 1)
Default value: 1e-06
Saved in: General.OptionsFileName

Mesh.Triangles
Display mesh triangles?
Default value: 1
Saved in: General.OptionsFileName

Mesh.Trihedra
Display mesh trihedra?
Default value: 1
Saved in: General.OptionsFileName

Mesh.TransfiniteTri
Use alternative transfinite arrangement when meshing 3-sided surfaces
Default value: 0
Saved in: General.OptionsFileName

Mesh.UnvStrictFormat
Use strict format specification for UNV files, with ’D’ for exponents (instead of ’E’
as used by some tools)
Default value: 1
Saved in: General.OptionsFileName

Mesh.VolumeEdges
Display edges of volume mesh?
Default value: 1
Saved in: General.OptionsFileName

Mesh.VolumeFaces
Display faces of volume mesh?
Default value: 0
Saved in: General.OptionsFileName

Mesh.VolumeLabels
Display volume mesh element labels?
Default value: 0
Saved in: General.OptionsFileName

Mesh.Voronoi
Display the voronoi diagram
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 273

Mesh.ZoneDefinition
Method for defining a zone (0: single zone, 1: by partition, 2: by physical)
Default value: 0
Saved in: General.OptionsFileName
Mesh.Color.Nodes
Mesh node color
Default value: {0,0,255}
Saved in: General.OptionsFileName
Mesh.Color.NodesSup
Second order mesh node color
Default value: {255,0,255}
Saved in: General.OptionsFileName
Mesh.Color.Lines
Mesh line color
Default value: {0,0,0}
Saved in: General.OptionsFileName
Mesh.Color.Triangles
Mesh triangle color (if Mesh.ColorCarousel=0)
Default value: {160,150,255}
Saved in: General.OptionsFileName
Mesh.Color.Quadrangles
Mesh quadrangle color (if Mesh.ColorCarousel=0)
Default value: {130,120,225}
Saved in: General.OptionsFileName
Mesh.Color.Tetrahedra
Mesh tetrahedron color (if Mesh.ColorCarousel=0)
Default value: {160,150,255}
Saved in: General.OptionsFileName
Mesh.Color.Hexahedra
Mesh hexahedron color (if Mesh.ColorCarousel=0)
Default value: {130,120,225}
Saved in: General.OptionsFileName
Mesh.Color.Prisms
Mesh prism color (if Mesh.ColorCarousel=0)
Default value: {232,210,23}
Saved in: General.OptionsFileName
Mesh.Color.Pyramids
Mesh pyramid color (if Mesh.ColorCarousel=0)
Default value: {217,113,38}
Saved in: General.OptionsFileName
Mesh.Color.Trihedra
Mesh trihedron color (if Mesh.ColorCarousel=0)
Default value: {20,255,0}
Saved in: General.OptionsFileName
Mesh.Color.Tangents
Tangent mesh vector color
Default value: {255,255,0}
Saved in: General.OptionsFileName
274 Gmsh 4.11.1

Mesh.Color.Normals
Normal mesh vector color
Default value: {255,0,0}
Saved in: General.OptionsFileName
Mesh.Color.Zero
Color 0 in color carousel
Default value: {255,120,0}
Saved in: General.OptionsFileName
Mesh.Color.One
Color 1 in color carousel
Default value: {0,255,132}
Saved in: General.OptionsFileName
Mesh.Color.Two
Color 2 in color carousel
Default value: {255,160,0}
Saved in: General.OptionsFileName
Mesh.Color.Three
Color 3 in color carousel
Default value: {0,255,192}
Saved in: General.OptionsFileName
Mesh.Color.Four
Color 4 in color carousel
Default value: {255,200,0}
Saved in: General.OptionsFileName
Mesh.Color.Five
Color 5 in color carousel
Default value: {0,216,255}
Saved in: General.OptionsFileName
Mesh.Color.Six
Color 6 in color carousel
Default value: {255,240,0}
Saved in: General.OptionsFileName
Mesh.Color.Seven
Color 7 in color carousel
Default value: {0,176,255}
Saved in: General.OptionsFileName
Mesh.Color.Eight
Color 8 in color carousel
Default value: {228,255,0}
Saved in: General.OptionsFileName
Mesh.Color.Nine
Color 9 in color carousel
Default value: {0,116,255}
Saved in: General.OptionsFileName
Mesh.Color.Ten
Color 10 in color carousel
Default value: {188,255,0}
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 275

Mesh.Color.Eleven
Color 11 in color carousel
Default value: {0,76,255}
Saved in: General.OptionsFileName
Mesh.Color.Twelve
Color 12 in color carousel
Default value: {148,255,0}
Saved in: General.OptionsFileName
Mesh.Color.Thirteen
Color 13 in color carousel
Default value: {24,0,255}
Saved in: General.OptionsFileName
Mesh.Color.Fourteen
Color 14 in color carousel
Default value: {108,255,0}
Saved in: General.OptionsFileName
Mesh.Color.Fifteen
Color 15 in color carousel
Default value: {84,0,255}
Saved in: General.OptionsFileName
Mesh.Color.Sixteen
Color 16 in color carousel
Default value: {68,255,0}
Saved in: General.OptionsFileName
Mesh.Color.Seventeen
Color 17 in color carousel
Default value: {104,0,255}
Saved in: General.OptionsFileName
Mesh.Color.Eighteen
Color 18 in color carousel
Default value: {0,255,52}
Saved in: General.OptionsFileName
Mesh.Color.Nineteen
Color 19 in color carousel
Default value: {184,0,255}
Saved in: General.OptionsFileName

7.5 Solver options

Solver.Executable0
System command to launch solver 0
Default value: ""
Saved in: General.SessionFileName
Solver.Executable1
System command to launch solver 1
Default value: ""
Saved in: General.SessionFileName
276 Gmsh 4.11.1

Solver.Executable2
System command to launch solver 2
Default value: ""
Saved in: General.SessionFileName
Solver.Executable3
System command to launch solver 3
Default value: ""
Saved in: General.SessionFileName
Solver.Executable4
System command to launch solver 4
Default value: ""
Saved in: General.SessionFileName
Solver.Executable5
System command to launch solver 5
Default value: ""
Saved in: General.SessionFileName
Solver.Executable6
System command to launch solver 6
Default value: ""
Saved in: General.SessionFileName
Solver.Executable7
System command to launch solver 7
Default value: ""
Saved in: General.SessionFileName
Solver.Executable8
System command to launch solver 8
Default value: ""
Saved in: General.SessionFileName
Solver.Executable9
System command to launch solver 9
Default value: ""
Saved in: General.SessionFileName
Solver.Name0
Name of solver 0
Default value: "GetDP"
Saved in: General.SessionFileName
Solver.Name1
Name of solver 1
Default value: ""
Saved in: General.SessionFileName
Solver.Name2
Name of solver 2
Default value: ""
Saved in: General.SessionFileName
Solver.Name3
Name of solver 3
Default value: ""
Saved in: General.SessionFileName
Chapter 7: Gmsh options 277

Solver.Name4
Name of solver 4
Default value: ""
Saved in: General.SessionFileName
Solver.Name5
Name of solver 5
Default value: ""
Saved in: General.SessionFileName
Solver.Name6
Name of solver 6
Default value: ""
Saved in: General.SessionFileName
Solver.Name7
Name of solver 7
Default value: ""
Saved in: General.SessionFileName
Solver.Name8
Name of solver 8
Default value: ""
Saved in: General.SessionFileName
Solver.Name9
Name of solver 9
Default value: ""
Saved in: General.SessionFileName
Solver.Extension0
File extension for solver 0
Default value: ".pro"
Saved in: General.SessionFileName
Solver.Extension1
File extension for solver 1
Default value: ""
Saved in: General.SessionFileName
Solver.Extension2
File extension for solver 2
Default value: ""
Saved in: General.SessionFileName
Solver.Extension3
File extension for solver 3
Default value: ""
Saved in: General.SessionFileName
Solver.Extension4
File extension for solver 4
Default value: ""
Saved in: General.SessionFileName
Solver.Extension5
File extension for solver 5
Default value: ""
Saved in: General.SessionFileName
278 Gmsh 4.11.1

Solver.Extension6
File extension for solver 6
Default value: ""
Saved in: General.SessionFileName
Solver.Extension7
File extension for solver 7
Default value: ""
Saved in: General.SessionFileName
Solver.Extension8
File extension for solver 8
Default value: ""
Saved in: General.SessionFileName
Solver.Extension9
File extension for solver 9
Default value: ""
Saved in: General.SessionFileName
Solver.OctaveInterpreter
Name of the Octave interpreter (used to run .m files)
Default value: "octave"
Saved in: General.SessionFileName
Solver.PythonInterpreter
Name of the Python interpreter (used to run .py files if they are not executable)
Default value: "python"
Saved in: General.SessionFileName
Solver.RemoteLogin0
Command to login to a remote host to launch solver 0
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin1
Command to login to a remote host to launch solver 1
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin2
Command to login to a remote host to launch solver 2
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin3
Command to login to a remote host to launch solver 3
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin4
Command to login to a remote host to launch solver 4
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin5
Command to login to a remote host to launch solver 5
Default value: ""
Saved in: General.SessionFileName
Chapter 7: Gmsh options 279

Solver.RemoteLogin6
Command to login to a remote host to launch solver 6
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin7
Command to login to a remote host to launch solver 7
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin8
Command to login to a remote host to launch solver 8
Default value: ""
Saved in: General.SessionFileName
Solver.RemoteLogin9
Command to login to a remote host to launch solver 9
Default value: ""
Saved in: General.SessionFileName
Solver.SocketName
Base name of socket (UNIX socket if the name does not contain a colon, TCP/IP
otherwise, in the form ’host:baseport’; the actual name/port is constructed by ap-
pending the unique client id. If baseport is 0 or is not provided, the port is chosen
automatically (recommended))
Default value: ".gmshsock"
Saved in: General.OptionsFileName
Solver.AlwaysListen
Always listen to incoming connection requests?
Default value: 0
Saved in: General.OptionsFileName
Solver.AutoArchiveOutputFiles
Automatically archive output files after each computation
Default value: 0
Saved in: General.OptionsFileName
Solver.AutoCheck
Automatically check model every time a parameter is changed
Default value: 1
Saved in: General.OptionsFileName
Solver.AutoLoadDatabase
Automatically load the ONELAB database when launching a solver
Default value: 0
Saved in: General.OptionsFileName
Solver.AutoSaveDatabase
Automatically save the ONELAB database after each computation
Default value: 1
Saved in: General.OptionsFileName
Solver.AutoMesh
Automatically mesh (0: never; 1: if geometry changed, but use existing mesh on
disk if available; 2: if geometry changed; -1: the geometry script creates the mesh)
Default value: 2
Saved in: General.OptionsFileName
280 Gmsh 4.11.1

Solver.AutoMergeFile
Automatically merge result files
Default value: 1
Saved in: General.OptionsFileName
Solver.AutoShowViews
Automcatically show newly merged results (0: none; 1: all; 2: last one)
Default value: 2
Saved in: General.OptionsFileName
Solver.AutoShowLastStep
Automatically show the last step in newly merged results, if there are more than 2
steps
Default value: 1
Saved in: General.OptionsFileName
Solver.Plugins
Enable default solver plugins?
Default value: 0
Saved in: General.OptionsFileName
Solver.ShowInvisibleParameters
Show all parameters, even those marked invisible
Default value: 0
Saved in: General.OptionsFileName
Solver.Timeout
Time (in seconds) before closing the socket if no connection is happening
Default value: 5
Saved in: General.OptionsFileName

7.6 Post-processing options

PostProcessing.DoubleClickedGraphPointCommand
Command parsed when double-clicking on a graph data point (e.g. Merge
Sprintf(’file %g.pos’, PostProcessing.GraphPointX);)
Default value: ""
Saved in: General.OptionsFileName
PostProcessing.GraphPointCommand
Synonym for ‘DoubleClickedGraphPointCommand’
Default value: ""
Saved in: General.OptionsFileName
PostProcessing.AnimationDelay
Delay (in seconds) between frames in automatic animation mode
Default value: 0.1
Saved in: General.OptionsFileName
PostProcessing.AnimationCycle
Cycle through time steps (0) or views (1) for animations
Default value: 0
Saved in: General.OptionsFileName
PostProcessing.AnimationStep
Step increment for animations
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 281

PostProcessing.Binary
Write post-processing files in binary format (if possible)
Default value: 0
Saved in: General.OptionsFileName
PostProcessing.CombineRemoveOriginal
Remove original views after a Combine operation
Default value: 1
Saved in: General.OptionsFileName
PostProcessing.CombineCopyOptions
Copy options during Combine operation
Default value: 1
Saved in: General.OptionsFileName
PostProcessing.DoubleClickedGraphPointX
Abscissa of last double-clicked graph point
Default value: 0
Saved in: -
PostProcessing.DoubleClickedGraphPointY
Ordinate of last double-clicked graph point
Default value: 0
Saved in: -
PostProcessing.DoubleClickedView
Index of last double-clicked view
Default value: 0
Saved in: -
PostProcessing.ForceElementData
Try to force saving datasets as ElementData
Default value: 0
Saved in: General.OptionsFileName
PostProcessing.ForceNodeData
Try to force saving datasets as NodeData
Default value: 0
Saved in: General.OptionsFileName
PostProcessing.Format
Default file format for post-processing views (0: ASCII view, 1: binary view, 2:
parsed view, 3: STL triangulation, 4: raw text, 5: Gmsh mesh, 6: MED file, 10:
automatic)
Default value: 10
Saved in: General.OptionsFileName
PostProcessing.GraphPointX
Synonym for ‘DoubleClickedGraphPointX’
Default value: 0
Saved in: -
PostProcessing.GraphPointY
Synonym for ‘DoubleClickedGraphPointY’
Default value: 0
Saved in: -
282 Gmsh 4.11.1

PostProcessing.HorizontalScales
Display value scales horizontally
Default value: 1
Saved in: General.OptionsFileName

PostProcessing.Link
Post-processing view links (0: apply next option changes to selected views, 1: force
same options for all selected views)
Default value: 0
Saved in: General.OptionsFileName

PostProcessing.NbViews
Current number of views merged (read-only)
Default value: 0
Saved in: -

PostProcessing.Plugins
Enable default post-processing plugins?
Default value: 1
Saved in: General.OptionsFileName

PostProcessing.SaveInterpolationMatrices
Save the interpolation matrices when exporting model-based data
Default value: 1
Saved in: General.OptionsFileName

PostProcessing.SaveMesh
Save the mesh when exporting model-based data
Default value: 1
Saved in: General.OptionsFileName

PostProcessing.Smoothing
Apply (non-reversible) smoothing to post-processing view when merged
Default value: 0
Saved in: General.OptionsFileName

7.7 Post-processing view options

Options related to post-processing views take two forms.
1. options that should apply to all views can be set through ‘View.string ’, before any view
is loaded ;
2. options that should apply only to the n-th view take the form ‘View[n ].string ’ (n = 0,
1, 2, . . . ), after the n-th view is loaded.

View.Attributes
Optional string attached to the view. If the string contains ’AlwaysVisible’, the
view will not be hidden when new ones are merged.
Default value: ""
Saved in: General.OptionsFileName

View.AxesFormatX
Number format for X-axis (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 283

View.AxesFormatY
Number format for Y-axis (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
View.AxesFormatZ
Number format for Z-axis (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
View.AxesLabelX
X-axis label
Default value: ""
Saved in: General.OptionsFileName
View.AxesLabelY
Y-axis label
Default value: ""
Saved in: General.OptionsFileName
View.AxesLabelZ
Z-axis label
Default value: ""
Saved in: General.OptionsFileName
View.DoubleClickedCommand
Command parsed when double-clicking on the view
Default value: ""
Saved in: General.OptionsFileName
View.FileName
Default post-processing view file name
Default value: ""
Saved in: -
View.Format
Number format (in standard C form)
Default value: "%.3g"
Saved in: General.OptionsFileName
View.GeneralizedRaiseX
Generalized elevation of the view along X-axis (in model coordinates, using formula
possibly containing x, y, z, s[tep], t[ime], v0, ... v8)
Default value: "v0"
Saved in: General.OptionsFileName
View.GeneralizedRaiseY
Generalized elevation of the view along Y-axis (in model coordinates, using formula
possibly containing x, y, z, s[tep], t[ime], v0, ... v8)
Default value: "v1"
Saved in: General.OptionsFileName
View.GeneralizedRaiseZ
Generalized elevation of the view along Z-axis (in model coordinates, using formula
possibly containing x, y, z, s[tep], t[ime], v0, ... v8)
Default value: "v2"
Saved in: General.OptionsFileName
284 Gmsh 4.11.1

View.Group
Group to which this view belongs
Default value: ""
Saved in: General.OptionsFileName
View.Name
Default post-processing view name
Default value: ""
Saved in: -
View.Stipple0
First stippling pattern
Default value: "1*0x1F1F"
Saved in: General.OptionsFileName
View.Stipple1
Second stippling pattern
Default value: "1*0x3333"
Saved in: General.OptionsFileName
View.Stipple2
Third stippling pattern
Default value: "1*0x087F"
Saved in: General.OptionsFileName
View.Stipple3
Fourth stippling pattern
Default value: "1*0xCCCF"
Saved in: General.OptionsFileName
View.Stipple4
Fifth stippling pattern
Default value: "2*0x1111"
Saved in: General.OptionsFileName
View.Stipple5
Sixth stippling pattern
Default value: "2*0x0F0F"
Saved in: General.OptionsFileName
View.Stipple6
Seventh stippling pattern
Default value: "1*0xCFFF"
Saved in: General.OptionsFileName
View.Stipple7
Eighth stippling pattern
Default value: "2*0x0202"
Saved in: General.OptionsFileName
View.Stipple8
Ninth stippling pattern
Default value: "2*0x087F"
Saved in: General.OptionsFileName
View.Stipple9
Tenth stippling pattern
Default value: "1*0xFFFF"
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 285

View.AbscissaRangeType
Ascissa scale range type (1: default, 2: custom)
Default value: 1
Saved in: General.OptionsFileName
View.AdaptVisualizationGrid
Use adaptive visualization grid (for high-order elements)?
Default value: 0
Saved in: General.OptionsFileName
View.AngleSmoothNormals
Threshold angle below which normals are not smoothed
Default value: 30
Saved in: General.OptionsFileName
View.ArrowSizeMax
Maximum display size of arrows (in pixels)
Default value: 60
Saved in: General.OptionsFileName
View.ArrowSizeMin
Minimum display size of arrows (in pixels)
Default value: 0
Saved in: General.OptionsFileName
View.AutoPosition
Position the scale or 2D plot automatically (0: manual, 1: automatic, 2: top left, 3:
top right, 4: bottom left, 5: bottom right, 6: top, 7: bottom, 8: left, 9: right, 10:
full, 11: top third, 12: in model coordinates)
Default value: 1
Saved in: General.OptionsFileName
View.Axes
Axes (0: none, 1: simple axes, 2: box, 3: full grid, 4: open grid, 5: ruler)
Default value: 0
Saved in: General.OptionsFileName
View.AxesMikado
Mikado axes style
Default value: 0
Saved in: General.OptionsFileName
View.AxesAutoPosition
Position the axes automatically
Default value: 1
Saved in: General.OptionsFileName
View.AxesMaxX
Maximum X-axis coordinate
Default value: 1
Saved in: General.OptionsFileName
View.AxesMaxY
Maximum Y-axis coordinate
Default value: 1
Saved in: General.OptionsFileName
286 Gmsh 4.11.1

View.AxesMaxZ
Maximum Z-axis coordinate
Default value: 1
Saved in: General.OptionsFileName

View.AxesMinX
Minimum X-axis coordinate
Default value: 0
Saved in: General.OptionsFileName

View.AxesMinY
Minimum Y-axis coordinate
Default value: 0
Saved in: General.OptionsFileName

View.AxesMinZ
Minimum Z-axis coordinate
Default value: 0
Saved in: General.OptionsFileName

View.AxesTicsX
Number of tics on the X-axis
Default value: 5
Saved in: General.OptionsFileName

View.AxesTicsY
Number of tics on the Y-axis
Default value: 5
Saved in: General.OptionsFileName

View.AxesTicsZ
Number of tics on the Z-axis
Default value: 5
Saved in: General.OptionsFileName

View.Boundary
Draw the ‘N minus b’-dimensional boundary of the element (N: element dimension,
b: option value)
Default value: 0
Saved in: General.OptionsFileName

View.CenterGlyphs
Center glyphs (arrows, numbers, etc.)? (0: left, 1: centered, 2: right)
Default value: 0
Saved in: General.OptionsFileName

View.Clip
Enable clipping planes? (Plane[i]=2^i, i=0,...,5)
Default value: 0
Saved in: -

View.Closed
Close the subtree containing this view
Default value: 0
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 287

View.ColormapAlpha
Colormap alpha channel value (used only if != 1)
Default value: 1
Saved in: General.OptionsFileName
View.ColormapAlphaPower
Colormap alpha channel power
Default value: 0
Saved in: General.OptionsFileName
View.ColormapBeta
Colormap beta parameter (gamma = 1-beta)
Default value: 0
Saved in: General.OptionsFileName
View.ColormapBias
Colormap bias
Default value: 0
Saved in: General.OptionsFileName
View.ColormapCurvature
Colormap curvature or slope coefficient
Default value: 0
Saved in: General.OptionsFileName
View.ColormapInvert
Invert the color values, i.e., replace x with (255-x) in the colormap?
Default value: 0
Saved in: General.OptionsFileName
View.ColormapNumber
Default colormap number (0: black, 1: vis5d, 2: jet, 3: lucie, 4: rainbow, 5:
emc2000, 6: incadescent, 7: hot, 8: pink, 9: grayscale, 10: french, 11: hsv, 12:
spectrum, 13: bone, 14: spring, 15: summer, 16: autumm, 17: winter, 18: cool, 19:
copper, 20: magma, 21: inferno, 22: plasma, 23: viridis, 24: turbo)
Default value: 2
Saved in: General.OptionsFileName
View.ColormapRotation
Incremental colormap rotation
Default value: 0
Saved in: General.OptionsFileName
View.ColormapSwap
Swap the min/max values in the colormap?
Default value: 0
Saved in: General.OptionsFileName
View.ComponentMap0
Forced component 0 (if View.ForceNumComponents > 0)
Default value: 0
Saved in: General.OptionsFileName
View.ComponentMap1
Forced component 1 (if View.ForceNumComponents > 0)
Default value: 1
Saved in: General.OptionsFileName
288 Gmsh 4.11.1

View.ComponentMap2
Forced component 2 (if View.ForceNumComponents > 0)
Default value: 2
Saved in: General.OptionsFileName
View.ComponentMap3
Forced component 3 (if View.ForceNumComponents > 0)
Default value: 3
Saved in: General.OptionsFileName
View.ComponentMap4
Forced component 4 (if View.ForceNumComponents > 0)
Default value: 4
Saved in: General.OptionsFileName
View.ComponentMap5
Forced component 5 (if View.ForceNumComponents > 0)
Default value: 5
Saved in: General.OptionsFileName
View.ComponentMap6
Forced component 6 (if View.ForceNumComponents > 0)
Default value: 6
Saved in: General.OptionsFileName
View.ComponentMap7
Forced component 7 (if View.ForceNumComponents > 0)
Default value: 7
Saved in: General.OptionsFileName
View.ComponentMap8
Forced component 8 (if View.ForceNumComponents > 0)
Default value: 8
Saved in: General.OptionsFileName
View.CustomAbscissaMax
User-defined maximum abscissa value
Default value: 0
Saved in: -
View.CustomAbscissaMin
User-defined minimum abscissa value
Default value: 0
Saved in: -
View.CustomMax
User-defined maximum value to be displayed
Default value: 0
Saved in: -
View.CustomMin
User-defined minimum value to be displayed
Default value: 0
Saved in: -
View.DisplacementFactor
Displacement amplification
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 289

View.DrawHexahedra
Display post-processing hexahedra?
Default value: 1
Saved in: General.OptionsFileName
View.DrawLines
Display post-processing lines?
Default value: 1
Saved in: General.OptionsFileName
View.DrawPoints
Display post-processing points?
Default value: 1
Saved in: General.OptionsFileName
View.DrawPrisms
Display post-processing prisms?
Default value: 1
Saved in: General.OptionsFileName
View.DrawPyramids
Display post-processing pyramids?
Default value: 1
Saved in: General.OptionsFileName
View.DrawTrihedra
Display post-processing trihedra?
Default value: 1
Saved in: General.OptionsFileName
View.DrawQuadrangles
Display post-processing quadrangles?
Default value: 1
Saved in: General.OptionsFileName
View.DrawScalars
Display scalar values?
Default value: 1
Saved in: General.OptionsFileName
View.DrawSkinOnly
Draw only the skin of 3D scalar views?
Default value: 0
Saved in: General.OptionsFileName
View.DrawStrings
Display post-processing annotation strings?
Default value: 1
Saved in: General.OptionsFileName
View.DrawTensors
Display tensor values?
Default value: 1
Saved in: General.OptionsFileName
View.DrawTetrahedra
Display post-processing tetrahedra?
Default value: 1
Saved in: General.OptionsFileName
290 Gmsh 4.11.1

View.DrawTriangles
Display post-processing triangles?
Default value: 1
Saved in: General.OptionsFileName
View.DrawVectors
Display vector values?
Default value: 1
Saved in: General.OptionsFileName
View.Explode
Element shrinking factor (between 0 and 1)
Default value: 1
Saved in: General.OptionsFileName
View.ExternalView
Index of the view used to color vector fields (-1: self)
Default value: -1
Saved in: General.OptionsFileName
View.FakeTransparency
Use fake transparency (cheaper than the real thing, but incorrect)
Default value: 0
Saved in: General.OptionsFileName
View.ForceNumComponents
Force number of components to display (see View.ComponentMapN for mapping)
Default value: 0
Saved in: General.OptionsFileName
View.GeneralizedRaiseFactor
Generalized raise amplification factor
Default value: 1
Saved in: General.OptionsFileName
View.GeneralizedRaiseView
Index of the view used for generalized raise (-1: self)
Default value: -1
Saved in: General.OptionsFileName
View.GlyphLocation
Glyph (arrow, number, etc.) location (1: center of gravity, 2: node)
Default value: 1
Saved in: General.OptionsFileName
View.Height
Height (in pixels) of the scale or 2D plot
Default value: 200
Saved in: General.OptionsFileName
View.IntervalsType
Type of interval display (1: iso, 2: continuous, 3: discrete, 4: numeric)
Default value: 2
Saved in: General.OptionsFileName
View.Light
Enable lighting for the view
Default value: 1
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 291

View.LightLines
Light element edges
Default value: 1
Saved in: General.OptionsFileName
View.LightTwoSide
Light both sides of surfaces (leads to slower rendering)
Default value: 1
Saved in: General.OptionsFileName
View.LineType
Display lines as solid color segments (0) or 3D cylinders (1)
Default value: 0
Saved in: General.OptionsFileName
View.LineWidth
Display width of lines (in pixels)
Default value: 1
Saved in: General.OptionsFileName
View.MaxRecursionLevel
Maximum recursion level for adaptive views
Default value: 0
Saved in: General.OptionsFileName
View.Max Maximum value in the view (read-only)
Default value: 0
Saved in: -
View.MaxVisible
Maximum value in the visible parts of the view, taking current time step and tensor
display type into account (read-only)
Default value: 0
Saved in: -
View.MaxX
Maximum view coordinate along the X-axis (read-only)
Default value: 0
Saved in: -
View.MaxY
Maximum view coordinate along the Y-axis (read-only)
Default value: 0
Saved in: -
View.MaxZ
Maximum view coordinate along the Z-axis (read-only)
Default value: 0
Saved in: -
View.Min Minimum value in the view (read-only)
Default value: 0
Saved in: -
View.MinVisible
Minimum value in the visible parts of the view, taking current time step and tensor
display type into account (read-only)
Default value: 0
Saved in: -
292 Gmsh 4.11.1

View.MinX
Minimum view coordinate along the X-axis (read-only)
Default value: 0
Saved in: -
View.MinY
Minimum view coordinate along the Y-axis (read-only)
Default value: 0
Saved in: -
View.MinZ
Minimum view coordinate along the Z-axis (read-only)
Default value: 0
Saved in: -
View.NbIso
Number of intervals
Default value: 10
Saved in: General.OptionsFileName
View.NbTimeStep
Number of time steps in the view (do not change this!)
Default value: 1
Saved in: -
View.NormalRaise
Elevation of the view along the normal (in model coordinates)
Default value: 0
Saved in: -
View.Normals
Display size of normal vectors (in pixels)
Default value: 0
Saved in: General.OptionsFileName
View.OffsetX
Translation of the view along X-axis (in model coordinates)
Default value: 0
Saved in: -
View.OffsetY
Translation of the view along Y-axis (in model coordinates)
Default value: 0
Saved in: -
View.OffsetZ
Translation of the view along Z-axis (in model coordinates)
Default value: 0
Saved in: -
View.PointSize
Display size of points (in pixels)
Default value: 3
Saved in: General.OptionsFileName
View.PointType
Display points as solid color dots (0), 3D spheres (1), scaled dots (2) or scaled
spheres (3)
Chapter 7: Gmsh options 293

Default value: 0
Saved in: General.OptionsFileName
View.PositionX
X position (in pixels) of the scale or 2D plot (< 0: measure from right edge; >= 1e5:
centered)
Default value: 100
Saved in: General.OptionsFileName
View.PositionY
Y position (in pixels) of the scale or 2D plot (< 0: measure from bottom edge; >=
1e5: centered)
Default value: 50
Saved in: General.OptionsFileName
View.RaiseX
Elevation of the view along X-axis (in model coordinates)
Default value: 0
Saved in: -
View.RaiseY
Elevation of the view along Y-axis (in model coordinates)
Default value: 0
Saved in: -
View.RaiseZ
Elevation of the view along Z-axis (in model coordinates)
Default value: 0
Saved in: -
View.RangeType
Value scale range type (1: default, 2: custom, 3: per time step)
Default value: 1
Saved in: General.OptionsFileName
View.Sampling
Element sampling rate (draw one out every ‘Sampling’ elements)
Default value: 1
Saved in: General.OptionsFileName
View.SaturateValues
Saturate the view values to custom min and max (1: true, 0: false)
Default value: 0
Saved in: General.OptionsFileName
View.ScaleType
Value scale type (1: linear, 2: logarithmic, 3: double logarithmic)
Default value: 1
Saved in: General.OptionsFileName
View.ShowElement
Show element boundaries?
Default value: 0
Saved in: General.OptionsFileName
View.ShowScale
Show value scale?
Default value: 1
Saved in: General.OptionsFileName
294 Gmsh 4.11.1

View.ShowTime
Time display mode (0: none, 1: time series, 2: harmonic data, 3: automatic, 4: step
data, 5: multi-step data, 6: real eigenvalues, 7: complex eigenvalues)
Default value: 3
Saved in: General.OptionsFileName
View.SmoothNormals
Smooth the normals?
Default value: 0
Saved in: General.OptionsFileName
View.Stipple
Stipple curves in 2D and line plots?
Default value: 0
Saved in: General.OptionsFileName
View.Tangents
Display size of tangent vectors (in pixels)
Default value: 0
Saved in: General.OptionsFileName
View.TargetError
Target representation error for adaptive views
Default value: 0.0001
Saved in: General.OptionsFileName
View.TensorType
Tensor display type (1: Von-Mises, 2: maximum eigenvalue, 3: minimum eigenvalue,
4: eigenvectors, 5: ellipse, 6: ellipsoid, 7: frame)
Default value: 1
Saved in: General.OptionsFileName
View.TimeStep
Current time step displayed
Default value: 0
Saved in: -
View.Time
Current time displayed (if positive, sets the time step corresponding the given time
value)
Default value: 0
Saved in: -
View.TransformXX
Element (1,1) of the 3x3 coordinate transformation matrix
Default value: 1
Saved in: -
View.TransformXY
Element (1,2) of the 3x3 coordinate transformation matrix
Default value: 0
Saved in: -
View.TransformXZ
Element (1,3) of the 3x3 coordinate transformation matrix
Default value: 0
Saved in: -
Chapter 7: Gmsh options 295

View.TransformYX
Element (2,1) of the 3x3 coordinate transformation matrix
Default value: 0
Saved in: -

View.TransformYY
Element (2,2) of the 3x3 coordinate transformation matrix
Default value: 1
Saved in: -

View.TransformYZ
Element (2,3) of the 3x3 coordinate transformation matrix
Default value: 0
Saved in: -

View.TransformZX
Element (3,1) of the 3x3 coordinate transformation matrix
Default value: 0
Saved in: -

View.TransformZY
Element (3,2) of the 3x3 coordinate transformation matrix
Default value: 0
Saved in: -

View.TransformZZ
Element (3,3) of the 3x3 coordinate transformation matrix
Default value: 1
Saved in: -

View.Type
Type of plot (1: 3D, 2: 2D space, 3: 2D time, 4: 2D)
Default value: 1
Saved in: -

View.UseGeneralizedRaise
Use generalized raise?
Default value: 0
Saved in: General.OptionsFileName

View.VectorType
Vector display type (1: segment, 2: arrow, 3: pyramid, 4: 3D arrow, 5: displace-
ment, 6: comet)
Default value: 4
Saved in: General.OptionsFileName

View.Visible
Is the view visible?
Default value: 1
Saved in: -

View.Width
Width (in pixels) of the scale or 2D plot
Default value: 300
Saved in: General.OptionsFileName
296 Gmsh 4.11.1

View.Color.Points
Point color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Lines
Line color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Triangles
Triangle color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Quadrangles
Quadrangle color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Tetrahedra
Tetrahedron color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Hexahedra
Hexahedron color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Prisms
Prism color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Pyramids
Pyramid color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Trihedra
Trihedron color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Tangents
Tangent vector color
Default value: {255,255,0}
Saved in: General.OptionsFileName
View.Color.Normals
Normal vector color
Default value: {255,0,0}
Saved in: General.OptionsFileName
View.Color.Text2D
2D text color
Default value: {0,0,0}
Saved in: General.OptionsFileName
Chapter 7: Gmsh options 297

View.Color.Text3D
3D text color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Axes
Axes color
Default value: {0,0,0}
Saved in: General.OptionsFileName
View.Color.Background2D
Bacground color for 2D plots
Default value: {255,255,255}
Saved in: General.OptionsFileName
View.ColorTable
Color table used to draw the view
Saved in: General.OptionsFileName
Chapter 8: Gmsh mesh size fields 299

8 Gmsh mesh size fields

This chapter lists all the Gmsh mesh size fields (see Section 1.2.2 [Specifying mesh element
sizes], page 10). Fields can be specified in script files (see Section 5.3.1 [Mesh element sizes],
page 111) or using the API (see Section 6.5 [Namespace gmsh/model/mesh/field], page 167).
See Section 2.10 [t10], page 37 for an example on how to use fields.
AttractorAnisoCurve
Compute the distance to the given curves and specify the mesh size independently
in the direction normal and parallel to the nearest curve. For efficiency each curve
is replaced by a set of Sampling points, to which the distance is actually computed.

Options:

CurvesList
Tags of curves in the geometric model
Type: list
Default value: {}
DistMax Maxmium distance, above this distance from the curves, prescribe the
maximum mesh sizes
Type: float
Default value: 0.5
DistMin Minimum distance, below this distance from the curves, prescribe the
minimum mesh sizes
Type: float
Default value: 0.1
Sampling Number of sampling points on each curve
Type: integer
Default value: 20
SizeMaxNormal
Maximum mesh size in the direction normal to the closest curve
Type: float
Default value: 0.5
SizeMaxTangent
Maximum mesh size in the direction tangeant to the closest curve
Type: float
Default value: 0.5
SizeMinNormal
Minimum mesh size in the direction normal to the closest curve
Type: float
Default value: 0.05
SizeMinTangent
Minimum mesh size in the direction tangeant to the closest curve
Type: float
Default value: 0.5
AutomaticMeshSizeField
Compute a mesh size field that is quite automatic Takes into account surface cur-
vatures and closeness of objects
300 Gmsh 4.11.1

Options:

features Enable computation of local feature size (thin channels)

Type: boolean
Default value: 1
gradation
Maximum growth ratio for the edges lengths
Type: float
Default value: 1.1
hBulk Default size where it is not prescribed
Type: float
Default value: -1
hMax Maximum size
Type: float
Default value: -1
hMin Minimum size
Type: float
Default value: -1
nPointsPerCircle
Number of points per circle (adapt to curvature of surfaces)
Type: integer
Default value: 20
nPointsPerGap
Number of layers of elements in thin layers
Type: integer
Default value: 1
p4estFileToLoad
p4est file containing the size field
Type: string
Default value: ""
smoothing
Enable size smoothing (should always be true)
Type: boolean
Default value: 1
Ball Return VIn inside a spherical ball, and VOut outside. The ball is defined by

||dX||^2 < R^2 &&

dX = (X - XC)^2 + (Y-YC)^2 + (Z-ZC)^2

If Thickness is > 0, the mesh size is interpolated between VIn and VOut in a layer
around the ball of the prescribed thickness.

Options:

Radius Radius
Type: float
Default value: 0
Chapter 8: Gmsh mesh size fields 301

Thickness
Thickness of a transition layer outside the ball
Type: float
Default value: 0
VIn Value inside the ball
Type: float
Default value: 1e+22
VOut Value outside the ball
Type: float
Default value: 1e+22
XCenter X coordinate of the ball center
Type: float
Default value: 0
YCenter Y coordinate of the ball center
Type: float
Default value: 0
ZCenter Z coordinate of the ball center
Type: float
Default value: 0
BoundaryLayer
Insert a 2D boundary layer mesh next to some curves in the model.

Options:

AnisoMax Threshold angle for creating a mesh fan in the boundary layer
Type: float
Default value: 10000000000
Beta Beta coefficient of the Beta Law
Type: float
Default value: 1.01
BetaLaw Use Beta Law instead of geometric progression
Type: integer
Default value: 0
CurvesList
Tags of curves in the geometric model for which a boundary layer is
needed
Type: list
Default value: {}
ExcludedSurfacesList
Tags of surfaces in the geometric model where the boundary layer should
not be constructed
Type: list
Default value: {}
FanPointsList
Tags of points in the geometric model for which a fan is created
Type: list
Default value: {}
302 Gmsh 4.11.1

FanPointsSizesList
Number of elements in the fan for each fan node. If not present default
value Mesh.BoundaryLayerFanElements
Type: list
Default value: {}
IntersectMetrics
Intersect metrics of all surfaces
Type: integer
Default value: 0
NbLayers Number of Layers in theBeta Law
Type: integer
Default value: 10
PointsList
Tags of points in the geometric model for which a boundary layer ends
Type: list
Default value: {}
Quads Generate recombined elements in the boundary layer
Type: integer
Default value: 0
Ratio Size ratio between two successive layers
Type: float
Default value: 1.1
Size Mesh size normal to the curve
Type: float
Default value: 0.1
SizeFar Mesh size far from the curves
Type: float
Default value: 1
SizesList
Mesh size normal to the curve, per point (overwrites Size when defined)
Type: list double
Default value: {}
Thickness
Maximal thickness of the boundary layer
Type: float
Default value: 0.01
Box Return VIn inside the box, and VOut outside. The box is defined by

Xmin <= x <= XMax &&

YMin <= y <= YMax &&
ZMin <= z <= ZMax

If Thickness is > 0, the mesh size is interpolated between VIn and VOut in a layer
around the box of the prescribed thickness.

Options:
Chapter 8: Gmsh mesh size fields 303

Thickness
Thickness of a transition layer outside the box
Type: float
Default value: 0
VIn Value inside the box
Type: float
Default value: 1e+22
VOut Value outside the box
Type: float
Default value: 1e+22
XMax Maximum X coordinate of the box
Type: float
Default value: 0
XMin Minimum X coordinate of the box
Type: float
Default value: 0
YMax Maximum Y coordinate of the box
Type: float
Default value: 0
YMin Minimum Y coordinate of the box
Type: float
Default value: 0
ZMax Maximum Z coordinate of the box
Type: float
Default value: 0
ZMin Minimum Z coordinate of the box
Type: float
Default value: 0
Constant Return VIn when inside the entities (and on their boundary if IncludeBoundary is
set), and VOut outside.

Options:

CurvesList
Curve tags
Type: list
Default value: {}
IncludeBoundary
Include the boundary of the entities
Type: boolean
Default value: 1
PointsList
Point tags
Type: list
Default value: {}
304 Gmsh 4.11.1

SurfacesList
Surface tags
Type: list
Default value: {}
VIn Value inside the entities
Type: float
Default value: 1e+22
VOut Value outside the entities
Type: float
Default value: 1e+22
VolumesList
Volume tags
Type: list
Default value: {}
Curvature
Compute the curvature of Field[InField]:

F = div(norm(grad(Field[InField])))

Options:

Delta Step of the finite differences

Type: float
Default value: 0.0003464101615137755
InField Input field tag
Type: integer
Default value: 1
Cylinder Return VIn inside a frustrated cylinder, and VOut outside. The cylinder is defined
by

||dX||^2 < R^2 &&

(X-X0).A < ||A||^2
dX = (X - X0) - ((X - X0).A)/(||A||^2) . A

Options:

Radius Radius
Type: float
Default value: 0
VIn Value inside the cylinder
Type: float
Default value: 1e+22
VOut Value outside the cylinder
Type: float
Default value: 1e+22
XAxis X component of the cylinder axis
Type: float
Default value: 0
Chapter 8: Gmsh mesh size fields 305

XCenter X coordinate of the cylinder center

Type: float
Default value: 0
YAxis Y component of the cylinder axis
Type: float
Default value: 0
YCenter Y coordinate of the cylinder center
Type: float
Default value: 0
ZAxis Z component of the cylinder axis
Type: float
Default value: 1
ZCenter Z coordinate of the cylinder center
Type: float
Default value: 0
Distance Compute the distance to the given points, curves or surfaces. For efficiency, curves
and surfaces are replaced by a set of points (sampled according to Sampling), to
which the distance is actually computed.

Options:

CurvesList
Tags of curves in the geometric model
Type: list
Default value: {}
PointsList
Tags of points in the geometric model
Type: list
Default value: {}
Sampling Linear (i.e. per dimension) number of sampling points to discretize each
curve and surface
Type: integer
Default value: 20
SurfacesList
Tags of surfaces in the geometric model (only OpenCASCADE and
discrete surfaces are currently supported)
Type: list
Default value: {}
Extend Compute an extension of the mesh sizes from the given boundary curves (resp. sur-
faces) inside the surfaces (resp. volumes) being meshed. If the mesh size on the
boundary, computed as the local average length of the edges of the boundary ele-
ments, is denoted by SizeBnd, the extension is computed as:

F = f * SizeBnd + (1 - f) * SizeMax, if d < DistMax

F = SizeMax, if d >= DistMax

306 Gmsh 4.11.1

where d denotes the distance to the boundary and f = ((DistMax - d) / Dist-

Max)^Power.

Options:

CurvesList
Tags of curves in the geometric model
Type: list
Default value: {}
DistMax Maximum distance of the size extension
Type: float
Default value: 1
Power Power exponent used to interpolate the mesh size
Type: float
Default value: 1
SizeMax Mesh size outside DistMax
Type: float
Default value: 1
SurfacesList
Tags of surfaces in the geometric model
Type: list
Default value: {}
ExternalProcess
**This Field is experimental**
Call an external process that received coordinates triple (x,y,z) as binary double
precision numbers on stdin and is supposed to write the field value on stdout as a
binary double precision number.
NaN,NaN,NaN is sent as coordinate to indicate the end of the process.

Example of client (python2):

import os
import struct
import math
import sys
if sys.platform == "win32" :
import msvcrt
msvcrt.setmode(0, os.O BINARY)
msvcrt.setmode(1, os.O BINARY)
while(True):
xyz = struct.unpack("ddd", os.read(0,24))
if math.isnan(xyz[0]):
break
f = 0.001 + xyz[1]*0.009
os.write(1,struct.pack("d",f))

Example of client (python3):

import struct
import sys
import math
Chapter 8: Gmsh mesh size fields 307

while(True):
xyz = struct.unpack("ddd", sys.stdin.buffer.read(24))
if math.isnan(xyz[0]):
break
f = 0.001 + xyz[1]*0.009
sys.stdout.buffer.write(struct.pack("d",f))
sys.stdout.flush()

Example of client (c, unix):

#include <unistd.h>
int main(int argc, char **argv) {
double xyz[3];
while(read(STDIN FILENO, &xyz, 3*sizeof(double)) == 3*sizeof(double)) {
if (xyz[0] != xyz[0]) break; //nan
double f = 0.001 + 0.009 * xyz[1];
write(STDOUT FILENO, &f, sizeof(double));
}
return 0;
}

Example of client (c, windows):

#include <stdio.h>
#include <io.h>
#include <fcntl.h>
int main(int argc, char **argv) {
double xyz[3];
setmode(fileno(stdin),O BINARY);
setmode(fileno(stdout),O BINARY);
while(read(fileno(stdin), &xyz, 3*sizeof(double)) == 3*sizeof(double)) {
if (xyz[0] != xyz[0])
break;
double f = f = 0.01 + 0.09 * xyz[1];
write(fileno(stdout), &f, sizeof(double));
}
}

Options:

CommandLine
Command line to launch
Type: string
Default value: ""
Frustum Interpolate mesh sizes on a extended cylinder frustrum defined by inner (R1i and
R2i) and outer (R1o and R2o) radii and two endpoints P1 and P2.The field value
F for a point P is given by :

u = P1P . P1P2 / ||P1P2||

r = || P1P - u*P1P2 ||
Ri = (1 - u) * R1i + u * R2i
Ro = (1 - u) * R1o + u * R2o
308 Gmsh 4.11.1

v = (r - Ri) / (Ro - Ri)

F = (1 - v) * ((1 - u) * v1i + u * v2i) + v * ((1 - u) * v1o + u * v2o)
with (u, v) in [0, 1] x [0, 1].

Options:

InnerR1 Inner radius of Frustum at endpoint 1

Type: float
Default value: 0
InnerR2 Inner radius of Frustum at endpoint 2
Type: float
Default value: 0
InnerV1 Mesh size at point 1, inner radius
Type: float
Default value: 0.1
InnerV2 Mesh size at point 2, inner radius
Type: float
Default value: 0.1
OuterR1 Outer radius of Frustum at endpoint 1
Type: float
Default value: 1
OuterR2 Outer radius of Frustum at endpoint 2
Type: float
Default value: 1
OuterV1 Mesh size at point 1, outer radius
Type: float
Default value: 1
OuterV2 Mesh size at point 2, outer radius
Type: float
Default value: 1
X1 X coordinate of endpoint 1
Type: float
Default value: 0
X2 X coordinate of endpoint 2
Type: float
Default value: 0
Y1 Y coordinate of endpoint 1
Type: float
Default value: 0
Y2 Y coordinate of endpoint 2
Type: float
Default value: 0
Z1 Z coordinate of endpoint 1
Type: float
Default value: 1
Chapter 8: Gmsh mesh size fields 309

Z2 Z coordinate of endpoint 2
Type: float
Default value: 0
Gradient Compute the finite difference gradient of Field[InField]:

F = (Field[InField](X + Delta/2) - Field[InField](X - Delta/2)) / Delta

Options:

Delta Finite difference step

Type: float
Default value: 0.0003464101615137755
InField Input field tag
Type: integer
Default value: 1
Kind Component of the gradient to evaluate: 0 for X, 1 for Y, 2 for Z, 3 for
the norm
Type: integer
Default value: 3
IntersectAniso
Take the intersection of 2 anisotropic fields according to Alauzet.

Options:

FieldsList
Field indices
Type: list
Default value: {}
Laplacian
Compute finite difference the Laplacian of Field[InField]:

F = G(x+d,y,z) + G(x-d,y,z) +
G(x,y+d,z) + G(x,y-d,z) +
G(x,y,z+d) + G(x,y,z-d) - 6 * G(x,y,z),

where G = Field[InField] and d = Delta.

Options:

Delta Finite difference step

Type: float
Default value: 0.0003464101615137755
InField Input field tag
Type: integer
Default value: 1
LonLat Evaluate Field[InField] in geographic coordinates (longitude, latitude):
310 Gmsh 4.11.1

F = Field[InField](atan(y / x), asin(z / sqrt(x^2 + y^2 + z^2))

Options:

FromStereo
If = 1, the mesh is in stereographic coordinates: xi = 2Rx/(R+z), eta
= 2Ry/(R+z)
Type: integer
Default value: 0
InField Tag of the field to evaluate
Type: integer
Default value: 1
RadiusStereo
Radius of the sphere of the stereograpic coordinates
Type: float
Default value: 6371000
MathEval Evaluate a mathematical expression. The expression can contain x, y, z for spatial
coordinates, F0, F1, ... for field values, and mathematical functions.

Options:

F Mathematical function to evaluate.

Type: string
Default value: "F2 + Sin(z)"
MathEvalAniso
Evaluate a metric expression. The expressions can contain x, y, z for spatial coor-
dinates, F0, F1, ... for field values, and mathematical functions.

Options:

M11 Element 11 of the metric tensor

Type: string
Default value: "F2 + Sin(z)"
M12 Element 12 of the metric tensor
Type: string
Default value: "F2 + Sin(z)"
M13 Element 13 of the metric tensor
Type: string
Default value: "F2 + Sin(z)"
M22 Element 22 of the metric tensor
Type: string
Default value: "F2 + Sin(z)"
M23 Element 23 of the metric tensor
Type: string
Default value: "F2 + Sin(z)"
M33 Element 33 of the metric tensor
Type: string
Default value: "F2 + Sin(z)"
Chapter 8: Gmsh mesh size fields 311

Max Take the maximum value of a list of fields.

Options:

FieldsList
Field indices
Type: list
Default value: {}
MaxEigenHessian
Compute the maximum eigenvalue of the Hessian matrix of Field[InField], with the
gradients evaluated by finite differences:

F = max(eig(grad(grad(Field[InField]))))

Options:

Delta Step used for the finite differences

Type: float
Default value: 0.0003464101615137755
InField Input field tag
Type: integer
Default value: 1
Mean Return the mean value

F = (G(x + delta, y, z) + G(x - delta, y, z) +

G(x, y + delta, z) + G(x, y - delta, z) +
G(x, y, z + delta) + G(x, y, z - delta) +
G(x, y, z)) / 7,

where G = Field[InField].

Options:

Delta Distance used to compute the mean value

Type: float
Default value: 0.0003464101615137755
InField Input field tag
Type: integer
Default value: 1
Min Take the minimum value of a list of fields.

Options:

FieldsList
Field indices
Type: list
Default value: {}
312 Gmsh 4.11.1

MinAniso Take the intersection of a list of possibly anisotropic fields.

Options:

FieldsList
Field indices
Type: list
Default value: {}

Octree Pre compute another field on an octree to speed-up evalution.

Options:

InField Id of the field to represent on the octree

Type: integer
Default value: 1

Param Evaluate Field[InField] in parametric coordinates:

F = Field[InField](FX,FY,FZ)

See the MathEval Field help to get a description of valid FX, FY and FZ expressions.

Options:

FX X component of parametric function

Type: string
Default value: ""

FY Y component of parametric function

Type: string
Default value: ""

FZ Z component of parametric function

Type: string
Default value: ""

InField Input field tag

Type: integer
Default value: 1

PostView Evaluate the post processing view with index ViewIndex, or with tag ViewTag if
ViewTag is positive.

Options:

CropNegativeValues
return MAX LC instead of a negative value (this option is needed for
backward compatibility with the BackgroundMesh option
Type: boolean
Default value: 1
Chapter 8: Gmsh mesh size fields 313

UseClosest
Use value at closest node if no exact match is found
Type: boolean
Default value: 1
ViewIndex
Post-processing view index
Type: integer
Default value: 0
ViewTag Post-processing view tag
Type: integer
Default value: -1
Restrict Restrict the application of a field to a given list of geometrical points, curves, surfaces
or volumes (as well as their boundaries if IncludeBoundary is set).

Options:

CurvesList
Curve tags
Type: list
Default value: {}
InField Input field tag
Type: integer
Default value: 1
IncludeBoundary
Include the boundary of the entities
Type: boolean
Default value: 1
PointsList
Point tags
Type: list
Default value: {}
SurfacesList
Surface tags
Type: list
Default value: {}
VolumesList
Volume tags
Type: list
Default value: {}
Structured
Linearly interpolate between data provided on a 3D rectangular structured grid.

The format of the input file is:

Ox Oy Oz
Dx Dy Dz
nx ny nz
314 Gmsh 4.11.1

v(0,0,0) v(0,0,1) v(0,0,2) ...

v(0,1,0) v(0,1,1) v(0,1,2) ...
v(0,2,0) v(0,2,1) v(0,2,2) ...
... ... ...
v(1,0,0) ... ...

where O are the coordinates of the first node, D are the distances between nodes in
each direction, n are the numbers of nodes in each direction, and v are the values
on each node.

Options:

FileName Name of the input file

Type: path
Default value: ""
OutsideValue
Value of the field outside the grid (only used if the "SetOutsideValue"
option is true).
Type: float
Default value: 1e+22
SetOutsideValue
True to use the "OutsideValue" option. If False, the last values of the
grid are used.
Type: boolean
Default value: 0
TextFormat
True for ASCII input files, false for binary files (4 bite signed integers
for n, double precision floating points for v, D and O)
Type: boolean
Default value: 0
Threshold
Return F = SizeMin if Field[InField] <= DistMin, F = SizeMax if Field[InField]
>= DistMax, and the interpolation between SizeMin and SizeMax if DistMin <
Field[InField] < DistMax.

Options:

DistMax Value after which the mesh size will be SizeMax

Type: float
Default value: 10
DistMin Value up to which the mesh size will be SizeMin
Type: float
Default value: 1
InField Tag of the field computing the input value, usually a distance
Type: integer
Default value: 0
Sigmoid True to interpolate between SizeMin and LcMax using a sigmoid, false
to interpolate linearly
Chapter 8: Gmsh mesh size fields 315

Type: boolean
Default value: 0
SizeMax Mesh size when value > DistMax
Type: float
Default value: 1
SizeMin Mesh size when value < DistMin
Type: float
Default value: 0.1
StopAtDistMax
True to not impose mesh size outside DistMax (i.e., F = a very big value
if Field[InField] > DistMax)
Type: boolean
Default value: 0
Chapter 9: Gmsh plugins 317

9 Gmsh plugins
This chapter lists all the plugins that are bundled in the official Gmsh distribution. Plugins are
available in the GUI (by right-clicking on a view button, or by clicking on the black arrow next
to the view button, and then selecting the ‘Plugin’ submenu), in the scripting language (see
Section 5.4 [Post-processing scripting commands], page 117) and in the API (see Section 6.12
[Namespace gmsh/plugin], page 208). See Section 2.9 [t9], page 36 for an example on how to
use plugins.
Plugin(AnalyseMeshQuality)
Plugin(AnalyseMeshQuality) analyses the quality of the elements of a given dimen-
sion in the current model. Depending on the input parameters it computes the
minimum of the Jacobian determinant (J), the IGE quality measure (Inverse Gra-
dient Error) and/or the ICN quality measure (Condition Number). Statistics are
printed and, if requested, a model-based post-processing view is created for each
quality measure. The plugin can optionally hide elements by comparing the mea-
sure to a prescribed threshold.

J is faster to compute but gives information only on element validity while the other
measures also give information on element quality. The IGE measure is related to
the error on the gradient of the finite element solution. It is the scaled Jacobian for
quads and hexes and a new measure for triangles and tetrahedra. The ICN measure
is related to the condition number of the stiffness matrix. (See the article "Effi-
cient computation of the minimum of shape quality measures on curvilinear finite
elements" for details.)

Parameters:

- ‘JacobianDeterminant’: compute J?

- ‘IGEMeasure’: compute IGE?

- ‘ICNMeasure’: compute ICN?

- ‘HidingThreshold’: hide all elements for which min(mu) is strictly greater than (if
‘ThresholdGreater’ == 1) or less than (if ‘ThresholdGreater’ == 0) the thresh-
old, where mu is ICN if ‘ICNMeasure’ == 1, IGE if ‘IGEMeasure’ == 1 or
min(J)/max(J) if ‘JacobianDeterminant’ == 1.

- ‘CreateView’: create a model-based view of min(J)/max(J), min(IGE) and/or

min(ICN)?

- ‘Recompute’: force recomputation (set to 1 if the mesh has changed).

- ‘DimensionOfElements’: analyse elements of the given dimension if equal to 1, 2

or 3; analyse 2D and 3D elements if equal to 4; or analyse elements of the highest
dimension if equal to -1. Numeric options:
JacobianDeterminant
Default value: 0
IGEMeasure
Default value: 0
318 Gmsh 4.11.1

ICNMeasure
Default value: 0
HidingThreshold
Default value: 99
ThresholdGreater
Default value: 1
CreateView
Default value: 0
Recompute
Default value: 0
DimensionOfElements
Default value: -1
Plugin(Annotate)
Plugin(Annotate) adds the text string ‘Text’, in font ‘Font’ and size ‘FontSize’, in
the view ‘View’. The string is aligned according to ‘Align’.

If ‘ThreeD’ is equal to 1, the plugin inserts the string in model coordinates at the
position (‘X’,‘Y’,‘Z’). If ‘ThreeD’ is equal to 0, the plugin inserts the string in screen
coordinates at the position (‘X’,‘Y’).

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Annotate) is executed in-place for list-based datasets or creates a new list-

based view for other datasets. String options:
Text Default value: "My Text"
Font Default value: "Helvetica"
Align Default value: "Left"
Numeric options:
X Default value: 50
Y Default value: 30
Z Default value: 0
ThreeD Default value: 0
FontSize Default value: 14
View Default value: -1
Plugin(BoundaryAngles)
Plugin(BoundaryAngles) computes the (interior) angles between the line elements
on the boundary of all surfaces. The angles, computed modulo 2*Pi, are stored
in a new post-processing view, one for each surface. The plugin currently only
works for planar surfaces.Available options:- Visible (1=True, 0 = False, Default =
1): Visibility of the Views in the GUI - Save (1=True, 0 = False, Default = 0):
Save the Views on disk ?- Remove (1=True, 0 = False, Default = 0): Remove the
View from the memory after execution?- Filename (Default = ’Angles Surface’):
Root name for the Views (in case of save / Visibility)- Dir (Default = ”): Output
directory (possibly nested) String options:
Chapter 9: Gmsh plugins 319

Filename Default value: "Angles_Surface"

Dir Default value: ""
Numeric options:
View Default value: -1
Save Default value: 0
Visible Default value: 0
Remove Default value: 0
Plugin(Bubbles)
Plugin(Bubbles) constructs a geometry consisting of ‘bubbles’ inscribed in the
Voronoi of an input triangulation. ‘ShrinkFactor’ allows to change the size of the
bubbles. The plugin expects a triangulation in the ‘z = 0’ plane to exist in the
current model.

Plugin(Bubbles) creates one ‘.geo’ file. String options:

OutputFile
Default value: "bubbles.geo"
Numeric options:
ShrinkFactor
Default value: 0
Plugin(Crack)
Plugin(Crack) creates a crack around the physical group ‘PhysicalGroup’ of dimen-
sion ‘Dimension’ (1 or 2), embedded in a mesh of dimension ‘Dimension’ + 1. The
plugin duplicates the nodes and the elements on the crack and stores them in a new
discrete curve (‘Dimension’ = 1) or surface (‘Dimension’ = 2). The elements touch-
ing the crack on the positive side are modified to use the newly generated nodes.If
‘OpenBoundaryPhysicalGroup’ is given (> 0), its nodes are duplicated and the crack
will be left open on that (part of the) boundary. Otherwise, the lips of the crack
are sealed, i.e., its nodes are not duplicated. If ‘AuxiliaryPhysicalGroup’ is given (>
0), its elements are considered in addition to those in ‘PhysicalGroup’ for the logic
that groups the elements into the positive and negative side of the crack. However,
the nodes in ‘AuxiliaryPhysicalGroup’ are not duplicated (unless they are also in
‘PhysicalGroup’). This can be useful to treat corner cases in non-trivial geometries.
For 1D cracks, ‘NormalX’, ‘NormalY’ and ‘NormalZ’ provide the reference normal of
the surface in which the crack is supposed to be embedded. If ‘NewPhysicalGroup’
is positive, use it as the tag of the newly created curve or surface; otherwise use
‘PhysicalGroup’. Numeric options:
Dimension
Default value: 1
PhysicalGroup
Default value: 1
OpenBoundaryPhysicalGroup
Default value: 0
AuxiliaryPhysicalGroup
Default value: 0
NormalX Default value: 0
320 Gmsh 4.11.1

NormalY Default value: 0

NormalZ Default value: 1
NewPhysicalGroup
Default value: 0
DebugView
Default value: 0
Plugin(Curl)
Plugin(Curl) computes the curl of the field in the view ‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Curl) creates one new list-based view. Numeric options:

View Default value: -1
Plugin(CurvedBndDist)
Plugin(CurvedBndDist) ...
Plugin(CutBox)
Plugin(CutBox) cuts the view ‘View’ with a rectangular box defined by the 4 points
(‘X0’,‘Y0’,‘Z0’) (origin), (‘X1’,‘Y1’,‘Z1’) (axis of U), (‘X2’,‘Y2’,‘Z2’) (axis of V) and
(‘X3’,‘Y3’,‘Z3’) (axis of W).

The number of points along U, V, W is set with the options ‘NumPointsU’, ‘Num-
PointsV’ and ‘NumPointsW’.

If ‘ConnectPoints’ is zero, the plugin creates points; otherwise, the plugin generates
hexahedra, quadrangles, lines or points depending on the values of ‘NumPointsU’,
‘NumPointsV’ and ‘NumPointsW’.

If ‘Boundary’ is zero, the plugin interpolates the view inside the box; otherwise the
plugin interpolates the view at its boundary.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(CutBox) creates one new list-based view. Numeric options:

X0 Default value: 0
Y0 Default value: 0
Z0 Default value: 0
X1 Default value: 1
Y1 Default value: 0
Z1 Default value: 0
X2 Default value: 0
Y2 Default value: 1
Z2 Default value: 0
X3 Default value: 0
Y3 Default value: 0
Chapter 9: Gmsh plugins 321

Z3 Default value: 1
NumPointsU
Default value: 20
NumPointsV
Default value: 20
NumPointsW
Default value: 20
ConnectPoints
Default value: 1
Boundary Default value: 1
View Default value: -1
Plugin(CutGrid)
Plugin(CutGrid) cuts the view ‘View’ with a rectangular grid defined by the 3 points
(‘X0’,‘Y0’,‘Z0’) (origin), (‘X1’,‘Y1’,‘Z1’) (axis of U) and (‘X2’,‘Y2’,‘Z2’) (axis of V).

The number of points along U and V is set with the options ‘NumPointsU’ and
‘NumPointsV’.

If ‘ConnectPoints’ is zero, the plugin creates points; otherwise, the plugin generates
quadrangles, lines or points depending on the values of ‘NumPointsU’ and ‘Num-
PointsV’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(CutGrid) creates one new list-based view. Numeric options:

X0 Default value: 0
Y0 Default value: 0
Z0 Default value: 0
X1 Default value: 1
Y1 Default value: 0
Z1 Default value: 0
X2 Default value: 0
Y2 Default value: 1
Z2 Default value: 0
NumPointsU
Default value: 20
NumPointsV
Default value: 20
ConnectPoints
Default value: 1
View Default value: -1
322 Gmsh 4.11.1

Plugin(CutMesh)
Plugin(CutMesh) cuts the mesh of the current GModel with the zero value of the
levelset defined with the view ’View’.Sub-elements are created in the new model
(polygons in 2D and polyhedra in 3D) and border elements are created on the zero-
levelset.

If ‘Split’ is nonzero, the plugin splits the meshalong the edges of the cut elements
in the positive side.

If ’SaveTri’ is nonzero, the sub-elements are saved as simplices.

Plugin(CutMesh) creates one new GModel. Numeric options:

View Default value: -1
Split Default value: 0
SaveTri Default value: 0
Plugin(CutParametric)
Plugin(CutParametric) cuts the view ‘View’ with the parametric function (‘X’(u,v),
‘Y’(u,v), ‘Z’(u,v)), using ‘NumPointsU’ values of the parameter u in [‘MinU’,
‘MaxU’] and ‘NumPointsV’ values of the parameter v in [‘MinV’, ‘MaxV’].

If ‘ConnectPoints’ is set, the plugin creates surface or line elements; otherwise, the
plugin generates points.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(CutParametric) creates one new list-based view. String options:

X Default value: "2 * Cos(u) * Sin(v)"
Y Default value: "4 * Sin(u) * Sin(v)"
Z Default value: "0.1 + 0.5 * Cos(v)"
Numeric options:
MinU Default value: 0
MaxU Default value: 6.2832
NumPointsU
Default value: 180
MinV Default value: 0
MaxV Default value: 6.2832
NumPointsV
Default value: 180
ConnectPoints
Default value: 0
View Default value: -1
Plugin(CutPlane)
Plugin(CutPlane) cuts the view ‘View’ with the plane ‘A’*X + ‘B’*Y + ‘C’*Z + ‘D’
= 0.
Chapter 9: Gmsh plugins 323

If ‘ExtractVolume’ is nonzero, the plugin extracts the elements on one side of the
plane (depending on the sign of ‘ExtractVolume’).

If ‘View’ < 0, the plugin is run on the current view.

Plugin(CutPlane) creates one new list-based view. Numeric options:

A Default value: 1
B Default value: 0
C Default value: 0
D Default value: -0.01
ExtractVolume
Default value: 0
RecurLevel
Default value: 3
TargetError
Default value: 0.0001
View Default value: -1
Plugin(CutSphere)
Plugin(CutSphere) cuts the view ‘View’ with the sphere (X-‘Xc’)^2 + (Y-‘Yc’)^2 +
(Z-‘Zc’)^2 = ‘R’^2.

If ‘ExtractVolume’ is nonzero, the plugin extracts the elements inside (if ‘ExtractVol-
ume’ < 0) or outside (if ‘ExtractVolume’ > 0) the sphere.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(CutSphere) creates one new list-based view. Numeric options:

Xc Default value: 0
Yc Default value: 0
Zc Default value: 0
R Default value: 0.25
ExtractVolume
Default value: 0
RecurLevel
Default value: 3
TargetError
Default value: 0.0001
View Default value: -1
Plugin(DiscretizationError)
Plugin(DiscretizationError) computes the error between the mesh and the geometry.
It does so by supersampling the elements and computing the distance between the
supersampled points dans their projection on the geometry. Numeric options:
324 Gmsh 4.11.1

SuperSamplingNodes
Default value: 10
Plugin(Distance)
Plugin(Distance) computes distances to entities in a mesh.

If ‘PhysicalPoint’, ‘PhysicalLine’ and ‘PhysicalSurface’ are 0, the distance is com-

puted to all the boundaries. Otherwise the distance is computed to the given phys-
ical group.

If ‘DistanceType’ is 0, the plugin computes the geometrical Euclidean distance using

the naive O(N^2) algorithm. If ‘DistanceType’ > 0, the plugin computes an approx-
imate distance by solving a PDE with a diffusion constant equal to ‘DistanceType’
time the maximum size of the bounding box of the mesh as in [Legrand et al. 2006].

Positive ‘MinScale’ and ‘MaxScale’ scale the distance function.

Plugin(Distance) creates one new list-based view. Numeric options:

PhysicalPoint
Default value: 0
PhysicalLine
Default value: 0
PhysicalSurface
Default value: 0
DistanceType
Default value: 0
MinScale Default value: 0
MaxScale Default value: 0
Plugin(Divergence)
Plugin(Divergence) computes the divergence of the field in the view ‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Divergence) creates one new list-based view. Numeric options:

View Default value: -1
Plugin(Eigenvalues)
Plugin(Eigenvalues) computes the three real eigenvalues of each tensor in the view
‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Eigenvalues) creates three new list-based scalar views. Numeric options:

View Default value: -1
Plugin(Eigenvectors)
Plugin(Eigenvectors) computes the three (right) eigenvectors of each tensor in the
view ‘View’ and sorts them according to the value of the associated eigenvalues.

If ‘ScaleByEigenvalues’ is set, each eigenvector is scaled by its associated eigenvalue.

Chapter 9: Gmsh plugins 325

The plugin gives an error if the eigenvectors are complex.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Eigenvectors) creates three new list-based vector view. Numeric options:

ScaleByEigenvalues
Default value: 1
View Default value: -1
Plugin(ExtractEdges)
Plugin(ExtractEdges) extracts sharp edges from a triangular mesh.

Plugin(ExtractEdges) creates one new view. Numeric options:

Angle Default value: 40
IncludeBoundary
Default value: 1
Plugin(ExtractElements)
Plugin(ExtractElements) extracts some elements from the view ‘View’. If ‘MinVal’
!= ‘MaxVal’, it extracts the elements whose ‘TimeStep’-th values (averaged by ele-
ment) are comprised between ‘MinVal’ and ‘MaxVal’. If ‘Visible’ != 0, it extracts
visible elements.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(ExtractElements) creates one new list-based view. Numeric options:

MinVal Default value: 0
MaxVal Default value: 0
TimeStep Default value: 0
Visible Default value: 1
Dimension
Default value: -1
View Default value: -1
Plugin(FieldFromAmplitudePhase)
Plugin(FieldFromAmplitudePhase) builds a complex field ’u’ from amplitude ’a’
(complex) and phase ’phi’ given in two different ’Views’ u = a * exp(k*phi), with k
the wavenumber.

The result is to be interpolated in a sufficiently fine mesh: ’MeshFile’.

Plugin(FieldFromAmplitudePhase) generates one new view. String options:

MeshFile Default value: "fine.msh"
Numeric options:
Wavenumber
Default value: 5
AmplitudeView
Default value: 0
326 Gmsh 4.11.1

PhaseView
Default value: 1
Plugin(GaussPoints)
Given an input mesh, Plugin(GaussPoints) creates a list-based view containing the
Gauss points for a given polynomial ‘Order’.

If ‘PhysicalGroup’ is nonzero, the plugin only creates points for the elements be-
longing to the group. Numeric options:
Order Default value: 0
Dimension
Default value: 2
PhysicalGroup
Default value: 0
Plugin(Gradient)
Plugin(Gradient) computes the gradient of the field in the view ‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Gradient) creates one new list-based view. Numeric options:

View Default value: -1
Plugin(HarmonicToTime)
Plugin(HarmonicToTime) takes the values in the time steps ‘RealPart’ and ‘Imagi-
naryPart’ of the view ‘View’, and creates a new view containing

‘View’[‘RealPart’] * cos(p) +- ‘View’[‘ImaginaryPart’] * sin(p)

with
p = 2*Pi*k/‘NumSteps’, k = 0, ..., ‘NumSteps’-1
and ’NumSteps’ the total number of time steps
over ’NumPeriods’ periods at frequency ’Frequency’ [Hz].
The ’+’ sign is used if ‘TimeSign’>0, the ’-’ sign otherwise.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(HarmonicToTime) creates one new list-based view. Numeric options:

RealPart Default value: 0
ImaginaryPart
Default value: 1
NumSteps Default value: 20
TimeSign Default value: -1
Frequency
Default value: 1
NumPeriods
Default value: 1
View Default value: -1
Chapter 9: Gmsh plugins 327

Plugin(HomologyComputation)
Plugin(HomologyComputation) computes representative chains of basis elements of
(relative) homology and cohomology spaces.

Define physical groups in order to specify the computation domain and the relative
subdomain. Otherwise the whole mesh is the domain and the relative subdomain is
empty.

Plugin(HomologyComputation) creates new views, one for each basis element. The
resulting basis chains of desired dimension together with the mesh are saved to the
given file. String options:
DomainPhysicalGroups
Default value: ""
SubdomainPhysicalGroups
Default value: ""
ReductionImmunePhysicalGroups
Default value: ""
DimensionOfChainsToSave
Default value: "0, 1, 2, 3"
Filename Default value: "homology.msh"
Numeric options:
ComputeHomology
Default value: 1
ComputeCohomology
Default value: 0
HomologyPhysicalGroupsBegin
Default value: -1
CohomologyPhysicalGroupsBegin
Default value: -1
CreatePostProcessingViews
Default value: 1
ReductionOmit
Default value: 1
ReductionCombine
Default value: 3
PostProcessSimplify
Default value: 1
ReductionHeuristic
Default value: 1
Plugin(HomologyPostProcessing)
Plugin(HomologyPostProcessing) operates on representative basis chains of homol-
ogy and cohomology spaces. Functionality:

1. (co)homology basis transformation:

’TransformationMatrix’: Integer matrix of the transformation.
328 Gmsh 4.11.1

’PhysicalGroupsOfOperatedChains’: (Co)chains of a (co)homology space basis to

be transformed.
Results a new (co)chain basis that is an integer combination of the given basis.

2. Make basis representations of a homology space and a cohomology space com-

patible:
’PhysicalGroupsOfOperatedChains’: Chains of a homology space basis.
’PhysicalGroupsOfOperatedChains2’: Cochains of a cohomology space basis.
Results a new basis for the homology space such that the incidence matrix of the
new basis and the basis of the cohomology space is the identity matrix.

Options:
’PhysicalGroupsToTraceResults’: Trace the resulting (co)chains to the given physi-
cal groups.
’PhysicalGroupsToProjectResults’: Project the resulting (co)chains to the comple-
ment of the given physical groups.
’NameForResultChains’: Post-processing view name prefix for the results.
’ApplyBoundaryOperatorToResults’: Apply boundary operator to the resulting
chains.

String options:
TransformationMatrix
Default value: "1, 0; 0, 1"
PhysicalGroupsOfOperatedChains
Default value: "1, 2"
PhysicalGroupsOfOperatedChains2
Default value: ""
PhysicalGroupsToTraceResults
Default value: ""
PhysicalGroupsToProjectResults
Default value: ""
NameForResultChains
Default value: "c"
Numeric options:
ApplyBoundaryOperatorToResults
Default value: 0
Plugin(Integrate)
Plugin(Integrate) integrates a scalar field over all the elements of the view ‘View’
(if ‘Dimension’ < 0), or over all elements of the prescribed dimension (if ‘Dimension’
> 0). If the field is a vector field, the circulation/flux of the field over line/surface
elements is calculated.

If ‘View’ < 0, the plugin is run on the current view.

If ‘OverTime’ = i > -1 , the plugin integrates the scalar view over time (using the
trapezoidal rule) instead of over space, starting at step i. If ‘Visible’ = 1, the plugin
only integrates over visible entities.
Chapter 9: Gmsh plugins 329

Plugin(Integrate) creates one new list-based view. Numeric options:

View Default value: -1
OverTime Default value: -1
Dimension
Default value: -1
Visible Default value: 1
Plugin(Invisible)
Plugin(Invisible) deletes (if ‘DeleteElements’ is set) or reverses (if ‘ReverseElements’
is set) all the invisible elements in the current model. If the bounding box defined
by ‘XMin’ < x < ‘XMax, ‘YMin’ < y < ‘YMax and ‘ZMin’ < z < ‘ZMax’ is not empty,
mark all elements outside the bounding box as invisible prior to deleting or inverting
the elements. Numeric options:
DeleteElements
Default value: 1
ReverseElements
Default value: 0
XMin Default value: 0
YMin Default value: 0
ZMin Default value: 0
XMax Default value: 0
YMax Default value: 0
ZMax Default value: 0
Plugin(Isosurface)
Plugin(Isosurface) extracts the isosurface of value ‘Value’ from the view ‘View’, and
draws the ‘OtherTimeStep’-th step of the view ‘OtherView’ on this isosurface.

If ‘ExtractVolume’ is nonzero, the plugin extracts the isovolume with values greater
(if ‘ExtractVolume’ > 0) or smaller (if ‘ExtractVolume’ < 0) than the isosurface
‘Value’.

If ‘OtherTimeStep’ < 0, the plugin uses, for each time step in ‘View’, the corre-
sponding time step in ‘OtherView’. If ‘OtherView’ < 0, the plugin uses ‘View’ as
the value source.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Isosurface) creates as many list-based views as there are time steps in ‘View’.
Numeric options:
Value Default value: 0
ExtractVolume
Default value: 0
RecurLevel
Default value: 3
330 Gmsh 4.11.1

TargetError
Default value: 0.0001
View Default value: -1
OtherTimeStep
Default value: -1
OtherView
Default value: -1
Plugin(Lambda2)
Plugin(Lambda2) computes the eigenvalues Lambda(1,2,3) of the tensor (S ik S kj
+ Om ik Om kj), where S ij = 0.5 (ui,j + uj,i) and Om ij = 0.5 (ui,j - uj,i) are
respectively the symmetric and antisymmetric parts of the velocity gradient tensor.

Vortices are well represented by regions where Lambda(2) is negative.

If ‘View’ contains tensor elements, the plugin directly uses the tensors as the values
of the velocity gradient tensor; if ‘View’ contains vector elements, the plugin uses
them as the velocities from which to derive the velocity gradient tensor.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Lambda2) creates one new list-based view. Numeric options:

Eigenvalue
Default value: 2
View Default value: -1
Plugin(LongitudeLatitude)
Plugin(LongituteLatitude) projects the view ‘View’ in longitude-latitude.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(LongituteLatitude) is executed in place. Numeric options:

View Default value: -1
Plugin(MakeSimplex)
Plugin(MakeSimplex) decomposes all non-simplectic elements (quadrangles, prisms,
hexahedra, pyramids) in the view ‘View’ into simplices (triangles, tetrahedra).

If ‘View’ < 0, the plugin is run on the current view.

Plugin(MakeSimplex) is executed in-place. Numeric options:

View Default value: -1
Plugin(MathEval)
Plugin(MathEval) creates a new view using data from the time step ‘TimeStep’ in
the view ‘View’.

If only ‘Expression0’ is given (and ‘Expression1’, ..., ‘Expression8’ are all empty),
the plugin creates a scalar view. If ‘Expression0’, ‘Expression1’ and/or ‘Expression2’
are given (and ‘Expression3’, ..., ‘Expression8’ are all empty) the plugin creates a
vector view. Otherwise the plugin creates a tensor view.
Chapter 9: Gmsh plugins 331

In addition to the usual mathematical functions (Exp, Log, Sqrt, Sin, Cos, Fabs,
etc.) and operators (+, -, *, /, ^), all expressions can contain:

- the symbols v0, v1, v2, ..., vn, which represent the n components in ‘View’;

- the symbols w0, w1, w2, ..., wn, which represent the n components of ‘OtherView’,
at time step ‘OtherTimeStep’;

- the symbols x, y and z, which represent the three spatial coordinates.

If ‘TimeStep’ < 0, the plugin extracts data from all the time steps in the view.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(MathEval) creates one new view.If ‘PhysicalRegion’ < 0, the plugin is run
on all physical regions.

Plugin(MathEval) creates one new list-based view. String options:

Expression0
Default value: "Sqrt(v0^2+v1^2+v2^2)"
Expression1
Default value: ""
Expression2
Default value: ""
Expression3
Default value: ""
Expression4
Default value: ""
Expression5
Default value: ""
Expression6
Default value: ""
Expression7
Default value: ""
Expression8
Default value: ""
Numeric options:
TimeStep Default value: -1
View Default value: -1
OtherTimeStep
Default value: -1
OtherView
Default value: -1
ForceInterpolation
Default value: 0
332 Gmsh 4.11.1

PhysicalRegion
Default value: -1
Plugin(MeshSizeFieldView)
Plugin(MeshSizeFieldView) evaluates the mesh size field ‘MeshSizeField’ on speci-
fied ‘Component‘ (0 for scalar) of the post-processing view ‘View’. Numeric options:
MeshSizeField
Default value: 0
View Default value: -1
Component
Default value: 0
Plugin(MeshSubEntities)
Plugin(MeshSubEntities) creates mesh elements for the entities of dimension ‘Out-
putDimension’ (0 for vertices, 1 for edges, 2 for faces) of the ‘InputPhysicalGroup’
of dimension ‘InputDimension’. The plugin creates new elements belonging to ‘Out-
putPhysicalGroup’. Numeric options:
InputDimension
Default value: 1
InputPhysicalGroup
Default value: 1
OuputDimension
Default value: 0
OuputPhysicalGroup
Default value: 2000
Plugin(MeshVolume)
Plugin(MeshVolume) computes the volume of the mesh.

Only the elements in the physical group ‘PhysicalGroup’ of dimension ‘Dimension’

are taken into account, unless ’PhysicalGroup’ is negative, in which case all the
elements of the given ‘Dimension’ are considered. If ‘Dimension‘ is negative, all the
elements are considered.

Plugin(MeshVolume) creates one new list-based view. Numeric options:

PhysicalGroup
Default value: -1
Dimension
Default value: 3
Plugin(MinMax)
Plugin(MinMax) computes the min/max of a view.

If ‘View’ < 0, the plugin is run on the current view. If ‘OverTime’ = 1, the plugin
calculates the min/max over space and time. If ‘Argument’ = 1, the plugin calculates
the min/max and the argmin/argmax. If ‘Visible’ = 1, the plugin is only applied to
visible entities.

Plugin(MinMax) creates two new list-based views. Numeric options:

View Default value: -1
Chapter 9: Gmsh plugins 333

OverTime Default value: 0

Argument Default value: 0
Visible Default value: 1
Plugin(ModifyComponents)
Plugin(ModifyComponents) modifies the components of the ‘TimeStep’-th time step
in the view ‘View’, using the expressions provided in ‘Expression0’, ..., ‘Expression8’.
If an expression is empty, the corresponding component in the view is not modified.

The expressions can contain:

- the usual mathematical functions (Log, Sqrt, Sin, Cos, Fabs, ...) and operators (+,
-, *, /, ^);

- the symbols x, y and z, to retrieve the coordinates of the current node;

- the symbols Time and TimeStep, to retrieve the current time and time step values;

- the symbols v0, v1, v2, ..., v8, to retrieve each component of the field in ‘View’ at
the ‘TimeStep’-th time step;

- the symbols w0, w1, w2, ..., w8, to retrieve each component of the field in ‘Oth-
erView’ at the ‘OtherTimeStep’-th time step. If ‘OtherView’ and ‘View’ are based
on different spatial grids, or if their data types are different, ‘OtherView’ is inter-
polated onto ‘View’.

If ‘TimeStep’ < 0, the plugin automatically loops over all the time steps in ‘View’
and evaluates the expressions for each one.

If ‘OtherTimeStep’ < 0, the plugin uses ‘TimeStep’ instead.

If ‘View’ < 0, the plugin is run on the current view.

If ‘OtherView’ < 0, the plugin uses ‘View’ instead.

Plugin(ModifyComponents) is executed in-place. String options:

Expression0
Default value: "v0 * Sin(x)"
Expression1
Default value: ""
Expression2
Default value: ""
Expression3
Default value: ""
Expression4
Default value: ""
Expression5
Default value: ""
334 Gmsh 4.11.1

Expression6
Default value: ""
Expression7
Default value: ""
Expression8
Default value: ""
Numeric options:
TimeStep Default value: -1
View Default value: -1
OtherTimeStep
Default value: -1
OtherView
Default value: -1
ForceInterpolation
Default value: 0
Plugin(ModulusPhase)
Plugin(ModulusPhase) interprets the time steps ‘realPart’ and ‘imaginaryPart’ in
the view ‘View’ as the real and imaginary parts of a complex field and replaces them
with their corresponding modulus and phase.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(ModulusPhase) is executed in-place. Numeric options:

RealPart Default value: 0
ImaginaryPart
Default value: 1
View Default value: -1
Plugin(NearToFarField)
Plugin(NearToFarField) computes the far field pattern from the near electric E and
magnetic H fields on a surface enclosing the radiating device (antenna).

Parameters: the wavenumber, the angular discretisation (phi in [0, 2*Pi] and theta
in [0, Pi]) of the far field sphere and the indices of the views containing the complex-
valued E and H fields. If ‘Normalize’ is set, the far field is normalized to 1. If ‘dB’ is
set, the far field is computed in dB. If ‘NegativeTime’ is set, E and H are assumed to
have exp(-iwt) time dependency; otherwise they are assume to have exp(+iwt) time
dependency. If ‘MatlabOutputFile’ is given the raw far field data is also exported
in Matlab format.

Plugin(NearToFarField) creates one new view. String options:

MatlabOutputFile
Default value: "farfield.m"
Numeric options:
Wavenumber
Default value: 1
Chapter 9: Gmsh plugins 335

PhiStart Default value: 0

PhiEnd Default value: 6.28319
NumPointsPhi
Default value: 60
ThetaStart
Default value: 0
ThetaEnd Default value: 3.14159
NumPointsTheta
Default value: 30
EView Default value: 0
HView Default value: 1
Normalize
Default value: 1
dB Default value: 1
NegativeTime
Default value: 0
RFar Default value: 0
Plugin(NearestNeighbor)
Plugin(NearestNeighbor) computes the distance from each point in ‘View’ to its
nearest neighbor.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(NearestNeighbor) is executed in-place. Numeric options:

View Default value: -1
Plugin(NewView)
Plugin(NewView) creates a new model-based view from the current mesh, with
‘NumComp’ field components, set to value ‘Value’.

If ‘ViewTag’ is positive, force that tag for the created view. The view type is de-
termined by ‘Type’ (NodeData or ElementData). In the case of an ElementData
type, the view can be restricted to a specific physical group with a positive ‘Physi-
calGroup’. String options:
Type Default value: "NodeData"
Numeric options:
NumComp Default value: 1
Value Default value: 0
ViewTag Default value: -1
PhysicalGroup
Default value: -1
Plugin(Particles)
Plugin(Particles) computes the trajectory of particules in the force field given by
the ‘TimeStep’-th time step of a vector view ‘View’.
336 Gmsh 4.11.1

The plugin takes as input a grid defined by the 3 points (‘X0’,‘Y0’,‘Z0’) (origin),
(‘X1’,‘Y1’,‘Z1’) (axis of U) and (‘X2’,‘Y2’,‘Z2’) (axis of V).

The number of particles along U and V that are to be transported is set with the
options ‘NumPointsU’ and ‘NumPointsV’. The equation

A2 * d^2X(t)/dt^2 + A1 * dX(t)/dt + A0 * X(t) = F

is then solved with the initial conditions X(t=0) chosen as the grid, dX/dt(t=0)=0,
and with F interpolated from the vector view.

Time stepping is done using a Newmark scheme with step size ‘DT’ and ‘MaxIter’
maximum number of iterations.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Particles) creates one new list-based view containing multi-step vector points.
Numeric options:
X0 Default value: 0
Y0 Default value: 0
Z0 Default value: 0
X1 Default value: 1
Y1 Default value: 0
Z1 Default value: 0
X2 Default value: 0
Y2 Default value: 1
Z2 Default value: 0
NumPointsU
Default value: 10
NumPointsV
Default value: 1
A2 Default value: 1
A1 Default value: 0
A0 Default value: 0
DT Default value: 0.1
MaxIter Default value: 100
TimeStep Default value: 0
View Default value: -1
Plugin(Probe)
Plugin(Probe) gets the value of the view ‘View’ at the point (‘X’,‘Y’,‘Z’).

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Probe) creates one new view. Numeric options:

Chapter 9: Gmsh plugins 337

X Default value: 0
Y Default value: 0
Z Default value: 0
View Default value: -1
Plugin(Remove)
Plugin(Remove) removes the marked items from the list-based view ‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Remove) is executed in-place. Numeric options:

Text2D Default value: 1
Text3D Default value: 1
Points Default value: 0
Lines Default value: 0
Triangles
Default value: 0
Quadrangles
Default value: 0
Tetrahedra
Default value: 0
Hexahedra
Default value: 0
Prisms Default value: 0
Pyramids Default value: 0
Scalar Default value: 1
Vector Default value: 1
Tensor Default value: 1
View Default value: -1
Plugin(Scal2Tens)
Plugin(Scal2Tens) converts some scalar fields into a tensor field. The number of
components must be given (max. 9). The new view ’NameNewView’ contains the
new tensor field. If the number of a view is -1, the value of the corresponding
component is 0. String options:
NameNewView
Default value: "NewView"
Numeric options:
NumberOfComponents
Default value: 9
View0 Default value: -1
View1 Default value: -1
View2 Default value: -1
338 Gmsh 4.11.1

View3 Default value: -1

View4 Default value: -1
View5 Default value: -1
View6 Default value: -1
View7 Default value: -1
View8 Default value: -1
Plugin(Scal2Vec)
Plugin(Scal2Vec) converts the scalar fields into a vectorial field. The new view
’NameNewView’ contains it. If the number of a view is -1, the value of the corre-
sponding component of the vector field is 0. String options:
NameNewView
Default value: "NewView"
Numeric options:
ViewX Default value: -1
ViewY Default value: -1
ViewZ Default value: -1
Plugin(ShowNeighborElements)
Plugin(ShowNeighborElements) sets visible some elements and a layer of elements
around them, the other being set invisible. Numeric options:
NumLayers
Default value: 1
Element1 Default value: 0
Element2 Default value: 0
Element3 Default value: 0
Element4 Default value: 0
Element5 Default value: 0
Plugin(SimplePartition)
Plugin(SimplePartition) partitions the current mesh into ‘NumSlicesX’, ‘Num-
SlicesY’ and ‘NumSlicesZ’ slices along the X-, Y- and Z-axis, respectively. The
distribution of these slices is governed by ‘MappingX’, ‘MappingY’ and ‘MappingZ’,
where ‘t’ is a normalized absissa along each direction. (Setting ‘MappingX’ to ‘t’
will thus lead to equidistant slices along the X-axis.) String options:
MappingX Default value: "t"
MappingY Default value: "t"
MappingZ Default value: "t"
Numeric options:
NumSlicesX
Default value: 4
NumSlicesY
Default value: 1
Chapter 9: Gmsh plugins 339

NumSlicesZ
Default value: 1
Plugin(Skin)
Plugin(Skin) extracts the boundary (skin) of the current mesh (if ‘FromMesh’ = 1),
or from the the view ‘View’ (in which case it creates a new view). If ‘View’ < 0 and
‘FromMesh’ = 0, the plugin is run on the current view.
If ‘Visible’ is set, the plugin only extracts the skin of visible entities. Numeric
options:
Visible Default value: 1
FromMesh Default value: 0
View Default value: -1
Plugin(Smooth)
Plugin(Smooth) averages the values at the nodes of the view ‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Smooth) is executed in-place. Numeric options:

View Default value: -1
Plugin(SpanningTree)
Plugin(SpanningTree) builds a tree spanning every vertex of a mesh and stores it
directly in the model.
The tree is constructed by starting first on the curves, then on the surfaces and
finally on the volumes.

Parameters
- PhysicalVolumes: list of the physical volumes upon which the tree must be built.
- PhysicalSurfaces: list of the physical surfaces upon which the tree must be built.
- PhysicalCurves: list of the physical curves upon which the tree must be built.
- OutputPhysical: physical tag of the generated tree (-1 will select a new tag auto-
matically).

Note - Lists must be comma separated integers and spaces are ignored.
Remark - This plugin does not overwrite a physical group.Therefore, if an existing
physical tag is used in OutputPhysical, the edges of the tree will be /added/ to the
specified group. String options:
PhysicalVolumes
Default value: ""
PhysicalSurfaces
Default value: ""
PhysicalCurves
Default value: ""
Numeric options:
OutputPhysical
Default value: -1
Plugin(SphericalRaise)
Plugin(SphericalRaise) transforms the coordinates of the elements in the view
‘View’ using the values associated with the ‘TimeStep’-th time step.
340 Gmsh 4.11.1

Instead of elevating the nodes along the X, Y and Z axes as with the
View[‘View’].RaiseX, View[‘View’].RaiseY and View[‘View’].RaiseZ options, the
raise is applied along the radius of a sphere centered at (‘Xc’, ‘Yc’, ‘Zc’).

To produce a standard radiation pattern, set ‘Offset’ to minus the radius of the
sphere the original data lives on.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(SphericalRaise) is executed in-place. Numeric options:

Xc Default value: 0
Yc Default value: 0
Zc Default value: 0
Raise Default value: 1
Offset Default value: 0
TimeStep Default value: 0
View Default value: -1
Plugin(StreamLines)
Plugin(StreamLines) computes stream lines from the ‘TimeStep’-th time step of a
vector view ‘View’ and optionally interpolates the scalar view ‘OtherView’ on the
resulting stream lines.

The plugin takes as input a grid defined by the 3 points (‘X0’,‘Y0’,‘Z0’) (origin),
(‘X1’,‘Y1’,‘Z1’) (axis of U) and (‘X2’,‘Y2’,‘Z2’) (axis of V).

The number of points along U and V that are to be transported is set with the
options ‘NumPointsU’ and ‘NumPointsV’. The equation

dX(t)/dt = V(x,y,z)

is then solved with the initial condition X(t=0) chosen as the grid and with V(x,y,z)
interpolated on the vector view.

The time stepping scheme is a RK44 with step size ‘DT’ and ‘MaxIter’ maximum
number of iterations.

If ‘TimeStep’ < 0, the plugin tries to compute streamlines of the unsteady flow.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(StreamLines) creates one new list-based view. This view contains multi-step
vector points if ‘OtherView’ < 0, or single-step scalar lines if ‘OtherView’ >= 0.
Numeric options:
X0 Default value: 0
Y0 Default value: 0
Z0 Default value: 0
Chapter 9: Gmsh plugins 341

X1 Default value: 1
Y1 Default value: 0
Z1 Default value: 0
X2 Default value: 0
Y2 Default value: 1
Z2 Default value: 0
NumPointsU
Default value: 10
NumPointsV
Default value: 1
DT Default value: 0.1
MaxIter Default value: 100
TimeStep Default value: 0
View Default value: -1
OtherView
Default value: -1
Plugin(Summation)
Plugin(Summation) sums every time steps of ’Reference View’ and (every) ’Other
View X’and store the result in a new view.
If ’View 0’ < 0 then the current view is selected.
If ’View 1...8’ < 0 then this view is skipped.
Views can have different number of time steps
Warning: the Plugin assume that every views sharethe same mesh and that meshes
do not move between time steps! String options:
Resuling View Name
Default value: "default"
Numeric options:
View 0 Default value: -1
View 1 Default value: -1
View 2 Default value: -1
View 3 Default value: -1
View 4 Default value: -1
View 5 Default value: -1
View 6 Default value: -1
View 7 Default value: -1
Plugin(Tetrahedralize)
Plugin(Tetrahedralize) tetrahedralizes the points in the view ‘View’.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Tetrahedralize) creates one new list-based view. Numeric options:

342 Gmsh 4.11.1

View Default value: -1

Plugin(Transform)
Plugin(Transform) transforms the homogeneous node coordinates (x,y,z,1) of the
elements in the view ‘View’ by the matrix

[‘A11’ ‘A12’ ‘A13’ ‘Tx’]

[‘A21’ ‘A22’ ‘A23’ ‘Ty’]
[‘A31’ ‘A32’ ‘A33’ ‘Tz’].

If ‘SwapOrientation’ is set, the orientation of the elements is reversed.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Transform) is executed in-place. Numeric options:

A11 Default value: 1
A12 Default value: 0
A13 Default value: 0
A21 Default value: 0
A22 Default value: 1
A23 Default value: 0
A31 Default value: 0
A32 Default value: 0
A33 Default value: 1
Tx Default value: 0
Ty Default value: 0
Tz Default value: 0
SwapOrientation
Default value: 0
View Default value: -1
Plugin(Triangulate)
Plugin(Triangulate) triangulates the points in the view ‘View’, assuming that all
the points belong to a surface that can be projected one-to-one onto a plane.

If ‘View’ < 0, the plugin is run on the current view.

Plugin(Triangulate) creates one new list-based view. Numeric options:

View Default value: -1
Plugin(VoroMetal)
Plugin(VoroMetal) creates microstructures using Voronoi diagrams.

String options:
SeedsFile
Default value: "seeds.txt"
Chapter 9: Gmsh plugins 343

Numeric options:
ComputeBestSeeds
Default value: 0
ComputeMicrostructure
Default value: 1
Plugin(Warp)
Plugin(Warp) transforms the elements in the view ‘View’ by adding to their node
coordinates the vector field stored in the ‘TimeStep’-th time step of the view ‘Oth-
erView’, scaled by ‘Factor’.

If ‘View’ < 0, the plugin is run on the current view.

If ‘OtherView’ < 0, the vector field is taken as the field of surface normals multi-
plied by the ‘TimeStep’ value in ‘View’. (The smoothing of the surface normals is
controlled by the ‘SmoothingAngle’ parameter.)

Plugin(Warp) is executed in-place. Numeric options:

Factor Default value: 1
TimeStep Default value: 0
SmoothingAngle
Default value: 180
View Default value: -1
OtherView
Default value: -1
 Chapter 10: Gmsh file formats 345

10 Gmsh file formats

This chapter describes Gmsh’s native “MSH” file format, used to store meshes and associated
post-processing datasets. The MSH format exists in two flavors: ASCII and binary. The format
has a version number that is independent of Gmsh’s main version number.
(Remember that for small post-processing datasets you can also use human-readable “parsed”
post-processing views, as described in Section 5.4 [Post-processing scripting commands],
page 117. Such “parsed” views do not require an underlying mesh, and can therefore be easier
to use in some cases.)

10.1 MSH file format

The MSH file format version 4 (current revision: version 4.1) contains one mandatory section
giving information about the file ($MeshFormat), followed by several optional sections defining
the physical group names ($PhysicalName), the elementary model entities ($Entities), the
partitioned entities ($PartitionedEntities), the nodes ($Nodes), the elements ($Elements),
the periodicity relations ($Periodic), the ghost elements ($GhostElements), the parametriza-
tions ($Parametrizations) and the post-processing datasets ($NodeData, $ElementData,
$ElementNodeData). The sections reflect the underlying Gmsh data model: $Entities store the
boundary representation of the model geometrical entities, $Nodes and $Elements store mesh
data classified on these entities, and $NodeData, $ElementData, $ElementNodeData store post-
processing data (views). (See Chapter 6 [Gmsh application programming interface], page 123
and Section B.1 [Source code structure], page 373 for a more detailed description of the internal
Gmsh data model.)
To represent a simple mesh, the minimal sections that should be present in the file are
$MeshFormat, $Nodes and $Elements. Nodes are assumed to be defined before elements. To
represent a mesh with the full topology (BRep) of the model and associated physical groups,
an $Entities section should be present before the $Nodes section. Sections can be repeated in
the same file, and post-processing sections can be put into separate files (e.g. one file per time
step). Any section with an unrecognized header is simply ignored: you can thus add comments
in a ‘.msh’ file by putting them e.g. inside a $Comments/$EndComments section.
All the node, element and entity tags (their global identification numbers) should be strictly
positive. (Tag 0 is reserved for internal use.) Important note about efficiency: tags can be
"sparse", i.e., do not have to constitute a continuous list of numbers (the format even allows
them to not be ordered). However, using sparse tags can lead to performance degradation.
For meshes, sparse indexing can1 force Gmsh to use a map instead of a vector to access nodes
and elements. The performance hit is on speed. For post-processing datasets, which always
use vectors to access data, the performance hit is on memory. A $NodeData with two nodes,
tagged 1 and 1000000, will allocate a (mostly empty) vector of 1000000 elements. By default,
for non-partitioned, single file meshes, Gmsh will create files with a continuous ordering of node
and element tags, starting at 1. Detecting if the numbering is continuous can be done easily
when reading a file by inspecting numNodes, minNodeTag and maxNodeTag in the $Nodes section;
and numElements, minElementTag and maxElementTag in the $Elements section.
In binary mode (Mesh.Binary=1 or -bin on the command line), all the numerical values (in-
teger and floating point) not marked as ASCII in the format description below are written in
binary form, using the type given between parentheses. The block structure of the $Nodes and
$Elements sections allows to read integer and floating point data in each block in a single step
(e.g. using fread in C).
The format is defined as follows:
1
If the numbering is not too sparse, Gmsh will still use a vector.
346 Gmsh 4.11.1

$MeshFormat // same as MSH version 2

version(ASCII double; currently 4.1)
file-type(ASCII int; 0 for ASCII mode, 1 for binary mode)
data-size(ASCII int; sizeof(size_t))
< int with value one; only in binary mode, to detect endianness >
$EndMeshFormat

$PhysicalNames // same as MSH version 2

numPhysicalNames(ASCII int)
dimension(ASCII int) physicalTag(ASCII int) "name"(127 characters max)
...
$EndPhysicalNames

$Entities
numPoints(size_t) numCurves(size_t)
numSurfaces(size_t) numVolumes(size_t)
pointTag(int) X(double) Y(double) Z(double)
numPhysicalTags(size_t) physicalTag(int) ...
...
curveTag(int) minX(double) minY(double) minZ(double)
maxX(double) maxY(double) maxZ(double)
numPhysicalTags(size_t) physicalTag(int) ...
numBoundingPoints(size_t) pointTag(int; sign encodes orientation) ...
...
surfaceTag(int) minX(double) minY(double) minZ(double)
maxX(double) maxY(double) maxZ(double)
numPhysicalTags(size_t) physicalTag(int) ...
numBoundingCurves(size_t) curveTag(int; sign encodes orientation) ...
...
volumeTag(int) minX(double) minY(double) minZ(double)
maxX(double) maxY(double) maxZ(double)
numPhysicalTags(size_t) physicalTag(int) ...
numBoundngSurfaces(size_t) surfaceTag(int; sign encodes orientation) ...
...
$EndEntities

$PartitionedEntities
numPartitions(size_t)
numGhostEntities(size_t)
ghostEntityTag(int) partition(int)
...
numPoints(size_t) numCurves(size_t)
numSurfaces(size_t) numVolumes(size_t)
pointTag(int) parentDim(int) parentTag(int)
numPartitions(size_t) partitionTag(int) ...
X(double) Y(double) Z(double)
numPhysicalTags(size_t) physicalTag(int) ...
...
curveTag(int) parentDim(int) parentTag(int)
numPartitions(size_t) partitionTag(int) ...
minX(double) minY(double) minZ(double)
maxX(double) maxY(double) maxZ(double)
Chapter 10: Gmsh file formats 347

numPhysicalTags(size_t) physicalTag(int) ...

numBoundingPoints(size_t) pointTag(int) ...
...
surfaceTag(int) parentDim(int) parentTag(int)
numPartitions(size_t) partitionTag(int) ...
minX(double) minY(double) minZ(double)
maxX(double) maxY(double) maxZ(double)
numPhysicalTags(size_t) physicalTag(int) ...
numBoundingCurves(size_t) curveTag(int) ...
...
volumeTag(int) parentDim(int) parentTag(int)
numPartitions(size_t) partitionTag(int) ...
minX(double) minY(double) minZ(double)
maxX(double) maxY(double) maxZ(double)
numPhysicalTags(size_t) physicalTag(int) ...
numBoundingSurfaces(size_t) surfaceTag(int) ...
...
$EndPartitionedEntities

$Nodes
numEntityBlocks(size_t) numNodes(size_t)
minNodeTag(size_t) maxNodeTag(size_t)
entityDim(int) entityTag(int) parametric(int; 0 or 1)
numNodesInBlock(size_t)
nodeTag(size_t)
...
x(double) y(double) z(double)
< u(double; if parametric and entityDim >= 1) >
< v(double; if parametric and entityDim >= 2) >
< w(double; if parametric and entityDim == 3) >
...
...
$EndNodes

$Elements
numEntityBlocks(size_t) numElements(size_t)
minElementTag(size_t) maxElementTag(size_t)
entityDim(int) entityTag(int) elementType(int; see below)
numElementsInBlock(size_t)
elementTag(size_t) nodeTag(size_t) ...
...
...
$EndElements

$Periodic
numPeriodicLinks(size_t)
entityDim(int) entityTag(int) entityTagMaster(int)
numAffine(size_t) value(double) ...
numCorrespondingNodes(size_t)
nodeTag(size_t) nodeTagMaster(size_t)
...
...
348 Gmsh 4.11.1

$EndPeriodic

$GhostElements
numGhostElements(size_t)
elementTag(size_t) partitionTag(int)
numGhostPartitions(size_t) ghostPartitionTag(int) ...
...
$EndGhostElements

$Parametrizations
numCurveParam(size_t) numSurfaceParam(size_t)
curveTag(int) numNodes(size_t)
nodeX(double) nodeY(double) nodeZ(double) nodeU(double)
...
...
surfaceTag(int) numNodes(size_t) numTriangles(size_t)
nodeX(double) nodeY(double) nodeZ(double)
nodeU(double) nodeV(double)
curvMaxX(double) curvMaxY(double) curvMaxZ(double)
curvMinX(double) curvMinY(double) curvMinZ(double)
...
nodeIndex1(int) nodeIndex2(int) nodeIndex3(int)
...
...
$EndParametrizations

$NodeData
numStringTags(ASCII int)
stringTag(string) ...
numRealTags(ASCII int)
realTag(ASCII double) ...
numIntegerTags(ASCII int)
integerTag(ASCII int) ...
nodeTag(int) value(double) ...
...
$EndNodeData

$ElementData
numStringTags(ASCII int)
stringTag(string) ...
numRealTags(ASCII int)
realTag(ASCII double) ...
numIntegerTags(ASCII int)
integerTag(ASCII int) ...
elementTag(int) value(double) ...
...
$EndElementData

$ElementNodeData
numStringTags(ASCII int)
stringTag(string) ...
numRealTags(ASCII int)
Chapter 10: Gmsh file formats 349

realTag(ASCII double) ...

numIntegerTags(ASCII int)
integerTag(ASCII int) ...
elementTag(int) numNodesPerElement(int) value(double) ...
...
$EndElementNodeData

$InterpolationScheme
name(string)
numElementTopologies(ASCII int)
elementTopology
numInterpolationMatrices(ASCII int)
numRows(ASCII int) numColumns(ASCII int) value(ASCII double) ...
$EndInterpolationScheme
In the format description above, elementType is e.g.:
1 2-node line.
2 3-node triangle.
3 4-node quadrangle.
4 4-node tetrahedron.
5 8-node hexahedron.
6 6-node prism.
7 5-node pyramid.
8 3-node second order line (2 nodes associated with the vertices and 1 with the edge).
9 6-node second order triangle (3 nodes associated with the vertices and 3 with the
edges).
10 9-node second order quadrangle (4 nodes associated with the vertices, 4 with the
edges and 1 with the face).
11 10-node second order tetrahedron (4 nodes associated with the vertices and 6 with
the edges).
12 27-node second order hexahedron (8 nodes associated with the vertices, 12 with the
edges, 6 with the faces and 1 with the volume).
13 18-node second order prism (6 nodes associated with the vertices, 9 with the edges
and 3 with the quadrangular faces).
14 14-node second order pyramid (5 nodes associated with the vertices, 8 with the
edges and 1 with the quadrangular face).
15 1-node point.
16 8-node second order quadrangle (4 nodes associated with the vertices and 4 with
the edges).
17 20-node second order hexahedron (8 nodes associated with the vertices and 12 with
the edges).
18 15-node second order prism (6 nodes associated with the vertices and 9 with the
edges).
19 13-node second order pyramid (5 nodes associated with the vertices and 8 with the
edges).
350 Gmsh 4.11.1

20 9-node third order incomplete triangle (3 nodes associated with the vertices, 6 with
the edges)
21 10-node third order triangle (3 nodes associated with the vertices, 6 with the edges,
1 with the face)
22 12-node fourth order incomplete triangle (3 nodes associated with the vertices, 9
with the edges)
23 15-node fourth order triangle (3 nodes associated with the vertices, 9 with the edges,
3 with the face)
24 15-node fifth order incomplete triangle (3 nodes associated with the vertices, 12 with
the edges)
25 21-node fifth order complete triangle (3 nodes associated with the vertices, 12 with
the edges, 6 with the face)
26 4-node third order edge (2 nodes associated with the vertices, 2 internal to the edge)
27 5-node fourth order edge (2 nodes associated with the vertices, 3 internal to the
edge)
28 6-node fifth order edge (2 nodes associated with the vertices, 4 internal to the edge)
29 20-node third order tetrahedron (4 nodes associated with the vertices, 12 with the
edges, 4 with the faces)
30 35-node fourth order tetrahedron (4 nodes associated with the vertices, 18 with the
edges, 12 with the faces, 1 in the volume)
31 56-node fifth order tetrahedron (4 nodes associated with the vertices, 24 with the
edges, 24 with the faces, 4 in the volume)
92 64-node third order hexahedron (8 nodes associated with the vertices, 24 with the
edges, 24 with the faces, 8 in the volume)
93 125-node fourth order hexahedron (8 nodes associated with the vertices, 36 with the
edges, 54 with the faces, 27 in the volume)
...
All the currently supported elements in the format are defined in GmshDefines.h. See
Section 10.2 [Node ordering], page 352 for the ordering of the nodes.
The post-processing sections ($NodeData, $ElementData, $ElementNodeData) can contain
numStringTags string tags, numRealTags real value tags and numIntegerTags integer tags.
The default set of tags understood by Gmsh is as follows:
stringTag
The first is interpreted as the name of the post-processing view and the second as
the name of the interpolation scheme, as provided in the $InterpolationScheme
section.
realTag The first is interpreted as a time value associated with the dataset.
integerTag
The first is interpreted as a time step index (starting at 0), the second as the number
of field components of the data in the view (1, 3 or 9), the third as the number of
entities (nodes or elements) in the view, and the fourth as the partition index for
the view data (0 for no partition).
In the $InterpolationScheme section:
Chapter 10: Gmsh file formats 351

numElementTopologies
is the number of element topologies for which interpolation matrices are provided.
elementTopology
is the id tag of a given element topology: 1 for points, 2 for lines, 3 for triangles, 4
for quadrangles, 5 for tetrahedra, 6 for pyramids, 7 for prisms, 8 for hexahedra, 9
for polygons and 10 for polyhedra.
numInterpolationMatrices
is the number of interpolation matrices provided for the given element topology.
Currently you should provide 2 matrices, i.e., the matrices that specify how to
interpolate the data (they have the same meaning as in Section 5.4 [Post-processing
scripting commands], page 117). The matrices are specified by 2 integers (numRows
and numColumns) followed by the values, by row.
Here is a small example of a minimal ASCII MSH4.1 file, with a mesh consisting of two quad-
rangles and an associated nodal scalar dataset (the comments are not part of the actual file):
$MeshFormat
4.1 0 8 MSH4.1, ASCII
$EndMeshFormat
$Nodes
1 6 1 6 1 entity bloc, 6 nodes total, min/max node tags: 1 and 6
2 1 0 6 2D entity (surface) 1, no parametric coordinates, 6 nodes
1 node tag #1
2 node tag #2
3 etc.
4
5
6
0. 0. 0. node #1 coordinates (0., 0., 0.)
1. 0. 0. node #2 coordinates (1., 0., 0.)
1. 1. 0. etc.
0. 1. 0.
2. 0. 0.
2. 1. 0.
$EndNodes
$Elements
1 2 1 2 1 entity bloc, 2 elements total, min/max element tags: 1 and 2
2 1 3 2 2D entity (surface) 1, element type 3 (4-node quad), 2 elements
1 1 2 3 4 quad tag #1, nodes 1 2 3 4
2 2 5 6 3 quad tag #2, nodes 2 5 6 3
$EndElements
$NodeData
1 1 string tag:
"My view" the name of the view ("My view")
1 1 real tag:
0.0 the time value (0.0)
3 3 integer tags:
0 the time step (0; time steps always start at 0)
1 1-component (scalar) field
6 6 associated nodal values
1 0.0 value associated with node #1 (0.0)
2 0.1 value associated with node #2 (0.1)
352 Gmsh 4.11.1

3 0.2 etc.
4 0.0
5 0.2
6 0.4
$EndNodeData
The 4.1 revision of the format includes the following modifications with respect to the initial 4.0
version:
• All the unsigned long entries have been changed to size_t. All the entries designating
counts which were previously encoded as int have also been changed to size_t. (This only
impacts binary files.)
• The $Entities section is now optional.
• Integer and floating point data in the $Nodes section is not mixed anymore: all the tags
are given first, followed by all the coordinates.
• The bounding box for point entities has been replaced simply by the 3 coordinates of the
point (instead of the six bounding box values).
• The entityDim and entityTag values have been switched in the $Nodes and $Elements
sections (for consistency with the ordering used elsewhere in the file and in the Chapter 6
[Gmsh application programming interface], page 123).
• The minimum and the maximum tag of nodes (resp. elements) have been added in the
header of the $Nodes (resp. $Elements) section, to facilitate the detection of sparse or
dense numberings when reading the file.
• The $Periodic section has been changed to always provide the number of values in the
affine transform (which can be zero, if the transform is not provided).

The following changes are foreseen in a future revision of the MSH format:
• The $GhostElements, $NodeData, $ElementData and $ElementNodeData will be reworked
for greater IO efficiency, with separation of entries by type and a block structure with
predictable sizes.
• Node and element tags in $NodeData, $ElementData and $ElementNodeData will be
switched to size_t.

10.2 Node ordering

Historically, Gmsh first supported linear elements (lines, triangles, quadrangles, tetrahedra,
prisms and hexahedra). Then, support for second and some third order elements has been
added. Below we distinguish such “low order elements”, which are hardcoded (i.e. they are
explicitly defined in the code), and general “high-order elements”, that have been coded in a
more general fashion, theoretically valid for any order.

10.2.1 Low order elements

For all mesh and post-processing file formats, the reference elements are defined as follows.
Line: Line3: Line4:

v
^
|
|
0-----+-----1 --> u 0----2----1 0---2---3---1
Chapter 10: Gmsh file formats 353

Triangle: Triangle6: Triangle9/10:

v
^
|
2 2 2
|‘\ |‘\ | \
| ‘\ | ‘\ 7 6
| ‘\ 5 ‘4 | \
| ‘\ | ‘\ 8 (9) 5
| ‘\ | ‘\ | \
0----------1--> u 0-----3----1 0---3---4---1

Triangle12/15:

v
^
|
2
| \
9 8
| \
10 (14) 7
| \
11 (12) (13) 6
| \
0---3---4---5---1--> u

Quadrangle: Quadrangle8: Quadrangle9:

v
^
|
3-----------2 3-----6-----2 3-----6-----2
| | | | | | |
| | | | | | |
| +---- | --> u 7 5 7 8 5
| | | | | |
| | | | | |
0-----------1 0-----4-----1 0-----4-----1
354 Gmsh 4.11.1

Tetrahedron: Tetrahedron10:

v
.
,/
/
2 2
,/|‘\ ,/|‘\
,/ | ‘\ ,/ | ‘\
,/ ’. ‘\ ,6 ’. ‘5
,/ | ‘\ ,/ 8 ‘\
,/ | ‘\ ,/ | ‘\
0-----------’.--------1 --> u 0--------4--’.--------1
‘\. | ,/ ‘\. | ,/
‘\. | ,/ ‘\. | ,9
‘\. ’. ,/ ‘7. ’. ,/
‘\. |/ ‘\. |/
‘3 ‘3
‘\.
‘ w
Hexahedron: Hexahedron20: Hexahedron27:

v
3----------2 3----13----2 3----13----2
|\ ^ |\ |\ |\ |\ |\
| \ | | \ | 15 | 14 |15 24 | 14
| \ | | \ 9 \ 11 \ 9 \ 20 11 \
| 7------+---6 | 7----19+---6 | 7----19+---6
| | +-- |-- | -> u | | | | |22 | 26 | 23|
0---+---\--1 | 0---+-8----1 | 0---+-8----1 |
\ | \ \ | \ 17 \ 18 \ 17 25 \ 18
\ | \ \ | 10 | 12| 10 | 21 12|
\| w \| \| \| \| \|
4----------5 4----16----5 4----16----5
Chapter 10: Gmsh file formats 355

Prism: Prism15: Prism18:

w
^
|
3 3 3
,/|‘\ ,/|‘\ ,/|‘\
,/ | ‘\ 12 | 13 12 | 13
,/ | ‘\ ,/ | ‘\ ,/ | ‘\
4------+------5 4------14-----5 4------14-----5
| | | | 8 | | 8 |
| ,/|‘\ | | | | | ,/|‘\ |
| ,/ | ‘\ | | | | | 15 | 16 |
|,/ | ‘\| | | | |,/ | ‘\|
,| | |\ 10 | 11 10-----17-----11
,/ | 0 | ‘\ | 0 | | 0 |
u | ,/ ‘\ | v | ,/ ‘\ | | ,/ ‘\ |
| ,/ ‘\ | | ,6 ‘7 | | ,6 ‘7 |
|,/ ‘\| |,/ ‘\| |,/ ‘\|
1-------------2 1------9------2 1------9------2

Pyramid: Pyramid13:

4 4
,/|\ ,/|\
,/ .’|\ ,/ .’|\
,/ | | \ ,/ | | \
,/ .’ | ‘. ,/ .’ | ‘.
,/ | ’. \ ,7 | 12 \
,/ .’ w | \ ,/ .’ | \
,/ | ^ | \ ,/ 9 | 11
0----------.’--|-3 ‘. 0--------6-.’----3 ‘.
‘\ | | ‘\ \ ‘\ | ‘\ \
‘\ .’ +----‘\ - \ -> v ‘5 .’ 10 \
‘\ | ‘\ ‘\ \ ‘\ | ‘\ \
‘\.’ ‘\ ‘\‘ ‘\.’ ‘\‘
1----------------2 1--------8-------2
‘\
u
356 Gmsh 4.11.1

Pyramid14:

4
,/|\
,/ .’|\
,/ | | \
,/ .’ | ‘.
,7 | 12 \
,/ .’ | \
,/ 9 | 11
0--------6-.’----3 ‘.
‘\ | ‘\ \
‘5 .’ 13 10 \
‘\ | ‘\ \
‘\.’ ‘\‘
1--------8-------2
‘\
u

10.2.2 High-order elements

The node ordering of a higher order (possibly curved) element is compatible with the numbering
of low order element (it is a generalization). We number nodes in the following order:
– the element principal or corner vertices;
– the internal nodes for each edge;
– the internal nodes for each face;
– the volume internal nodes.
The numbering for internal nodes is recursive, i.e. the numbering follows that of the nodes
of an embedded edge/face/volume of lower order. The higher order nodes are assumed to be
equispaced. Edges and faces are numbered following the lowest order template that generates
a single high-order on this edge/face. Furthermore, an edge is oriented from the node with the
lowest to the highest index. The orientation of a face is such that the computed normal points
outward; the starting point is the node with the lowest index.

10.3 Legacy formats

This section describes Gmsh’s older native file formats. Future versions of Gmsh will continue
to support these formats, but we recommend that you do not use them in new applications.

10.3.1 MSH file format version 2 (Legacy)

The MSH file format version 2 is Gmsh’s previous native mesh file format, now superseded by
the format described in Section 10.1 [MSH file format], page 345. It is defined as follows:
$MeshFormat
version-number file-type data-size
$EndMeshFormat
$PhysicalNames
number-of-names
physical-dimension physical-tag "physical-name "
...
$EndPhysicalNames
$Nodes
Chapter 10: Gmsh file formats 357

number-of-nodes
node-number x-coord y-coord z-coord
...
$EndNodes
$Elements
number-of-elements
elm-number elm-type number-of-tags < tag > ... node-number-list
...
$EndElements
$Periodic
number-of-periodic-entities
<Affine value ...>
dimension entity-tag master-entity-tag
number-of-nodes
node-number master-node-number
...
$EndPeriodic
$NodeData
number-of-string-tags
< "string-tag " >
...
number-of-real-tags
< real-tag >
...
number-of-integer-tags
< integer-tag >
...
node-number value ...
...
$EndNodeData
$ElementData
number-of-string-tags
< "string-tag " >
...
number-of-real-tags
< real-tag >
...
number-of-integer-tags
< integer-tag >
...
elm-number value ...
...
$EndElementData
$ElementNodeData
number-of-string-tags
< "string-tag " >
...
number-of-real-tags
< real-tag >
...
number-of-integer-tags
< integer-tag >
358 Gmsh 4.11.1

...
elm-number number-of-nodes-per-element value ...
...
$EndElementNodeData
$InterpolationScheme
"name "
number-of-element-topologies
elm-topology
number-of-interpolation-matrices
num-rows num-columns value ...
...
$EndInterpolationScheme
where
version-number
is a real number equal to 2.2
file-type
is an integer equal to 0 in the ASCII file format.
data-size
is an integer equal to the size of the floating point numbers used in the file (currently
only data-size = sizeof(double) is supported).
number-of-nodes
is the number of nodes in the mesh.
node-number
is the number (index) of the n-th node in the mesh; node-number must be a positive
(non-zero) integer. Note that the node-numbers do not necessarily have to form a
dense nor an ordered sequence.
x-coord y-coord z-coord
are the floating point values giving the X, Y and Z coordinates of the n-th node.
number-of-elements
is the number of elements in the mesh.
elm-number
is the number (index) of the n-th element in the mesh; elm-number must be a
positive (non-zero) integer. Note that the elm-numbers do not necessarily have to
form a dense nor an ordered sequence.
elm-type defines the geometrical type of the n-th element: see Section 10.1 [MSH file format],
page 345.
number-of-tags
gives the number of integer tags that follow for the n-th element. By default, the
first tag is the tag of the physical entity to which the element belongs; the second is
the tag of the elementary model entity to which the element belongs; the third is the
number of mesh partitions to which the element belongs, followed by the partition
ids (negative partition ids indicate ghost cells). A zero tag is equivalent to no tag.
Gmsh and most codes using the MSH 2 format require at least the first two tags
(physical and elementary tags).
node-number-list
is the list of the node numbers of the n-th element. The ordering of the nodes is
given in Section 10.2 [Node ordering], page 352.
Chapter 10: Gmsh file formats 359

number-of-string-tags
gives the number of string tags that follow. By default the first string-tag
is interpreted as the name of the post-processing view and the second as the
name of the interpolation scheme. The interpolation scheme is provided in the
$InterpolationScheme section (see below).
number-of-real-tags
gives the number of real number tags that follow. By default the first real-tag is
interpreted as a time value associated with the dataset.
number-of-integer-tags
gives the number of integer tags that follow. By default the first integer-tag is
interpreted as a time step index (starting at 0), the second as the number of field
components of the data in the view (1, 3 or 9), the third as the number of entities
(nodes or elements) in the view, and the fourth as the partition index for the view
data (0 for no partition).
number-of-nodes-per-elements
gives the number of node values for an element in an element-based view.
value is a real number giving the value associated with a node or an element. For NodeData
(respectively ElementData) views, there are ncomp values per node (resp. per
element), where ncomp is the number of field components. For ElementNodeData
views, there are ncomp times number-of-nodes-per-elements values per element.
number-of-element-topologies
is the number of element topologies for which interpolation matrices are provided
elm-topology
is the id tag of a given element topology: 1 for points, 2 for lines, 3 for triangles, 4
for quadrangles, 5 for tetrahedra, 6 for pyramids, 7 for prisms, 8 for hexahedra, 9
for polygons and 10 for polyhedra.
number-of-interpolation-matrices
is the number of interpolation matrices provided for the element topology elm-
topology. Currently you should provide 2 matrices, i.e., the matrices that specify
how to interpolate the data (they have the same meaning as in Section 5.4 [Post-
processing scripting commands], page 117). The matrices are specified by 2 integers
(num-rows and num-columns) followed by the values.
Below is a small example (a mesh consisting of two quadrangles with an associated nodal scalar
dataset; the comments are not part of the actual file!):
$MeshFormat
2.2 0 8
$EndMeshFormat
$Nodes
6 six mesh nodes:
1 0.0 0.0 0.0 node #1: coordinates (0.0, 0.0, 0.0)
2 1.0 0.0 0.0 node #2: coordinates (1.0, 0.0, 0.0)
3 1.0 1.0 0.0 etc.
4 0.0 1.0 0.0
5 2.0 0.0 0.0
6 2.0 1.0 0.0
$EndNodes
$Elements
2 two elements:
360 Gmsh 4.11.1

1 3 2 99 2 1 2 3 4 quad #1: type 3, phys 99, ent 2, nodes 1 2 3 4

2 3 2 99 2 2 5 6 3 quad #2: type 3, phys 99, ent 2, nodes 2 5 6 3
$EndElements
$NodeData
1 one string tag:
"My view" the name of the view ("My view")
1 one real tag:
0.0 the time value (0.0)
3 three integer tags:
0 the time step (0; time steps always start at 0)
1 1-component (scalar) field
6 six associated nodal values
1 0.0 value associated with node #1 (0.0)
2 0.1 value associated with node #2 (0.1)
3 0.2 etc.
4 0.0
5 0.2
6 0.4
$EndNodeData
The binary file format is similar to the ASCII format described above:
$MeshFormat
version-number file-type data-size
one-binary
$EndMeshFormat
$Nodes
number-of-nodes
nodes-binary
$EndNodes
$Elements
number-of-elements
element-header-binary
elements-binary
element-header-binary
elements-binary
...
$EndElements

[ All other sections are identical to ASCII, except that

node-number, elm-number, number-of-nodes-per-element
and values are written in binary format. Beware that all the
$End tags must start on a new line. ]
where

version-number
is a real number equal to 2.2.
file-type
is an integer equal to 1.
data-size
has the same meaning as in the ASCII file format. Currently only data-size =
sizeof(double) is supported.
Chapter 10: Gmsh file formats 361

one-binary
is an integer of value 1 written in binary form. This integer is used for detecting if
the computer on which the binary file was written and the computer on which the
file is read are of the same type (little or big endian).
Here is a pseudo C code to write one-binary:
int one = 1;
fwrite(&one, sizeof(int), 1, file);
number-of-nodes
has the same meaning as in the ASCII file format.
nodes-binary
is the list of nodes in binary form, i.e., a array of number-of-nodes * (4 + 3 * data-
size) bytes. For each node, the first 4 bytes contain the node number and the next
(3 * data-size) bytes contain the three floating point coordinates.
Here is a pseudo C code to write nodes-binary:
for(i = 0; i < number_of_nodes; i++){
fwrite(&num_i, sizeof(int), 1, file);
double xyz[3] = {node_i_x, node_i_y, node_i_z};
fwrite(xyz, sizeof(double), 3, file);
}
number-of-elements
has the same meaning as in the ASCII file format.
element-header-binary
is a list of 3 integers in binary form, i.e., an array of (3 * 4) bytes: the first four
bytes contain the type of the elements that follow (same as elm-type in the ASCII
format), the next four contain the number of elements that follow, and the last
four contain the number of tags per element (same as number-of-tags in the ASCII
format).
Here is a pseudo C code to write element-header-binary:
int header[3] = {elm_type, num_elm_follow, num_tags};
fwrite(header, sizeof(int), 3, file);
elements-binary
is a list of elements in binary form, i.e., an array of “number of elements that follow”
* (4 + number-of-tags * 4 + #node-number-list * 4) bytes. For each element, the
first four bytes contain the element number, the next (number-of-tags * 4) contain
the tags, and the last (#node-number-list * 4) contain the node indices.
Here is a pseudo C code to write elements-binary for triangles with the 2 standard
tags (the physical group and elementary entity):
for(i = 0; i < number_of_triangles; i++){
int data[6] = {num_i, physical, elementary,
node_i_1, node_i_2, node_i_3};
fwrite(data, sizeof(int), 6, file);
}

10.3.2 MSH file format version 1 (Legacy)

The MSH file format version 1 is Gmsh’s original native mesh file format, now superseded by
the format described in Section 10.1 [MSH file format], page 345. It is defined as follows:
$NOD
number-of-nodes
362 Gmsh 4.11.1

node-number x-coord y-coord z-coord

...
$ENDNOD
$ELM
number-of-elements
elm-number elm-type reg-phys reg-elem number-of-nodes node-number-list
...
$ENDELM
where
number-of-nodes
is the number of nodes in the mesh.
node-number
is the number (index) of the n-th node in the mesh; node-number must be a positive
(non-zero) integer. Note that the node-numbers do not necessarily have to form a
dense nor an ordered sequence.
x-coord y-coord z-coord
are the floating point values giving the X, Y and Z coordinates of the n-th node.
number-of-elements
is the number of elements in the mesh.
elm-number
is the number (index) of the n-th element in the mesh; elm-number must be a
positive (non-zero) integer. Note that the elm-numbers do not necessarily have to
form a dense nor an ordered sequence.
elm-type defines the geometrical type of the n-th element:
1 2-node line.
2 3-node triangle.
3 4-node quadrangle.
4 4-node tetrahedron.
5 8-node hexahedron.
6 6-node prism.
7 5-node pyramid.
8 3-node second order line (2 nodes associated with the vertices and 1
with the edge).
9 6-node second order triangle (3 nodes associated with the vertices and
3 with the edges).
10 9-node second order quadrangle (4 nodes associated with the vertices,
4 with the edges and 1 with the face).
11 10-node second order tetrahedron (4 nodes associated with the vertices
and 6 with the edges).
12 27-node second order hexahedron (8 nodes associated with the vertices,
12 with the edges, 6 with the faces and 1 with the volume).
13 18-node second order prism (6 nodes associated with the vertices, 9 with
the edges and 3 with the quadrangular faces).
Chapter 10: Gmsh file formats 363

14 14-node second order pyramid (5 nodes associated with the vertices, 8

with the edges and 1 with the quadrangular face).
15 1-node point.
16 8-node second order quadrangle (4 nodes associated with the vertices
and 4 with the edges).
17 20-node second order hexahedron (8 nodes associated with the vertices
and 12 with the edges).
18 15-node second order prism (6 nodes associated with the vertices and 9
with the edges).
19 13-node second order pyramid (5 nodes associated with the vertices and
8 with the edges).
See below for the ordering of the nodes.
reg-phys is the tag of the physical entity to which the element belongs; reg-phys must be a
positive integer, or zero. If reg-phys is equal to zero, the element is considered not
to belong to any physical entity.
reg-elem is the tag of the elementary entity to which the element belongs; reg-elem must be
a positive (non-zero) integer.
number-of-nodes
is the number of nodes for the n-th element. This is redundant, but kept for back-
ward compatibility.
node-number-list
is the list of the number-of-nodes node numbers of the n-th element. The ordering
of the nodes is given in Section 10.2 [Node ordering], page 352.

10.3.3 POS ASCII file format (Legacy)

The POS ASCII file is Gmsh’s old native post-processing format, now superseded by the format
described in Section 10.1 [MSH file format], page 345. It is defined as follows:
$PostFormat
1.4 file-type data-size
$EndPostFormat
$View
view-name nb-time-steps
nb-scalar-points nb-vector-points nb-tensor-points
nb-scalar-lines nb-vector-lines nb-tensor-lines
nb-scalar-triangles nb-vector-triangles nb-tensor-triangles
nb-scalar-quadrangles nb-vector-quadrangles nb-tensor-quadrangles
nb-scalar-tetrahedra nb-vector-tetrahedra nb-tensor-tetrahedra
nb-scalar-hexahedra nb-vector-hexahedra nb-tensor-hexahedra
nb-scalar-prisms nb-vector-prisms nb-tensor-prisms
nb-scalar-pyramids nb-vector-pyramids nb-tensor-pyramids
nb-scalar-lines2 nb-vector-lines2 nb-tensor-lines2
nb-scalar-triangles2 nb-vector-triangles2 nb-tensor-triangles2
nb-scalar-quadrangles2 nb-vector-quadrangles2 nb-tensor-quadrangles2
nb-scalar-tetrahedra2 nb-vector-tetrahedra2 nb-tensor-tetrahedra2
nb-scalar-hexahedra2 nb-vector-hexahedra2 nb-tensor-hexahedra2
nb-scalar-prisms2 nb-vector-prisms2 nb-tensor-prisms2
nb-scalar-pyramids2 nb-vector-pyramids2 nb-tensor-pyramids2
364 Gmsh 4.11.1

nb-text2d nb-text2d-chars nb-text3d nb-text3d-chars

time-step-values
< scalar-point-value > ... < vector-point-value > ...
< tensor-point-value > ...
< scalar-line-value > ... < vector-line-value > ...
< tensor-line-value > ...
< scalar-triangle-value > ... < vector-triangle-value > ...
< tensor-triangle-value > ...
< scalar-quadrangle-value > ... < vector-quadrangle-value > ...
< tensor-quadrangle-value > ...
< scalar-tetrahedron-value > ... < vector-tetrahedron-value > ...
< tensor-tetrahedron-value > ...
< scalar-hexahedron-value > ... < vector-hexahedron-value > ...
< tensor-hexahedron-value > ...
< scalar-prism-value > ... < vector-prism-value > ...
< tensor-prism-value > ...
< scalar-pyramid-value > ... < vector-pyramid-value > ...
< tensor-pyramid-value > ...
< scalar-line2-value > ... < vector-line2-value > ...
< tensor-line2-value > ...
< scalar-triangle2-value > ... < vector-triangle2-value > ...
< tensor-triangle2-value > ...
< scalar-quadrangle2-value > ... < vector-quadrangle2-value > ...
< tensor-quadrangle2-value > ...
< scalar-tetrahedron2-value > ... < vector-tetrahedron2-value > ...
< tensor-tetrahedron2-value > ...
< scalar-hexahedron2-value > ... < vector-hexahedron2-value > ...
< tensor-hexahedron2-value > ...
< scalar-prism2-value > ... < vector-prism2-value > ...
< tensor-prism2-value > ...
< scalar-pyramid2-value > ... < vector-pyramid2-value > ...
< tensor-pyramid2-value > ...
< text2d > ... < text2d-chars > ...
< text3d > ... < text3d-chars > ...
$EndView
where

file-type
is an integer equal to 0 in the ASCII file format.

data-size
is an integer equal to the size of the floating point numbers used in the file (usually,
data-size = sizeof(double)).

view-name
is a string containing the name of the view (max. 256 characters).

nb-time-steps
is an integer giving the number of time steps in the view.

nb-scalar-points
nb-vector-points
... are integers giving the number of scalar points, vector points, . . . , in the view.
Chapter 10: Gmsh file formats 365

nb-text2d
nb-text3d
are integers giving the number of 2D and 3D text strings in the view.
nb-text2d-chars
nb-text3d-chars
are integers giving the total number of characters in the 2D and 3D strings.
time-step-values
is a list of nb-time-steps double precision numbers giving the value of the time (or
any other variable) for which an evolution was saved.
scalar-point-value
vector-point-value
... are lists of double precision numbers giving the node coordinates and the values
associated with the nodes of the nb-scalar-points scalar points, nb-vector-points
vector points, . . . , for each of the time-step-values.
For example, vector-triangle-value is defined as:
coord1-node1 coord1-node2 coord1-node3
coord2-node1 coord2-node2 coord2-node3
coord3-node1 coord3-node2 coord3-node3
comp1-node1-time1 comp2-node1-time1 comp3-node1-time1
comp1-node2-time1 comp2-node2-time1 comp3-node2-time1
comp1-node3-time1 comp2-node3-time1 comp3-node3-time1
comp1-node1-time2 comp2-node1-time2 comp3-node1-time2
comp1-node2-time2 comp2-node2-time2 comp3-node2-time2
comp1-node3-time2 comp2-node3-time2 comp3-node3-time2
...
The ordering of the nodes is given in Section 10.2 [Node ordering], page 352.
text2d is a list of 4 double precision numbers:
coord1 coord2 style index
where coord1 and coord2 give the X-Y position of the 2D string in screen coordinates
(measured from the top-left corner of the window) and where index gives the start-
ing index of the string in text2d-chars. If coord1 (respectively coord2) is negative,
the position is measured from the right (respectively bottom) edge of the window. If
coord1 (respectively coord2) is larger than 99999, the string is centered horizontally
(respectively vertically). If style is equal to zero, the text is aligned bottom-left and
displayed using the default font and size. Otherwise, style is converted into an inte-
ger whose eight lower bits give the font size, whose eight next bits select the font (the
index corresponds to the position in the font menu in the GUI), and whose eight next
bits define the text alignment (0=bottom-left, 1=bottom-center, 2=bottom-right,
3=top-left, 4=top-center, 5=top-right, 6=center-left, 7=center-center, 8=center-
right).
text2d-chars
is a list of nb-text2d-chars characters. Substrings are separated with the null ‘\0’
character.
text3d is a list of 5 double precision numbers
coord1 coord2 coord3 style index
where coord1, coord2 and coord3 give the XYZ coordinates of the string in model
(real world) coordinates, index gives the starting index of the string in text3d-chars,
and style has the same meaning as in text2d.
366 Gmsh 4.11.1

text3d-chars
is a list of nb-text3d-chars chars. Substrings are separated with the null ‘\0’ char-
acter.

10.3.4 POS binary file format (Legacy)

The POS binary file format is the same as the POS ASCII file format described in Section 10.3.3
[POS ASCII file format (Legacy)], page 363, except that:
1. file-type equals 1.
2. all lists of floating point numbers and characters are written in binary format
3. there is an additional integer, of value 1, written before time-step-values. This integer is
used for detecting if the computer on which the binary file was written and the computer
on which the file is read are of the same type (little or big endian).

Here is a pseudo C code to write a post-processing file in binary format:

int one = 1;

fprintf(file, "$PostFormat\n");
fprintf(file, "%g %d %d\n", 1.4, 1, sizeof(double));
fprintf(file, "$EndPostFormat\n");
fprintf(file, "$View\n");
fprintf(file, "%s %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d %d %d %d %d %d "
"%d %d %d %d\n",
view-name, nb-time-steps,
nb-scalar-points, nb-vector-points, nb-tensor-points,
nb-scalar-lines, nb-vector-lines, nb-tensor-lines,
nb-scalar-triangles, nb-vector-triangles, nb-tensor-triangles,
nb-scalar-quadrangles, nb-vector-quadrangles, nb-tensor-quadrangles,
nb-scalar-tetrahedra, nb-vector-tetrahedra, nb-tensor-tetrahedra,
nb-scalar-hexahedra, nb-vector-hexahedra, nb-tensor-hexahedra,
nb-scalar-prisms, nb-vector-prisms, nb-tensor-prisms,
nb-scalar-pyramids, nb-vector-pyramids, nb-tensor-pyramids,
nb-scalar-lines2, nb-vector-lines2, nb-tensor-lines2,
nb-scalar-triangles2, nb-vector-triangles2, nb-tensor-triangles2,
nb-scalar-quadrangles2, nb-vector-quadrangles2,
nb-tensor-quadrangles2,
nb-scalar-tetrahedra2, nb-vector-tetrahedra2, nb-tensor-tetrahedra2,
nb-scalar-hexahedra2, nb-vector-hexahedra2, nb-tensor-hexahedra2,
nb-scalar-prisms2, nb-vector-prisms2, nb-tensor-prisms2,
nb-scalar-pyramids2, nb-vector-pyramids2, nb-tensor-pyramids2,
nb-text2d, nb-text2d-chars, nb-text3d, nb-text3d-chars);
fwrite(&one, sizeof(int), 1, file);
fwrite(time-step-values, sizeof(double), nb-time-steps, file);
fwrite(all-scalar-point-values, sizeof(double), ..., file);
...
fprintf(file, "\n$EndView\n");
Chapter 10: Gmsh file formats 367

In this pseudo-code, all-scalar-point-values is the array of double precision numbers containing

all the scalar-point-value lists, put one after each other in order to form a long array of doubles.
The principle is the same for all other kinds of values.
Appendix A: Compiling the source code 369

Appendix A Compiling the source code

Stable releases and source snapshots are available from https://gmsh.info/src/. You can also
access the Git repository directly:
1. The first time you want to download the latest full source, type:
git clone https://gitlab.onelab.info/gmsh/gmsh.git
2. To update your local version to the latest and greatest, go in the gmsh directory and type:
git pull
Once you have the source code, you need to run CMake to configure your build (see the
README.txt file in the top-level source directory for additional information on how to run
CMake, as well as the Gmsh-compilation wiki page for more detailed instructions on how to
compile Gmsh, including the compilation of common dependencies).
Each build can be configured using a series of options, to selectively enable optional modules or
features. Here is the list of all the Gmsh-specific CMake options:
ENABLE_3M
Enable proprietary 3M extension (default: OFF)
ENABLE_ALGLIB
Enable ALGLIB (used by some mesh optimizers) (default: ON)
ENABLE_ANN
Enable ANN (used for fast point search in mesh/post) (default: ON)
ENABLE_BAMG
Enable Bamg 2D anisotropic mesh generator (default: ON)
ENABLE_BLAS_LAPACK
Enable BLAS/Lapack for linear algebra (if Eigen if disabled) (default: OFF)
ENABLE_BLOSSOM
Enable Blossom algorithm (needed for full quad meshing) (default: ON)
ENABLE_BUILD_LIB
Enable ’lib’ target for building static Gmsh library (default: OFF)
ENABLE_BUILD_SHARED
Enable ’shared’ target for building shared Gmsh library (default: OFF)
ENABLE_BUILD_DYNAMIC
Enable dynamic Gmsh executable (linked with shared library) (default: OFF)
ENABLE_BUILD_ANDROID
Enable Android NDK library target (experimental) (default: OFF)
ENABLE_BUILD_IOS
Enable iOS library target (experimental) (default: OFF)
ENABLE_CGNS
Enable CGNS import/export (experimental) (default: ON)
ENABLE_CGNS_CPEX0045
Enable high-order CGNS import/export following CPEX0045 (experimental) (de-
fault: OFF)
ENABLE_CAIRO
Enable Cairo to render fonts (experimental) (default: ON)
370 Gmsh 4.11.1

ENABLE_PROFILE
Enable profiling compiler flags (default: OFF)
ENABLE_DINTEGRATION
Enable discrete integration (needed for levelsets) (default: ON)
ENABLE_DOMHEX
Enable experimental DOMHEX code (default: ON)
ENABLE_EIGEN
Enable Eigen for linear algebra (instead of Blas/Lapack) (default: ON)
ENABLE_FLTK
Enable FLTK graphical user interface (requires mesh/post) (default: ON)
ENABLE_GEOMETRYCENTRAL
Enable geometry-central library (experimental) (default: ON)
ENABLE_GETDP
Enable GetDP solver (linked as a library, experimental) (default: ON)
ENABLE_GMM
Enable GMM linear solvers (simple alternative to PETSc) (default: ON)
ENABLE_GMP
Enable GMP for Kbipack (advanced) (default: ON)
ENABLE_GRAPHICS
Enable building graphics lib even without GUI (advanced) (default: OFF)
ENABLE_HXT
Enable HXT library (for reparametrization and meshing) (default: ON)
ENABLE_KBIPACK
Enable Kbipack (neeeded by homology solver) (default: ON)
ENABLE_MATHEX
Enable Mathex expression parser (used by plugins and options) (default: ON)
ENABLE_MED
Enable MED mesh and post file formats (default: ON)
ENABLE_MESH
Enable mesh module (default: ON)
ENABLE_METIS
Enable Metis mesh partitioner (default: ON)
ENABLE_MMG
Enable Mmg mesh adaptation interface (default: ON)
ENABLE_MPEG_ENCODE
Enable built-in MPEG movie encoder (default: ON)
ENABLE_MPI
Enable MPI (experimental, not used for meshing) (default: OFF)
ENABLE_MSVC_STATIC_RUNTIME
Enable static Visual C++ runtime (default: OFF)
ENABLE_MUMPS
Enable MUMPS sparse direct linear solver (default: OFF)
Appendix A: Compiling the source code 371

ENABLE_NETGEN
Enable Netgen 3D frontal mesh generator (default: ON)
ENABLE_NUMPY
Enable fullMatrix and numpy array conversion for private API (default: OFF)
ENABLE_PETSC4PY
Enable petsc4py wrappers for petsc matrices for private API (default: OFF)
ENABLE_OCC
Enable OpenCASCADE CAD kernel (default: ON)
ENABLE_OCC_CAF
Enable OpenCASCADE CAF module (for STEP/IGES attributes) (default: ON)
ENABLE_OCC_STATIC
Link OpenCASCADE static instead of dynamic libraries (requires ENABLE OCC)
(default: OFF)
ENABLE_OCC_TBB
Add TBB libraries in list of OCC libraries (default: OFF)
ENABLE_ONELAB
Enable ONELAB solver interface (default: ON)
ENABLE_ONELAB_METAMODEL
Enable ONELAB metamodels (experimental) (default: ON)
ENABLE_OPENACC
Enable OpenACC (default: OFF)
ENABLE_OPENMP
Enable OpenMP (default: ON)
ENABLE_OPTHOM
Enable high-order mesh optimization tools (default: ON)
ENABLE_OS_SPECIFIC_INSTALL
Enable OS-specific (e.g. app bundle) installation (default: OFF)
ENABLE_OSMESA
Enable OSMesa for offscreen rendering (experimental) (default: OFF)
ENABLE_P4EST
Enable p4est for enabling automatic mesh size field (experimental) (default: OFF)
ENABLE_PACKAGE_STRIP
Strip symbols in install packages to reduce install size (default: ON)
ENABLE_PARSER
Enable GEO file parser (required for .geo/.pos scripts) (default: ON)
ENABLE_PETSC
Enable PETSc linear solvers (required for SLEPc) (default: OFF)
ENABLE_PLUGINS
Enable post-processing plugins (default: ON)
ENABLE_POST
Enable post-processing module (required by GUI) (default: ON)
ENABLE_POPPLER
Enable Poppler for displaying PDF documents (experimental) (default: OFF)
372 Gmsh 4.11.1

ENABLE_PRIVATE_API
Enable private API (default: OFF)
ENABLE_PRO
Enable PRO extensions (default: ON)
ENABLE_QUADMESHINGTOOLS
Enable QuadMeshingTools extensions (default: ON)
ENABLE_QUADTRI
Enable QuadTri structured meshing extensions (default: ON)
ENABLE_REVOROPT
Enable Revoropt (used for CVT remeshing) (default: OFF)
ENABLE_RPATH
Use RPATH in dynamically linked targets (default: ON)
ENABLE_SLEPC
Enable SLEPc eigensolvers (default: OFF)
ENABLE_SOLVER
Enable built-in finite element solvers (required for reparametrization) (default: ON)
ENABLE_SYSTEM_CONTRIB
Use system versions of contrib libraries, when possible (default: OFF)
ENABLE_TCMALLOC
Enable libtcmalloc (fast malloc that does not release memory) (default: OFF)
ENABLE_TESTS
Enable tests (default: ON)
ENABLE_TOUCHBAR
Enable Apple Touch bar (default: ON)
ENABLE_VISUDEV
Enable additional visualization capabilities for development purposes (default:
OFF)
ENABLE_VOROPP
Enable voro++ (for hex meshing, experimental) (default: ON)
ENABLE_WINSLOWUNTANGLER
Enable WinslowUntangler extensions (requires ALGLIB) (default: ON)
ENABLE_WRAP_JAVA
Generate SWIG Java wrappers for private API (default: OFF)
ENABLE_WRAP_PYTHON
Generate SWIG Python wrappers for private API (not used by public API) (default:
OFF)
ENABLE_ZIPPER
Enable Zip file compression/decompression (default: OFF)
Appendix B: Information for developers 373

Appendix B Information for developers

Gmsh is written in C++, the scripting language is parsed using Lex and Yacc (actually,
Flex and Bison), and the GUI relies on OpenGL for the 3D graphics and FLTK
(http://www.fltk.org) for the widgets (menus, buttons, etc.). Gmsh’s build system is based
on CMake (http://www.cmake.org). Practical notes on how to compile Gmsh’s source code
are provided in Appendix A [Compiling the source code], page 369 (see also Appendix C
[Frequently asked questions], page 375).
This section is for developers who would like to contribute directly to the Gmsh source code.
Gmsh’s official Git repository is located at https://gitlab.onelab.info/gmsh/gmsh. The
wiki (https://gitlab.onelab.info/gmsh/gmsh/wikis/Git-cheat-sheet) contains instruc-
tions on how to create feature branches and submit merge requests.

B.1 Source code structure

Gmsh’s code is structured in several subdirectories, roughly separated between the four
core modules (src/geo, src/mesh, src/solver, src/post) and associated utilities (src/common,
src/numeric) on one hand, and the graphics (src/graphics) and interface (src/fltk, src/parser,
api) code on the other.
The geometry module is based on a model class (src/geo/GModel.h), and abstract en-
tity classes for geometrical points (src/geo/GVertex.h), curves (src/geo/GEdge.h), surfaces
(src/geo/GFace.h) and volumes (src/geo/GRegion.h). Concrete implementations of these classes
are provided for each supported CAD kernel (e.g. src/geo/gmshVertex.h for points in Gmsh’s
built-in CAD kernel, or src/geo/OCCVertex.h for points from OpenCASCADE). All these el-
ementary model entities derive from src/geo/GEntity.h. Physical groups are simply stored as
integer tags in the entities.
A mesh is composed of elements: mesh points (src/geo/MPoint.h), lines (src/geo/MLine.h),
triangles (src/geo/MTriangle.h), quadrangles (src/geo/MQuadrangle.h), tetrahedra
(src/geo/MTetrahedron.h), etc. All the mesh elements are derived from src/geo/MElement.h,
and are stored in the corresponding model entities: one mesh point per geometrical point, mesh
lines in geometrical curves, triangles and quadrangles in surfaces, etc. The elements are defined
in terms of their nodes (src/geo/MVertex.h). Each model entity stores only its internal nodes:
nodes on boundaries or on embedded entities are stored in the associated bounding/embedded
entity.
The post-processing module is based on the concept of views (src/post/PView.h) and ab-
stract data containers (derived from src/post/PViewData.h). Data can be either mesh-based
(src/post/PViewDataGModel.h), in which case the view is linked to one or more models, or
list-based (src/post/PViewDataList.h), in which case all the relevant geometrical information is
self-contained in the view.

B.2 Coding style

If you plan to contribute code to the Gmsh project, here are some easy rules to make the code
easy to read/debug/maintain:
• See https://gitlab.onelab.info/gmsh/gmsh/wikis/Git-cheat-sheet for instructions
on how to contribute to Gmsh’s Git source code repository. All branches are tested; make
sure that all tests pass and that your code does not produce any warnings before submitting
merge requests.
• Follow the style used in the existing code when adding something new: indent using 2 spaces
(never use tabs!), put 1 space after commas, put opening braces for functions on a separate
line, opening braces for loops and tests on the same line, etc. You can use the clang-format
tool to apply these rules automatically (the rules are defined in the .clang-format file.)
374 Gmsh 4.11.1

• Always use the Msg:: class to print information or errors

• Use memory checking tools to detect memory leaks and other nasty memory problems. For
example, on Linux you can use valgrind --leak-check=full gmsh file.geo -3.

B.3 Adding a new option

To add a new option in Gmsh:
1. create the option in the CTX class (src/common/Context.h if it’s a classical option, or in
the PViewOptions class (src/post/PViewOptions.h) if it’s a post-processing view-dependent
option;
2. in src/common/DefaultOptions.h, give a name (for the parser to be able to access it), a
reference to a handling routine (i.e. opt_XXX) and a default value for this option;
3. create the handling routine opt_XXX in src/common/Options.cpp (and add the prototype
in src/common/Options.h);
4. optional: create the associated widget in src/fltk/optionWindow.h;
Appendix C: Frequently asked questions 375

Appendix C Frequently asked questions

C.1 The basics

1. What is Gmsh?
Gmsh is an automatic three-dimensional finite element mesh generator with built-in pre- and
post-processing facilities. With Gmsh you can create or import 1D, 2D and 3D geometrical
models, mesh them, launch external finite element solvers and visualize solutions. Gmsh
can be used either as a stand-alone program (graphical or not) or as a library to integrate
in C++, C, Python, Julia or Fortran codes.
2. What are the terms and conditions of use?
Gmsh is distributed under the terms of the GNU General Public License, with an exception
to allow for easier linking with external libraries. See Appendix F [License], page 409 for
more information.
3. What does ’Gmsh’ mean?
Nothing... The name was derived from a previous version called “msh” (a shortcut for
“mesh”), with the “g” prefix added to differentiate it. The default mesh file format used
by Gmsh still uses the ‘.msh’ extension.
In English people tend to pronounce ‘Gmsh’ as “gee-mesh”.
4. Can I embed ’Gmsh’ in my own software?
Yes, using the Gmsh API (see Chapter 6 [Gmsh application programming interface],
page 123). See [Copying conditions], page 3 for the licensing constraints.
5. Where can I find more information?
https://gmsh.info is the primary location to obtain information about Gmsh. There you
will for example find the complete reference manual and the bug tracking database.

C.2 Installation problems

1. Which OSes does Gmsh run on?
Gmsh runs on Windows, macOS, Linux and most Unix variants. Gmsh is also available as
part of the ONELAB package on Android and iOS tablets and phones.
2. Are there additional requirements to run Gmsh?
You should have the OpenGL libraries installed on your system, and in the path of the
library loader. A free replacement for OpenGL can be found at http://www.mesa3d.org.
3. How do I compile Gmsh from the source code?
You need cmake (http://www.cmake.org) and a C++ compiler. See Appendix A [Compiling
the source code], page 369 for more information.
4. Where does Gmsh save its configuration files?
Gmsh will attempt to save temporary files and persistent configuration options first in the
$GMSH_HOME directory, then in $APPDATA (on Windows) or $HOME (on other OSes), then in
$TMP, and finally in $TEMP, in that order. If none of these variables are defined, Gmsh will
try to save/load its configuration files from the current working directory.

C.3 General questions

1. Gmsh (from a binary distribution) complains about missing libraries.
On Windows, if your system complains about missing ‘OPENGL32.DLL’ or ‘GLU32.DLL’ li-
braries, then OpenGL is not properly installed on your machine. You can download OpenGL
from Microsoft’s web site, or directly from http://www.opengl.org.
376 Gmsh 4.11.1

On Unix try ‘ldd gmsh’ (or ‘otool -L gmsh’ on macOS) to check if all the required shared
libraries are installed on your system. If not, install them. If it still doesn’t work, recompile
Gmsh from the source code.
2. Gmsh keeps re-displaying its graphics when other windows partially hide the graphical
window.
Disable opaque move in your window manager.
3. The graphics display very slowly.
Are you are executing Gmsh from a remote host (via the network) without GLX? You
should turn double buffering off (with the ‘-nodb’ command-line switch).
4. There is an ugly “ghost triangulation” in the vector PostScript/PDF files generated by
Gmsh!
No, there isn’t. This “ghost triangulation” is due to the fact that most PostScript previewers
nowadays antialias the graphic primitives when they display the page on screen. (For
example, in gv, you can disable antialising with the ‘State->Antialias’ menu.) You should
not see this ghost triangulation in the printed output (on paper).
5. How can I save GIF, JPEG, ..., images?
Just choose the appropriate format in ‘File->Export’. By default Gmsh guesses the format
from the file extension, so you can just type ‘myfile.jpg’ in the dialog and Gmsh will
automatically create a JPEG image file.
6. How save high-resolution images?
You can specify the dimension in the dialog (e.g. set the width of the image to 5000 pixels;
leaving one dimension negative will rescale using the natural aspect ratio), or through the
Print.Width and Print.Height options. The maximum image size is graphics hardware
dependent.
7. How can I save MPEG, AVI, ..., animations?
You can create simple MPEG animations by choosing MPEG as the format in ‘File-
>Export’: this allows you to loop over time steps or post-processing data sets, or to change
parameters according to Print.Parameter. To create fully customized animations or to
use different output formats (AVI, MP4, etc.) you should write a script. Have a look at
Section 2.8 [t8], page 33 or examples/post processing/anim.script for some examples.
8. Can I change values in input fields with the mouse in the GUI?
Yes: dragging the mouse in a numeric input field slides the value! The left button moves
one step per pixel, the middle by ‘10*step’, and the right button by ‘100*step’.
9. Can I copy messages to the clipboard?
Yes: selecting the content of an input field, or lines in the message console (‘Tools->Message
Console’), copies the selected text to the clipboard.

C.4 Geometry module

1. Does Gmsh support trimmed NURBS surfaces?
Yes, but only with the OpenCASCADE kernel.
2. Gmsh is very slow when I use many transformations (Translate, Rotate, Symmetry, Extrude,
etc.) with the built-in CAD kernel. What’s wrong?
The default behavior of Gmsh is to check and suppress all duplicate entities (points, curves
and surfaces) each time a transformation command is issued with the built-in CAD kernel.
This can slow down things a lot if many transformations are performed. There are two
solutions to this problem:
Appendix C: Frequently asked questions 377

• you may save the serialized (“unrolled”) geometry in another file (using gmsh file.geo
-0 or exporting to “.geo unrolled”), and use this new file for subsequent computations;
• or you may set the Geometry.AutoCoherence option to 0. This will prevent any
automatic duplicate check/replacement. If you still need to remove the duplicates
entities, simply add Coherence; at strategic locations in your ‘.geo’ files (e.g. before
the creation of curve loops, etc.).
3. Why is my “.geo unrolled” file incomplete?
“Unrolled GEO” files can only fully represent geometries created with the built-in geometry
kernel. If you want to serialize a geometry created with the OpenCASCADE geometry
kernel, you should use the native OpenCASCADE “.brep” format.
4. How can I display only selected parts of my model?
Use ‘Tools->Visibility’. This allows you to select elementary entities and physical groups,
as well as mesh elements, in a variety of ways (in a list or tree browser, by tag, interactively,
or per window).
5. Can I edit STEP/IGES/BRep models?
Yes: with the OpenCASCADE kernel (SetFactory("OpenCASCADE");), load the file (Merge
"file.step"; or ShapeFromFile("file.step");) and add the relevant scripting com-
mands after that to delete parts, create new parts or apply boolean operators. See e.g.
examples/boolean/import.geo.
6. Why are there surfaces missing when I export a STEP as an unrolled ‘.geo’ file?
You should not export STEP models as ‘.geo’ files. By design, Gmsh never translates from
one CAD format to another. The “unrolled GEO” feature is there for unrolling complex
GEO scripts writted with the built-in geometry kernel. While it can indeed export a limited
subset of geometrical entities created by other CAD kernels (e.g. OpenCASCADE), this
feature is available for debugging purposes.
7. How can I build modular geometries?
Define common geometrical objects and options in separate files or using Macro, reusable
in all your problem definition structures. Or use the features of your language of choice and
the Gmsh API.
8. Some files take much more time to load with Gmsh 4 compared to Gmsh 3: what’s hap-
pening?
In Gmsh 4, some operations (Color, Show, Hide, BoundingBox, Boundary, PointsOf,
Periodic, In embedding constraints, ..) are now applied directly on the internal Gmsh
model, instead of being handled at the level of the CAD kernel. This implies a synchro-
nization between the CAD kernel and the Gmsh model. To minimize the number of syn-
chronizations (which can become costly for large models), you should always create your
geometry first; and use these commands once the geometry has been created.

C.5 Mesh module

1. What should I do when the 2D unstructured algorithm fails?
Verify that the curves in the model do not self-intersect. If ‘Mesh.RandomFactor * size of
triangle / size of model’ approaches machine accuracy, increase Mesh.RandomFactor.
If everything fails file a bug report with the version of your operating system and the full
geometry.
2. What should I do when the 3D unstructured algorithm fails?
Verify that the surfaces in your model do not self-intersect or partially overlap. If they
don’t, try the other 3D algorithms (‘Tool->Options->Mesh->General->3D algorithm’) or try
378 Gmsh 4.11.1

to adapt the mesh element sizes in your input file so that the surface mesh better matches
the geometrical details of the model.
If nothing works, file a bug report with the version of your operating system and the full
geometry.
3. How can I only save tetrahedral elements (not triangles and lines)?
By default, if physical groups are defined, the output mesh only contains those elements
that belong to physical entities. So to save only 3D elements, simply define one (or more)
physical volume(s) and don’t define any physical surfaces, physical curves or physical points.
4. How can I remove mesh nodes for geometrical construction points (centers of spheres, etc.)
from output mesh file?
By default Gmsh saves all the geometrical entities and their associated mesh. In particular,
since each geometry point is meshed with a point element, defined by a mesh node, the
output file will contain one 0-D mesh element and one mesh node for each geometry point.
To remove such elements/nodes from the mesh, simply define physical groups for the entities
you want to save (see previous question).
5. My 2D meshes of IGES files present gaps between surfaces
IGES files do not contain the topology of the model, and tolerance problems can thus
appear when the OpenCASCADE importer cannot identify two (close) curves as actually
being identical.
The best solution is to not use IGES and use STEP instead. If you really have to use
IGES, check that you don’t have duplicate curves (e.g. by displaying their tags in the
GUI with ‘Tools->Options->Geometry->Visibility->Curve labels’). If there are duplicates,
try to change the geometrical tolerance and sew the faces (see options in ‘Tools->Options-
>Geometry->General’).
6. The quality of the elements generated by the 3D algorithm is very bad.
Use ‘Optimize quality’ in the mesh menu.
7. Non-recombined 3D extruded meshes sometimes fail.
The swapping algorithm is not very clever. Try to change the surface mesh a bit, or
recombine your mesh to generate prisms or hexahedra instead of tetrahedra.
8. Does Gmsh automatically couple unstructured tetrahedral meshes and structured hexahe-
dral meshed using pyramids?
Yes, but only if pyramids need to be created on a single side of the quadrangular surface
mesh.
9. Can I explicitly assign region tags to extruded layers?
No, this feature has been removed in Gmsh 2.0. You must use the standard entity tag
instead.
10. Did you remove the elliptic mesh generator in Gmsh 2.0?
Yes. You can achieve the same result by using the transfinite algorithm with smoothing
(e.g., with Mesh.Smoothing = 10).
11. Does Gmsh support curved elements?
Yes, just choose the appropriate order in the mesh menu after the mesh is completed.
High-order optimization tools are also available in the mesh menu. You can select the
order on the command line with e.g. -order 2, and activcate high-order optimization with
-optimize_ho.
12. Can I import an existing surface mesh in Gmsh and use it to build a 3D mesh?
Yes, you can import a surface mesh in any one of the supported mesh file formats, define a
volume, and mesh it. For an example see examples/simple geo/sphere-discrete.geo.
Appendix C: Frequently asked questions 379

13. How do I define boundary conditions or material properties in Gmsh?

By design, Gmsh does not try to incorporate every possible definition of boundary conditions
or material properties—this is a job best left to the solver. Instead, Gmsh provides a simple
mechanism to tag groups of elements, and it is up to the solver to interpret these tags as
boundary conditions, materials, etc. Associating tags with elements in Gmsh is done by
defining physical groups (Physical Points, Physical Curves, Physical Surfaces and Physical
Volumes). See the reference manual as well as the tutorials (in particular Section 2.1 [t1],
page 15) for a detailed description and some examples.
The Gmsh API can be used to build sophisticated interactive workflows where the definition
of boundary conditions and material properties can be fully tailored to your preferred solver.
For an example see examples/api/prepro.py.
14. How can I display only the mesh associated with selected geometrical entities?
See “How can I display only selected parts of my model?”.
15. How can I “explore” a mesh (for example, to see inside a complex structure)?
You can use ‘Tools->Clipping’ to clip the region of interest. You can define up to 6 clipping
planes in Gmsh (i.e., enough to define a “cube” inside your model) and each plane can
clip either the geometry, the mesh, the post-processing views, or any combination of the
above. The clipping planes are defined using the four coefficients A,B,C,D of the equation
A*x+B*y+C*y+D=0, which can be adjusted interactively by dragging the mouse in the
input fields.
16. What is the signification of SICN, Gamma and SIGE in Tools->Statistics?
They measure the quality of the tetrahedra in a mesh:
• SICN: signed inverse condition number
• Gamma: inscribed radius / circumscribed radius
• SIGE: signed inverse error on the gradient of FE solution
For the exact definitions, see src/geo/MElement.cpp. The graphs plot the the number of
elements vs. the quality measure.
17. How can I save a mesh file with a given (e.g. older) MSH file format version?
• In the GUI: open ‘File->Export’, enter your ‘filename.msh’ and then pick the version
in the dropdown menu.
• On the command line: use the -format option (e.g. gmsh file.geo -format msh2
-2).
• In a ‘.geo’ script: add the line Mesh.MshFileVersion = x.y; for any version number
x.y. You can also save this in your default options.
• In the API: gmsh::option::setNumber("Mesh.MshFileVersion", x.y).
As an alternative method, you can also not specify the format explicitly, and just choose a
filename with the .msh2 or .msh4 extension.
18. Why isn’t neighboring element information stored in the MSH file?
Each numerical method has its own requirements: it might need neighboring elements con-
nected by a node, an edge or a face; it might require a single layer or multiple layers; it should
include elements of lower dimension (boundaries) or not, go across geometrical entities or
mesh partitions or not, etc. Given the number of possibilities, generating the appropriate in-
formation is thus best performed in the numerical solver itself. The Gmsh API makes these
computations easy: see tutorial Section 2.28 [x7], page 74 and examples/api/neighbors.py.
19. Could mesh edges/faces be stored in the MSH file?
Edge/faces can be easily generated from the information already available in the file (i.e.
nodes and elements), or through the Gmsh API: see tutorial Section 2.28 [x7], page 74,
examples/api/edges.cpp and examples/api/faces.cpp.
380 Gmsh 4.11.1

C.6 Solver module

1. How do I integrate my own solver with Gmsh?
Gmsh uses the ONELAB interface (http://www.onelab.info) to interact with external
solvers. See Section 1.3 [Solver module], page 12.
2. Can I launch Gmsh from my solver (instead of launching my solver from Gmsh) in order to
monitor a solution?
Using the Gmsh API, you can directly embed Gmsh in your own solver, use ONELAB for
interactive parameter definition and modification, and create visualization data on the fly.
See e.g. prepro.py, custom gui.py, custom gui.cpp.
Another (rather crude) approach if to launch the Gmsh app everytime you want to visualize
something (a simple C program showing how to do this is given in utils/misc/callgmsh.c).
Yet another approach is to modify your program so that it can communicate with Gmsh
through ONELAB over a socket. Select ‘Always listen to incoming connection requests’ in
the Gmsh solver option panel (or run gmsh with the -listen command line switch), and
Gmsh will always listen for your program on the given socket (or on the Solver.SocketName
if no socket is specified).

C.7 Post-processing module

1. How do I compute a section of a plot?
Use ‘Tools->Plugins->Cut Plane’.
2. Can I save an isosurface to a file?
Yes: first run ‘Tools->Plugins->Isosurface’ to extract the isosurface, then use ‘View->Export’
to save the new view.
3. Can Gmsh generate isovolumes?
Yes, with the CutMap plugin (set the ExtractVolume option to -1 or 1 to extract the
negative or positive levelset).
4. How do I animate my plots?
If the views contain multiple time steps, you can press the ‘play’ button at the bottom of
the graphic window, or change the time step by hand in the view option panel. You can
also use the left and right arrow keys on your keyboard to change the time step in all visible
views in real time.
If you want to loop through different views instead of time steps, you can use the ‘Loop
through views instead of time steps’ option in the view option panel, or use the up and
down arrow keys on your keyboard.
5. How do I visualize a deformed mesh?
Load a vector view containing the displacement field, and set ‘Vector display’ to ‘Displace-
ment’ in ‘View->Options->Aspect’. If the displacement is too small (or too large), you can
scale it with the ‘Displacement factor’ option. (Remember that you can drag the mouse in
all numeric input fields to slide the value!)
Another option is to use the ‘General transformation expressions’ (in View->Options-
>Offset) on a scalar view, with the displacement map selected as the data source.
6. Can I visualize a field on a deformed mesh?
Yes, there are several ways to do that.
The easiest is to load two views: the first one containing a displacement field (a vector
view that will be used to deform the mesh), and the second one containing the field you
want to display (this view has to contain the same number of elements as the displacement
view). You should then set ‘Vector display’ to ‘Displacement’ in the first view, as well as
Appendix C: Frequently asked questions 381

set ‘Data source’ to point to the second view. (You might want to make the second view
invisible, too. If you want to amplify or decrease the amount of deformation, just modify
the ‘Displacement factor’ option.)
Another solution is to use the ‘General transformation expressions’ (in ‘View->Options-
>Offset’) on the field you want to display, with the displacement map selected as the data
source.
And yet another solution is to use the Warp plugin.
7. Can I color the arrows representing a vector field with data from a scalar field?
Yes: load both the vector and the scalar fields (the two views must have the same number
of elements) and, in the vector field options, select the scalar view in ‘Data source’.
8. Can I color isovalue surfaces with data from another scalar view?
Yes, using either the CutMap plugin (with the ‘dView’ option) or the Evaluate plugin.
9. Is there a way to save animations?
You can save simple MPEG animations directly from the ‘File->Export’ menu. For
other formats you should write a script. Have a look at Section 2.8 [t8], page 33 or
examples/post processing/anim.script for some examples.
10. Is there a way to visualize only certain components of vector/tensor fields?
Yes, by using either the “Force field” options in ‘Tools->Options->View->Visibility’, or by
using ‘Tools->Plugins->MathEval’.
11. Can I do arithmetic operations on a view? Can I perform operations involving different
views?
Yes, with the Evaluate plugin.
12. Some plugins seem to create empty views. What’s wrong?
There can be several reasons:
• the plugin might be written for specific element types only (for example, only for scalar
triangles or tetrahedra). In that case, you should transform your view before running
the plugin (you can use Plugin(DecomposeinSimplex) to transform all quads, hexas,
prisms and pyramids into triangles and tetrahedra).
• the plugin might expect a mesh while all you provide is a point cloud. In 2D, you can
use Plugin(Triangulate) to transform a point cloud into a triangulated surface. In
3D you can use Plugin(Tetrahedralize).
• the input parameters are out of range.
In any case, you can automatically remove all empty views with ‘View->Remove->Empty
Views’ in the GUI, or with Delete Empty Views; in a script.
13. How can I see “inside” a complicated post-processing view?
Use ‘Tools->Clipping’.
When viewing 3D scalar fields, you can also modify the colormap (‘Tools->Options->View-
>Map’) to make the iso-surfaces “transparent”: either by holding Ctrl while dragging the
mouse to draw the alpha channel by hand, or by using the a, Ctrl+a, p and Ctrl+p keyboard
shortcuts.
Yet another (destructive) option is to use the ExtractVolume option in the CutSphere or
CutPlane plugins.
14. I am loading a valid 3D scalar view but Gmsh does not display anything!
If your dataset is constant per element make sure you don’t use the ‘Iso-values’ interval
type in ‘Tools->Options->View->Range’.
Appendix D: Version history 383

Appendix D Version history

4.11.1 (December 21, 2022): Mesh.TransfiniteTri improvements; small bug fixes.

4.11.0 (November 6, 2022): new Fortran API; improved copying ("Duplicata") of

multiple shapes with OCC; reduced default order for OCC surface filling;
arbitrary string attributes can now be stored in models and MSH files; new
Radioss export; added ability to specify spline tangents with OCC; new option
Mesh.SaveWithoutOrphans to prune orphan entities (e.g. geometrical construction
points) from MSH4 files; major overhaul of the reference manual; new official
macOS ARM builds; small bug fixes.

* New API functions: model/getAttributeNames, model/getAttribute,

model/setAttribute, model/removeAttribute

* Incompatible API changes: new argument to mesh/computeHomology; new optional

arguments to occ/addSpline and occ/addThruSections

4.10.5 (July 1, 2022): small bug fixes.

4.10.4 (June 19, 2022): improved graphical window tooltips; small bug fixes.

* New API function: mesh/removeDuplicateElements

4.10.3 (May 26, 2022): small bug fixes.

* New API function: fltk/finalize

4.10.2 (May 13, 2022): fixed regression introduced in 4.9 for recombined meshes
with boundary layers; new Geometry.OCCSafeUnbind option to disable boolean
optimization introduced in 4.10.0 (for backward compatibility); new HealShapes
command in .geo files; simplified calculation of OCC STL bounding boxes;
generalized Crack plugin; small bug fixes.

4.10.1 (May 1, 2022): small bug fixes.

4.10.0 (April 25, 2022): more flexible homology/cohomology workflow in the API;
"Attractor" field is now just a synonym for the newer (and more efficient)
"Distance" field; periodic bsplines now use the same default multiplicities in
OCC as in the built-in kernel; model/isInside now also handles discrete
entities; speed-up repeated simple boolean operations; C++ api now throws
std::runtime_error on errors; small bug fixes.

* New API functions: geo/addGeometry, geo/addPointOnGeometry,

mesh/addHomologyRequest, mesh/clearHomologyRequests, mesh/setVisibility,
mesh/getElementQualities

* Incompatible API changes: additional const qualifiers in C API; removed

mesh/computeCohomology; new arguments to occ/getCurveLoops and
occ/getSurfaceLoops; changed arguments of mesh/computeHomology; new optional
arguments to occ/addCircle, occ/addEllipse, occ/addDisk, occ/addTorus,
occ/addWedge, model/addPhysicalGroup, model/geo/addPhysicalGroup,
384 Gmsh 4.11.1

mesh/removeDuplicateNodes and mesh/setRecombine.

4.9.5 (February 21, 2022): dynamic Gmsh library now also only exports public
symbols on macOS and Linux, like it does on Windows; better handling of
max. thread settings; small bug fixes.

* New API function: mesh/getDuplicateNodes

4.9.4 (February 3, 2022): improved BSpline filling; new options

Mesh.MinimumLineNodes, Mesh.RecombineNodeRepositioning,
Mesh.RecombineMinimumQuality and Mesh.StlLinearDeflectionRelative; updated
bundled Eigen; small bug fixes.

* New API functions: gmsh/isInitialized, occ/convertToNURBS, occ/getCurveLoops,

occ/getSurfaceLoops, mesh/importStl, parser/getNames, parser/setNumber,
parser/setString, parser/getNumber, parser/getString, parser/clear,
parser/parse, onelab/getChanged, onelab/setChanged

4.9.3 (January 4, 2022): improved handling of degenerate curves in periodic

surfaces and boundary layer extrusion; extended Mesh.SaveGroupsOfElements
capabilities for INP export; extended Mesh.MeshSizeExtendFromBoundary + new
"Extend" mesh size field to enable alternative mesh size extensions from
boundary; enhanced X3D output; moved all kernel sources to src/ subdirectory;
renamed demos/ as examples/ and tutorial/ as tutorials/; small bug fixes.

4.9.2 (December 23, 2021): faster projection on OCC entities; extended

Mesh.SaveGroupsOfNodes capabilities for INP export; improved transfinite meshing
of surfaces with boundary on periodic seam.

4.9.1 (December 18, 2021): relax tolerance on curve parametrization match for
periodic meshing; enable extruded boundary layers on generic model entities;
activate IncludeBoundary by default in Restrict field; downgraded compiler for
official Linux releases to gcc 6 to improve compatibility with older systems;
small bug fixes (view tag generation with zero tag, model/setTag).

4.9.0 (December 3, 2021): new initial 2D meshing algorithm; new quasi-structured

quad algorithm; improved handling of imperfect curve reparametrization on
surfaces in 2D periodic meshing algorithm; mesh renumbering now also renumbers
dependent post-processing views; the mesh size callback is now per-model and its
returned value is not gathered with the other size constraints in a global min
reduction anymore: instead the callback takes as additional argument the mesh
size lc that would be prescribed in the absence of the callback, which allows to
perform any desired modification (the old behavior can be achieved by returning
min(lc, value)); OCC STL representation is now generated using relative
deflection tolerance; new TransformMesh command in .geo files; new behavior of
Mesh.SaveGroupsOf{Nodes,Elements} in UNV and INP exports; partitioned MSH4 files
now contain the full partition topology (i.e. all partition entities); fixed
metric calculation with Eigen (for anisotropic mesh generation); official binary
builds now support OpenMP parallelization and are 64 bit only (build OS upgraded
to Windows 10, macOS 10.15 and Linux glibc 2.24); new experimental Fortran API;
new API functions to handle view options by tag instead of by index; color
options in the API can now be specified as in .geo files, in the form
Appendix D: Version history 385

"Category.Color.Option"; small bug fixes.

* New API functions: model/setTag, mesh/reverse, mesh/affineTransform,

mesh/getMaxNodeTag, mesh/getMaxElementTag, mesh/getSizes, mesh/getPeriodic,
mesh/getAllEdges, mesh/getAllFaces, mesh/addEdge, mesh/addFace,
mesh/getNumberOfPartitions, field/list, field/getType, field/getNumber,
field/getNumbers, field/getString, view/option/setNumber,
view/option/getNumber, view/option/setString, view/option/getString,
view/option/setColor, view/option/getColor, view/option/copy.

* Incompatible API changes: new arguments to mesh/getNode, mesh/getElement and

view/probe; additional argument to the mesh size callback function provided to
mesh/setSizeCallback; new optional arguments to gmsh/initialize,
model/isInside, mesh/partition and occ/addSurfaceFilling; renamed
mesh/preallocateBasisFunctionsOrientationForElements as
mesh/preallocateBasisFunctionsOrientation, mesh/getNumberOfKeysForElements as
mesh/getNumberOfKeys, and mesh/getBasisFunctionsOrientationForElements as
mesh/getBasisFunctionsOrientation; renamed mesh/getKeysForElements as
mesh/getKeys and mesh/getInformationForElements as mesh/getKeysInformation,
and modified their arguments; modified arguments to mesh/getKeysForElement;
removed mesh/getLocalMultipliersForHcurl0; renamed view/copyOptions as
view/option/copy.

4.8.4 (April 28, 2021): set current model in gmsh/model/add; small bug fixes.

4.8.3 (April 6, 2021): better handling of errors in inverse surface mapping;

fixed Mesh.MedFileMinorVersion for MED 4; small bug fixes.

4.8.2 (March 27, 2021): fixed regression in OCC transforms; fixed cwrap API.

4.8.1 (March 21, 2021): improved performance when transforming many OCC
entities; fixed regression in high-order meshing of surfaces with singular
parametrizations; small bug fixes.

4.8.0 (March 2, 2021): new interactive and fully parametrizable definition of

boundary conditions, materials, etc. through ONELAB variables; new API functions
for creating trimmed BSpline/Bezier patches, perform raw triangulations and
tetrehedralizations, get upward adjacencies, and create extruded boundary layers
and automatic curve loops in built-in kernel; improved performance of high-order
meshing of OCC models; improved handling of high resolution displays; new
structured CGNS exporter; new transfinite Beta law; added support for embedded
curves in HXT; added automatic conversion from partitioned MSH2 files to new
partitioned entities; element groups can now be imported from UNV files; fixed
order of Gauss quadrature for quads and hexas; code modernization (C++11);
further uniformization of option names to match the documented terminology
(Mesh.Point -> Mesh.Node, ...; old names are still accepted, but deprecated);
deprecated Mesh.MinimumElementsPerTwoPi: set value directly to
Mesh.MeshSizeFromCurvature instead; Python and Julia APIs now also define "snake
case" aliases for all camelCase function names; small bug fixes and
improvements.

* New API functions: model/getFileName, model/setFileName, model/getAdjacencies,

386 Gmsh 4.11.1

model/getSecondDerivative, mesh/getEdges, mesh/getFaces, mesh/createEdges,

mesh/createFaces, mesh/removeConstraints, mesh/getEmbedded, mesh/triangulate,
mesh/tetrahedralize, geo/addCurveLoops, fltk/setStatusMessage,
fltk/showContextWindow, fltk/openTreeItem, fltk/closeTreeItem,
onelab/getNames.

* Incompatible API changes: new optional arguments to mesh/classifySurfaces,

occ/addBSplineSurface, occ/addBezierSurface, occ/addPipe and view/probe;
renamed mesh/getEdgeNumber as mesh/getEdges.

4.7.1 (November 16, 2020): small bug fixes and improvements.

4.7.0 (November 5, 2020): API errors now throw exceptions with the last error
message (instead of an integer error code); API functions now print messages on
the terminal by default, and throw exceptions on all errors unless in
interactive mode; new API functions to retrieve "homogeneous" model-based data
(for improved Python performance), to set interpolation matrices for high-order
datasets, to assign "automatic" transfinite meshing constraints and to pass
native (C++, C, Python or Julia) mesh size callback; added option to save
high-order periodic nodes info; added support for scripted window splitting;
improved VTK reader; new MatrixOfInertia command; added support for Unicode
command line arguments on Windows; uniformized commands, options and field
option names to match the documented terminology (CharacteristicLength ->
MeshSize, geometry Line -> Curve, ...; old names are still accepted, but
deprecated); improved handling of complex periodic cases; removed bundled Mmg3D
and added support for stock Mmg 5; Gmsh now requires C++11 and CMake 3.1, and
uses Eigen by default instead of Blas/Lapack for dense linear algebra; small bug
fixes.

* New API functions: model/setVisibilityPerWindow, mesh/setSizeCallback,

mesh/removeSizeCallback, mesh/setTransfiniteAutomatic, geo/addPhysicalGroup,
geo/removePhysicalGroups, view/setInterpolationMatrices,
view/setVisibilityPerWindow, fltk/splitCurrentWindow, fltk/setCurrentWindow,
logger/getLastError.

* Incompatible API changes: new optional argument to geo/addCurveLoop.

4.6.0 (June 22, 2020): new options to only generate initial 2D or 3D meshes
(without node insertion), and to only mesh non-meshed entities; added ability to
only remesh parts of discrete models; added support for mesh size fields and
embedded points and surfaces in HXT; improved reparametrization and partitioning
code; new OCC API functions to reduce the number of synchronizations for complex
models; new OCC spline surface interfaces; new functions and options to control
the first tag of entities, nodes and elements; fixed duplicated entities in STEP
output; improved mesh subdivision and high-order pipeline; MED output now
preserves node and element tags; small bug fixes.

* New API functions: model/getParametrizationBounds, model/isInside,

model/getClosestPoint, model/reparametrizeOnSurface, mesh/rebuildElementCache,
mesh/getBasisFunctionsOrientationForElements,
mesh/getBasisFunctionsOrientationForElement, mesh/getNumberOfOrientations,
mesh/preallocateBasisFunctionsOrientationForElements,
Appendix D: Version history 387

mesh/setSizeAtParametricPoints, geo/setMaxTag, geo/getMaxTag,

occ/addBSplineFilling, occ/addBezierFilling, occ/addBSplineSurface,
occ/addBezierSurface, occ/setMaxTag, occ/getMaxTag, occ/getEntities,
occ/getEntitiesInBoundingBox, occ/getBoundingBox,
view/addHomogeneousModelData.

* Incompatible API changes: new optional arguments to mesh/clear,

mesh/createTopology, mesh/createGeometry, occ/addThruSections,
mesh/getPeriodicNodes; new arguments to mesh/getBasisFunctions; removed
mesh/preallocateBasisFunctions, mesh/precomputeBasisFunctions and
mesh/getBasisFunctionsForElements; renamed occ/setMeshSize as
occ/mesh/setSize.

4.5.6 (March 30, 2020): better calculation of OCC bounding boxes using STL; API
tutorials; small bug fixes.

* New API functions: view/addListDataString, view/getListDataStrings.

4.5.5 (March 21, 2020): tooltips in GUI to help discovery of scripting options;
fixed MED IO of high-order elements; fixed OCC attribute search by bounding box;
fix parsing of mac-encoded scripts; new RecombineMesh command; added support for
extrusion of mixed-dimension entities with OCC; small bug fixes.

4.5.4 (February 29, 2020): periodic mesh optimization now ensures that the
master mesh is not modified; code cleanup; small bug fixes.

4.5.3 (February 22, 2020): improved positioning of corresponding nodes on

periodic entities; improved LaTeX output; improved curve splitting in
reparametrization; new binary PLY reader; small compilation fixes.

* New API functions: mesh/getEdgeNumber, mesh/getLocalMultipliersForHcurl0.

4.5.2 (January 30, 2020): periodic meshes now obey reorientation constraints;
physical group definitions now follow compound meshing constraints; small bug
fixes and improvements.

* New API function: geo/splitCurve.

4.5.1 (December 28, 2019): new Min and Max commands in .geo files;
Mesh.MinimumCirclePoints now behaves the same with all geometry kernels; fixed
issue with UTF16-encoded home directories on Windows.

4.5.0 (December 21, 2019): changed default 2D meshing algorithm to

Frontal-Delaunay; new compound Spline/BSpline commands; new MeshSizeFromBoundary
command; new CGNS importer/exporter; new X3D exporter for geometries and meshes;
improved surface mesh reclassification; new separate option to govern curvature
adapted meshes (Mesh.MinimumElementsPerTwoPi and "-clcurv val"); improved
handling of anisotropic surface meshes in 3D Delaunay; improved high-order
periodic meshing; improved 2D boolean unions; file chooser type is now
changeable at runtime; FLTK GUI can now be created and destroyed at will through
the API; fixed regression in MeshAdapt for non-periodic surfaces with
singularities; combining views now copies options; added API support for mesh
388 Gmsh 4.11.1

compounds, per-surface mesh algorithm and mesh size from boundary; renamed
plugin AnalyseCurvedMesh to AnalyseMeshQuality; fixed regression for built-in
kernel BSplines on non-flat geometries (Sphere, PolarSphere); small fixes and
improvements.

* New API functions: model/getCurrent, model/getParametrization,

mesh/computeCrossField, mesh/setNode, mesh/getElementsByCoordinates,
mesh/getLocalCoordinatesInElement, mesh/getNumberOfKeysForElements,
mesh/setAlgorithm, mesh.setSizeFromBoundary, mesh/setComound,
geo/addCompoundSpline, geo/addCompoundBSpline, fltk/isAvailable.

* Incompatible API changes: removed mesh/smooth (now handled by mesh/optimize

like all other mesh optimizers); renamed logger/time to logger/getWallTime and
logger/cputime to logger/getCpuTime; new arguments to mesh/optimize,
mesh/getElementProperties and occ/healShapes; added optional argument to
mesh/classifySurfaces and view/combine.

4.4.1 (July 25, 2019): small improvements (transfinite with degenerate curves,
renumbering for some mesh formats, empty MSH file sections, tunable accuracy of
compound meshes) and bug fixes (ellipse < pi, orientation and reclassification
of compound parts, serendip pyramids, periodic MeshAdapt robustness, invalidate
cache after mesh/addNodes).

4.4.0 (July 1, 2019): new STL remeshing workflow (with new ClassifySurfaces
command in .geo files); added API support for color options, mesh optimization,
recombination, smoothing and shape healing; exposed additional METIS options;
improved support for periodic entities (multiple curves with the same start/end
points, legacy MSH2 format, periodic surfaces with embedded entities); added
mesh renumbering also after interactive mesh modifications; improved support for
OpenCASCADE ellipse arcs; new interactive filter in visibility window; flatter
GUI; small bug fixes.

* New API functions: option/setColor, option/getColor, mesh/optimize,

mesh/recombine, mesh/smooth, mesh/clear, mesh/getNodesByElementType,
occ/healShapes.

* Incompatible API changes: mesh/getJacobians and mesh/getBasisFunctions now

take integration points explicitly; mesh/setNodes and mesh/setElements have
been replaced by mesh/addNodes and mesh/addElements; added optional arguments
to mesh/classifySurfaces and occ/addSurfaceLoop; changed arguments of
occ/addEllipseArc to follow geo/addEllipseArc.

4.3.0 (April 19, 2019): improved meshing of surfaces with singular

parametrizations; added API support for aliasing and combining views, copying
view options, setting point coordinates, extruding built-in CAD entities along
normals and retrieving mass, center of mass and inertia from OpenCASCADE CAD
entities; fixed regression introduced in 4.1.4 that could lead to
non-deterministic 2D meshes; small bug fixes.

* New API functions: model/setCoordinates, occ/getMass, occ/getCenterOfMass,

occ/getMatrixOfInertia, view/addAlias, view/copyOptions, view/combine
Appendix D: Version history 389

* Incompatible API changes: added optional arguments to mesh/getNodes and

mesh/getElementByCoordinates.

4.2.3 (April 3, 2019): added STL export by physical surface; added ability to
remove embedded entities; added handling of boundary entities in
addDiscreteEntity; small bug fixes.

* New API functions: mesh/getKeysForElements, mesh/getInformationForElements,

mesh/removeEmbedded.

4.2.2 (March 13, 2019): fixed regression in reading of extruded meshes; added
ability to export one solid per surface in STL format.

4.2.1 (March 7, 2019): fixed regression for STEP files without global compound
shape; added support for reading IGES labels and colors; improved search for
shared library in Python and Julia modules; improved Plugin(MeshVolume); updates
to the reference manual.

4.2.0 (March 5, 2019): new MSH4.1 revision of the MSH file format, with support
for size_t node and element tags (see the reference manual for detailed
changes); added support for reading STEP labels and colors with OCC CAF; changed
default "Geometry.OCCTargetUnit" value to none (i.e. use STEP file coordinates
as-is, without conversion); improved high-order mesh optimization; added ability
to import groups of nodes from MED files; enhanced Plugin(Distance) and
Plugin(SimplePartition); removed unmaintained plugins; removed default
dependency on PETSc; small improvements and bug fixes.

* New API functions: model/setEntityName, model/getEntityName,

model/removeEntityName.

* Incompatible API changes: changed type of node and element tags from int to
size_t to support (very) large meshes; changed logger/start,
mesh/getPeriodicNodes and mesh/setElementsByType.

4.1.5 (February 14, 2019): improved OpenMP parallelization, STL remeshing, mesh
partitioning and high-order mesh optimization; bug fixes.

* New API function: mesh/classifySurfces.

4.1.4 (February 3, 2019): improved ghost cell I/O; small improvements and bug
fixes.

* New API functions: mesh/relocateNodes, mesh/getElementType,

mesh/setElementsByType, mesh/getElementEdgeNodes, mesh/getElementFaceNodes,
mesh/getGhostElements, mesh/splitQuadrangles.

4.1.3 (January 23, 2019): improved quad meshing; new options for automatic
full-quad meshes; save nodesets also for physical points (Abaqus, Tochnog);
small bug fixes.

* New API functions: model/removePhysicalName, model/getPartitions,

mesh/unpartition.
390 Gmsh 4.11.1

4.1.2 (January 21, 2019): fixed full-quad subdivision if Mesh.SecondOrderLinear

is set; fixed packing of parallelograms regression in 4.1.1.

4.1.1 (January 20, 2019): added support for general affine transformations with
OpenCASCADE kernel; improved handling of boolean tolerance (snap vertices);
faster crossfield calculation by default (e.g. for Frontal-Delauany for quads
algorithm); fixed face vertices for PyramidN; renamed ONELAB "Action" and
"Button" parameters "ONELAB/Action" and "ONELAB/Button"; added support for
actions on any ONELAB button; added API functions for selections in user
interface.

* New API functions: occ/affineTransform, fltk/selectEntities,

fltk/selectElements, fltk/selectViews.

4.1.0 (January 13, 2019): improved ONELAB and Fltk support in API; improved
renumbering of mesh nodes/elements; major code refactoring.

* New API functions: fltk/update, fltk/awake, fltk/lock, fltk/unlock,

onelab/setNumber, onelab/getNumber, onelab/setString, onelab/getString,
onelab/clear, onelab/write, logger/time, logger/cputime.

* Incompatible API changes: changed onelab/get.

4.0.7 (December 9, 2018): fixed small memory leaks; removed unused code.

4.0.6 (November 25, 2018): moved private API wrappers to utils/wrappers;

improved Gmsh 3 compatibility for high-order periodic meshes; fixed ’-v 0’ not
being completely silent; fixed rendering of image textures on some OSes; small
compilation fixes.

4.0.5 (November 17, 2018): new automatic hybrid mesh generation (pyramid layer)
when 3D Delaunay algorithm is applied to a volume with quadrangles on boundary;
improved robustness of 2D MeshAdapt algorithm; bug fixes.

4.0.4 (October 19, 2018): fixed physical names regression in 4.0.3.

4.0.3 (October 18, 2018): bug fixes.

* New API function: model/removePhysicalGroups.

4.0.2 (September 26, 2018): added support for creating MED files with specific
MED (minor) version; small bug fixes.

4.0.1 (September 7, 2018): renumber mesh nodes/elements by default; new

SendToServer command for nodal views; small bug fixes.

* New API functions: model/setVisibility, model/getVisibility, model/setColor,

model/getColor.

4.0.0 (August 22, 2018): new C++, C, Python and Julia API; new MSH4 format; new
mesh partitioning code based on Metis 5; new 3D tetrahedralization algorithm as
Appendix D: Version history 391

default; new workflow for remeshing (compound entities as meshing constraints,

CreateGeometry for mesh reparametrization); added support for general BSplines,
fillets and chamfers with OpenCASCADE kernel and changed default BSpline
parameters with the built-in kernel to match OpenCASCADE’s; STEP files are now
be default interpreted in MKS units (see Geometry.OCCTargetUnit); improved
meshing of surfaces with singular parametrizations (spheres, etc.); uniformized
entity naming conventions (line/curve, vertex/node, etc.); generalized handling
of "all" entities in geo file (using {:} notation); added support for creating
LSDYNA mesh files; removed old CAD creation factory (GModelFactory), old
reparametrization code (G{Edge, Face, Region}Compound) and old partitioning
code (Metis 4 and Chaco); various cleanups, bug fixes and enhancements.

3.0.6 (November 5, 2017): improved meshing of spheres; improved handling of mesh

size constraints with OpenCASCADE kernel; implemented "Coherence" for
OpenCASCADE kernel (shortcut for BooleanFragments); added GAMBIT Neutral File
export; small improvements and bug fixes.

3.0.5 (September 6, 2017): bug fixes.

3.0.4 (July 28, 2017): moved vorometal code to plugin; OpenMP improvements; bug
fixes.

3.0.3 (June 27, 2017): new element quality measures; Block->Box; minor fixes.

3.0.2 (May 13, 2017): improved handling of meshing constraints and entity
numbering after boolean operations; improved handling of fast coarseness
transitions in MeshAdapt; new TIKZ export; small bug fixes.

3.0.1 (April 14, 2017): fixed OpenCASCADE plane surfaces with holes.

3.0.0 (April 13, 2017): new constructive solid geometry features and boolean
operations using OpenCASCADE; improved graphical user interface for interactive,
parametric geometry construction; new or modified commands in .geo files:
SetFactory, Circle, Ellipse, Wire, Surface, Sphere, Block, Torus, Rectangle,
Disk, Cylinder, Cone, Wedge, ThickSolid, ThruSections, Ruled ThruSections,
Fillet, Extrude, BooleanUnion, BooleanIntersection, BooleanDifference,
BooleanFragments, ShapeFromFile, Recursive Delete, Unique; "Surface" replaces
the deprecated "Ruled Surface" command; faster 3D tetrahedral mesh optimization
enabled by default; major code refactoring and numerous bug fixes.

2.16.0 (January 3, 2017): small improvements (list functions, second order hexes
for MED, GUI) and bug fixes.

2.15.0 (December 4, 2016): fixed several regressions (multi-file partitioned

grid export, mesh subdivision, old compound mesher); improved 2D boundary layer
field & removed non-functional 3D boundary layer field; faster rendering of
large meshes.

2.14.1 (October 30, 2016): fixed regression in periodic meshes; small bug fixes
and code cleanups.

2.14.0 (October 9, 2016): new Tochnog file format export; added ability to
392 Gmsh 4.11.1

remove last command in scripts generated interactively; ONELAB 1.3 with

usability and performance improvements; faster "Coherence Mesh".

2.13.2 (August 18, 2016)): small improvements (scale labels, periodic and
high-order meshes) and bug fixes.

2.13.1 (July 15, 2016): small bug fixes.

2.13.0 (July 11, 2016): new ONELAB 1.2 protocol with native support for lists;
new experimental 3D boundary recovery code and 3D refinement algorithm; better
adaptive visualization of quads and hexahedra; fixed several regressions
introduced in 2.12.

2.12.0 (March 5, 2016): improved interactive definition of physical groups and

handling of ONELAB clients; improved full quad algorithm; added support for list
of strings, trihedra elements and X3D format; improved message console; new
colormaps; various bugs fixes and small improvements all over.

2.11.0 (November 7, 2015): new Else/ElseIf commands; new OptimizeMesh command;

Plugin(ModifyComponents) replaces Plugin(ModifyComponent); new VTK and X3D
outputs; separate 0/Ctrl+0 shortcuts for geometry/full model reload; small bug
fixes in homology solver, handling of embedded entities, and Plugin(Crack).

2.10.1 (July 30, 2015): minor fixes.

2.10.0 (July 21, 2015): improved periodic meshing constraints; new Physical
specification with both label and numeric id; images can now be used as glyphs
in post-processing views, using text annotations with the ‘file://’ prefix;
Views can be grouped and organized in subtrees; improved visibility browser
navigation; geometrical entities and post-processing views can now react to
double-clicks, via new generic DoubleClicked options; new Get/SetNumber and
Get/SetString for direct access to ONELAB variables; small bug fixes and code
cleanups.

2.9.3 (April 18, 2015): updated versions of PETSc/SLEPc and OpenCASCADE/OCE

libraries used in official binary builds; new Find() command; miscellaneous code
cleanups and small fixes.

2.9.2 (March 31, 2015): added support for extrusion of embedded points/curves;
improved hex-dominant algorithm; fixed crashes in quad algorithm; fix regression
in MED reader introduced in 2.9.0; new dark interface mode.

2.9.1 (March 18, 2015): minor bug fixes.

2.9.0 (March 12, 2015): improved robustness of spatial searches (extruded meshes,
geometry coherence); improved reproductibility of 2D and 3D meshes; added
support for high resolution ("retina") graphics; interactive graph point
commands; on-the-fly creation of onelab clients in scripts; general periodic
meshes using afine transforms; scripted selection of entities in bounding boxes;
extended string and list handling functions; many small improvements and bug
fixes.
Appendix D: Version history 393

2.8.5 (Jul 9, 2014): improved stability and error handling, better Coherence
function, updated onelab API version and inline parameter definitions, new
background image modes, more robust Triangulate/Tetrahedralize plugins, new PGF
output, improved support for string~index variable names in parser, small
improvements and bug fixes all over the place.

2.8.4 (Feb 7, 2014): better reproductibility of 2D meshes; new mandatory ’Name’

attribute to define onelab variables in DefineConstant[] & co; new
-setnumber/-setstring command line arguments; small improvements and bug fixes.

2.8.3 (Sep 27, 2013): new quick access menu and multiple view selection in GUI;
enhanced animation creation; many small enhancements and bug fixes.

2.8.2 (Jul 16, 2013): improved high order tools interface; minor bug fixes.

2.8.1 (Jul 11, 2013): improved compound surfaces and transfinite arrangements.

2.8.0 (Jul 8, 2013): improved Delaunay point insertion; fixed mesh orientation
of plane surfaces; fixed mesh size prescribed at embedded points; improved
display of vectors at COG; new experimental text string display engines;
improved fullscreen mode; access time/step in transformations; new experimental
features: AdaptMesh and Surface In Volume; accept unicode file paths on Windows;
compilation and bug fixes.

2.7.1 (May 11, 2013): improved Delaunay point insertion; updated onelab; better
Abaqus and UNV export; small bug and compilation fixes.

2.7.0 (Mar 9, 2013): new single-window GUI, with dynamically customizable

widget tree; faster STEP/BRep import; arbitrary size image export; faster 2D
Delaunay/Frontal algorithms; full option viewer/editor; many bug fixes.

2.6.1 (Jul 15, 2012): minor improvements and bug fixes.

2.6.0 (Jun 19, 2012): new quadrilateral meshing algorithms (Blossom and
Delaunay-Frontal for quads); new solver module based on ONELAB project (requires
FLTK 1.3); new tensor field visualization modes (eigenvectors, ellipsoid, etc.);
added support for interpolation schemes in .msh file; added support for MED3
format; rescale viewport around visible entities (shift+1:1 in GUI); unified
post-processing field export; new experimental stereo+camera visualization mode;
added experimental BAMG & Mmg3D support for anisotropic mesh generation; new OCC
cut & merge algorithm imported from Salome; new ability to connect extruded
meshes to tetrahedral grids using pyramids; new homology solver; Abaqus (INP)
mesh export; new Python and Java wrappers; bug fixes and small improvements all
over the place.

2.5.0 (Oct 15, 2010): new compound geometrical entities (for remeshing and/or
trans-patch meshing); improved mesh reclassification tool; new client/server
visualization mode; new ability to watch a pattern of files to merge; new
integrated MPEG export; new option to force the type of views dynamically;
bumped mesh version format to 2.2 (small change in the meaning of the partition
tags; this only affects partitioned (i.e. parallel) meshes); renamed several
post-processing plugins (as well as plugin options) to make them easier to
394 Gmsh 4.11.1

understand; many bug fixes and usability improvements all over the place.

2.4.2 (Sep 21, 2009): solver code refactoring + better IDE integration.

2.4.1 (Sep 1, 2009): fixed surface mesh orientation bug introduced in 2.4.0;
mesh and graphics code refactoring, small usability enhancements and bug fixes.

2.4.0 (Aug 22, 2009): switched build system to CMake; optionally copy
transfinite mesh constraints during geometry transformations; bumped mesh
version format to 2.1 (small change in the $PhysicalNames section, where the
group dimension is now required); ported most plugins to the new
post-processing API; switched from MathEval to MathEx and Flu_Tree_Browser to
Fl_Tree; small bug fixes and improvements all over the place.

2.3.1 (Mar 18, 2009): removed GSL dependency (Gmsh now simply uses Blas and
Lapack); new per-window visibility; added support for composite window printing
and background images; fixed string option affectation in parser; fixed surface
mesh orientation for OpenCASCADE models; fixed random triangle orientations in
Delaunay and Frontal algorithms.

2.3.0 (Jan 23, 2009): major graphics and GUI code refactoring; new
full-quad/hexa subdivision algorithm; improved automatic transfinite corner
selection (now also for volumes); improved visibility browser; new automatic
adaptive visualization for high-order simplices; modified arrow size, clipping
planes and transform options; many improvements and bug fixes all over the
place.

2.2.6 (Nov 21, 2008): better transfinite smoothing and automatic corner
selection; fixed high order meshing crashes on Windows and Linux; new uniform
mesh refinement (thanks Brian!); fixed various other small bugs.

2.2.5 (Oct 25, 2008): Gmsh now requires FLTK 1.1.7 or above; various small
improvements (STL and VTK mesh I/O, Netgen upgrade, Visual C++ support, Fields,
Mesh.{Msh,Stl,...}Binary changed to Mesh.Binary) and bug fixes (pyramid
interpolation, Chaco crashes).

2.2.4 (Aug 14, 2008): integrated Metis and Chaco mesh partitioners; variables
can now be deleted in geo files; added support for point datasets in model-based
postprocessing views; small bug fixes.

2.2.3 (Jul 14, 2008): enhanced clipping interface; API cleanup; fixed various
bugs (Plugin(Integrate), high order meshes, surface info crash).

2.2.2 (Jun 20, 2008): added geometrical transformations on volumes; fixed bug in
high order mesh generation.

2.2.1 (Jun 15, 2008): various small improvements (adaptive views, GUI, code
cleanup) and bug fixes (high order meshes, Netgen interface).

2.2.0 (Apr 19, 2008): new model-based post-processing backend; added MED I/O for
mesh and post-processing; fixed BDF vertex ordering for 2nd order elements;
replaced Mesh.ConstrainedBackgroundMesh with
Appendix D: Version history 395

Mesh.CharacteristicLength{FromPoints,ExtendFromBoundary}; new Fields interface;

control windows are now non-modal by default; new experimental 2D frontal
algorithm; fixed various bugs.

2.1.1 (Mar 1, 2008): small bug fixes (second order meshes, combine views, divide
and conquer crash, ...).

2.1.0 (Feb 23, 2008): new post-processing database; complete rewrite of

post-processing drawing code; improved surface mesh algorithms; improved
STEP/IGES/BREP support; new 3D mesh optimization algorithm; new default native
file choosers; fixed ’could not find extruded vertex’ in extrusions; many
improvements and bug fixes all over the place.

2.0.8 (Jul 13, 2007): unused vertices are not saved in mesh files anymore; new
plugin GUI; automatic GUI font size selection; renamed
Plugin(DecomposeInSimplex) into Plugin(MakeSimplex); reintroduced enhanced
Plugin(SphericalRaise); clarified meshing algo names; new option to save groups
of nodes in UNV meshes; new background mesh infrastructure; many small
improvements and small bug fixes.

2.0.7 (Apr 3, 2007): volumes can now be defined from external CAD surfaces;
Delaunay/Tetgen algorithm is now used by default when available; re-added
support for Plot3D structured mesh format; added ability to export external CAD
models as GEO files (this only works for the limited set of geometrical
primitives available in the GEO language, of course--so trying to convert e.g. a
trimmed NURBS from a STEP file into a GEO file will fail); "lateral" entities
are now added at the end of the list returned by extrusion commands; fixed
various bugs.

2.0.0 (Feb 5, 2007): new geometry and mesh databases, with support for STEP and
IGES import via OpenCASCADE; complete rewrite of geometry and mesh drawing
code; complete rewrite of mesh I/O layer (with new native binary MSH format and
support for import/export of I-deas UNV, Nastran BDF, STL, Medit MESH and VRML
1.0 files); added support for incomplete second order elements; new 2D and 3D
meshing algorithms; improved integration of Netgen and TetGen algorithms;
removed anisotropic meshing algorithm (as well as attractors); removed explicit
region number specification in extrusions; option changes in the graphical
interface are now applied instantaneously; added support for offscreen rendering
using OSMesa; added support for SVG output; added string labels for Physical
entities; lots of other improvements all over the place.

1.65 (May 15, 2006): new Plugin(ExtractEdges); fixed compilation errors with
gcc4.1; replaced Plugin(DisplacementRaise) and Plugin(SphericalRaise) with the
more flexible Plugin(Warp); better handling of discrete curves; new Status
command in parser; added option to renumber nodes in .msh files (to avoid holes
in the numbering sequence); fixed 2 special cases in quad->prism extrusion;
fixed saving of 2nd order hexas with negative volume; small bug fixes and
cleanups.

1.64 (Mar 18, 2006): Windows versions do no depend on Cygwin anymore; various
bug fixes and cleanups.
396 Gmsh 4.11.1

1.63 (Feb 01, 2006): post-processing views can now be exported as meshes;
improved background mesh handling (a lot faster, and more accurate); improved
support for input images; new Plugin(ExtractElements); small bug fixes and
enhancements.

1.62 (Jan 15, 2006): new option to draw color gradients in the background;
enhanced perspective projection mode; new "lasso" selection mode (same as
"lasso" zoom, but in selection mode); new "invert selection" button in the
visibility browser; new snapping grid when adding points in the GUI; nicer
normal smoothing; new extrude syntax (old syntax still available, but
deprecated); various small bug fixes and enhancements.

1.61 (Nov 29, 2005): added support for second order (curved) elements in
post-processor; new version (1.4) of post-processing file formats; new stippling
options for 2D plots; removed limit on allowed number of files on command line;
all "Combine" operations are now available in the parser; changed
View.ArrowLocation into View.GlyphLocation; optimized memory usage when loading
many (>1000) views; optimized loading and drawing of line meshes and 2D iso
views; optimized handling of meshes with large number of physical entities;
optimized vertex array creation for large post-processing views on
Windows/Cygwin; removed Discrete Line and Discrete Surface commands (the same
functionality can now be obtained by simply loading a mesh in .msh format);
fixed coloring by mesh partition; added option to light wireframe meshes and
views; new "mesh statistics" export format; new full-quad recombine option; new
Plugin(ModulusPhase); hexas and prisms are now always saved with positive
volume; improved interactive entity selection; new experimental Tetgen
integration; new experimental STL remeshing algorithm; various small bug fixes
and improvements.

1.60 (Mar 15, 2005): added support for discrete curves; new Window menu on Mac
OS X; generalized all octree-based plugins (CutGrid, StreamLines, Probe, etc.)
to handle all element types (and not only scalar and vector
triangles+tetrahedra); generalized Plugin(Evaluate), Plugin(Extract) and
Plugin(Annotate); enhanced clipping plane interface; new grid/axes/rulers for 3D
post-processing views (renamed the AbscissaName, NbAbscissa and AbscissaFormat
options to more general names in the process); better automatic positioning of
2D graphs; new manipulator dialog to specify rotations, translations and
scalings "by hand"; various small enhancements and bug fixes.

1.59 (Feb 06, 2005): added support for discrete (triangulated) surfaces, either
in STL format or with the new "Discrete Surface" command; added STL and Text
output format for post-processing views and STL output format for surface
meshes; all levelset-based plugins can now also compute isovolumes; generalized
Plugin(Evaluate) to handle external view data (based on the same or on a
different mesh); generalized Plugin(CutGrid); new plugins (Eigenvalues,
Gradient, Curl, Divergence); changed default colormap to match Matlab’s "Jet"
colormap; new transformation matrix option for views (for non-destructive
rotations, symmetries, etc.); improved solver interface to keep the GUI
responsive during solver calls; new C++ and Python solver examples; simplified
Tools->Visibility GUI; transfinite lines with "Progression" now allow negative
line numbers to reverse the progression; added ability to retrieve Gmsh’s
version number in the parser (to help write backward compatible scripts); fixed
Appendix D: Version history 397

white space in unv mesh output; fixed various small bugs.

1.58 (Jan 01, 2005): fixed UNIX socket interface on Windows (broken by the TCP
solver patch in 1.57); bumped version number of default post-processing file
formats to 1.3 (the only small modification is the handling of the end-of-string
character for text2d and text3d objects in the ASCII format); new File->Rename
menu; new colormaps+improved colormap handling; new color+min/max options in
views; new GetValue() function to ask for values interactively in scripts;
generalized For/EndFor loops in parser; new plugins (Annotate, Remove, Probe);
new text attributes in views; renamed some shortcuts; fixed TeX output for large
scenes; new option dialogs for various output formats; fixed many small memory
leaks in parser; many small enhancements to polish the graphics and the user
interface.

1.57 (Dec 23, 2004): generalized displacement maps to display arbitrary view
types; the arrows representing a vector field can now also be colored by the
values from other scalar, vector or tensor fields; new adaptive high order
visualization mode; new options (Solver.SocketCommand, Solver.NameCommand,
View.ArrowSizeProportional, View.Normals, View.Tangents and General.ClipFactor);
fixed display of undesired solver plugin popups; enhanced interactive plugin
behavior; new plugins (HarmonicToTime, Integrate, Eigenvectors); tetrahedral
mesh file reading speedup (50% faster on large meshes); large memory footprint
reduction (up to 50%) for the visualization of triangular/tetrahedral meshes;
the solver interface now supports TCP/IP connections; new generalized raise mode
(allows one to use complex expressions to offset post-processing maps); upgraded
Netgen kernel to version 4.4; new optional TIME list in parsed views to specify
the values of the time steps; several bug fixes in the Elliptic mesh algorithm;
various other small bug fixes and enhancements.

1.56 (Oct 17, 2004): new post-processing option to draw a scalar view raised by
a displacement view without using Plugin(DisplacementRaise) (makes drawing
arbitrary scalar fields on deformed meshes much easier); better post-processing
menu (arbitrary number of views+scrollable+show view number); improved
view->combine; new horizontal post-processing scales; new option to draw the
mesh nodes per element; views can now also be saved in "parsed" format; fixed
various path problems on Windows; small bug fixes.

1.55 (Aug 21, 2004): added background mesh support for Triangle; meshes can now
be displayed using "smoothed" normals (like post-processing views); added GUI
for clipping planes; new interactive clipping/cutting plane definition;
reorganized the Options GUI; enhanced 3D iso computation; enhanced lighting;
many small bug fixes.

1.54 (Jul 03, 2004): integrated Netgen (3D mesh quality optimization +
alternative 3D algorithm); Extrude Surface now always automatically creates a
new volume (in the same way Extrude Point or Extrude Line create new lines and
surfaces, respectively); fixed UNV output; made the "Layers" region numbering
consistent between lines, surfaces and volumes; fixed home directory problem on
Win98; new Plugin(CutParametric); the default project file is now created in the
home directory if no current directory is defined (e.g., when double-clicking on
the icon on Windows/Mac); fixed the discrepancy between the orientation of
geometrical surfaces and the associated surface meshes; added automatic
398 Gmsh 4.11.1

orientation of surfaces in surface loops; generalized Plugin(Triangulate) to

handle vector and tensor views; much nicer display of discrete iso-surfaces and
custom ranges using smooth normals; small bug fixes and cleanups.

1.53 (Jun 04, 2004): completed support for second order elements in the mesh
module (line, triangles, quadrangles, tetrahedra, hexahedra, prisms and
pyramids); various background mesh fixes and enhancements; major performance
improvements in mesh and post-processing drawing routines (OpenGL vertex arrays
for tri/quads); new Plugin(Evaluate) to evaluate arbitrary expressions on
post-processing views; generalized Plugin(Extract) to handle any combination of
components; generalized "Coherence" to handle transfinite surface/volume
attributes; plugin options can now be set in the option file (like all other
options); added "undo" capability during geometry creation; rewrote the contour
guessing routines so that entities can be selected in an arbitrary order; Mac
users can now double click on geo/msh/pos files in the Finder to launch Gmsh;
removed support for FLTK 1.0; rewrote most of the code related to quadrangles;
fixed 2d elliptic algorithm; removed all OpenGL display list code and options;
fixed light positioning; new BoundingBox command to set the bounding box
explicitly; added support for inexpensive "fake" transparency mode; many code
cleanups.

1.52 (May 06, 2004): new raster ("bitmap") PostScript/EPS/PDF output formats;
new Plugin(Extract) to extract a given component from a post-processing view;
new Plugin(CutGrid) and Plugin(StreamLines); improved mesh projection on
non-planar surfaces; added support for second order tetrahedral elements; added
interactive control of element order; refined mesh entity drawing selection (and
renamed most of the corresponding options); enhanced log scale in
post-processing; better font selection; simplified View.Raise{X,Y,Z} by removing
the scaling; various bug fixes (default postscript printing mode, drawing of 3D
arrows/cylinders on Linux, default home directory on Windows, default initial
file browser directory, extrusion of points with non-normalized axes of
rotation, computation of the scene bounding box in scripts, + the usual
documentation updates).

1.51 (Feb 29, 2004): initial support for visualizing mesh partitions; integrated
version 2.0 of the MSH mesh file format; new option to compute post-processing
ranges (min/max) per time step; Multiple views can now be combined into multi
time step ones (e.g. for programs that generate data one time step at a time);
new syntax: #var[] returns the size of the list var[]; enhanced "gmsh -convert";
temporary and error files are now created in the home directory to avoid file
permission issues; new 3D arrows; better lighting support; STL facets can now be
converted into individual geometrical surfaces; many other small improvements
and bug fixes (multi timestep tensors, color by physical entity, parser cleanup,
etc.).

1.50 (Dec 06, 2003): small changes to the visibility browser + made visibility
scriptable (new Show/Hide commands); fixed (rare) crash when deleting views;
split File->Open into File->Open and File->New to behave like most other
programs; Mac versions now use the system menu bar by default (if possible);
fixed bug leading to degenerate and/or duplicate tetrahedra in extruded meshes;
fixed crash when reloading sms meshes.
Appendix D: Version history 399

1.49 (Nov 30, 2003): made Merge, Save and Print behave like Include (i.e., open
files in the same directory as the main project file if the path is relative);
new Plugin(DecomposeInSimplex); new option View.AlphaChannel to set the
transparency factor globally for a post-processing view; new "Combine Views"
command; various bug fixes and cleanups.

1.48 (Nov 23, 2003): new DisplacementRaise plugin to plot arbitrary fields on
deformed meshes; generalized CutMap, CutPlane, CutSphere and Skin plugins to
handle all kinds of elements and fields; new "Save View[n]" command to save
views from a script; many small bug fixes (configure tests for libpng, handling
of erroneous options, multi time step scalar prism drawings, copy of surface
mesh attributes, etc.).

1.47 (Nov 12, 2003): fixed extrusion of surfaces defined by only two curves; new
syntax to retrieve point coordinates and indices of entities created through
geometrical transformations; new PDF and compressed PostScript output formats;
fixed numbering of elements created with "Extrude Point/Line"; use $GMSH_HOME as
home directory if defined.

1.46 (Aug 23, 2003): fixed crash for very long command lines; new options for
setting the displacement factor and Triangle’s parameters + renamed a couple of
options to more sensible names (View.VectorType, View.ArrowSize); various small
bug fixes; documentation update.

1.45 (Jun 14, 2003): small bug fixes (min/max computation for tensor views,
missing physical points in read mesh, "jumping" geometry during interactive
manipulation of large models, etc.); variable definition speedup; restored
support for second order elements in one- and two-dimensional meshes;
documentation updates.

1.44 (Apr 21, 2003): new reference manual; added support for PNG output; fixed
small configure script bugs.

1.43 (Mar 28, 2003): fixed solver interface problem on Mac OS X; new option to
specify the interactive rotation center (default is now the pseudo "center of
gravity" of the object, instead of (0,0,0)).

1.42 (Mar 19, 2003): suppressed the automatic addition of a ".geo" extension if
the file given on the command line is not recognized; added missing Layer option
for Extrude Point; fixed various small bugs.

1.41 (Mar 04, 2003): Gmsh is now licensed under the GNU General Public License;
general code cleanup (indent).

1.40 (Feb 26, 2003): various small bug fixes (mainly GSL-related).

1.39 (Feb 23, 2003): removed all non-free routines; more build system work;
implemented Von-Mises tensor display for all element types; fixed small GUI
bugs.

1.38 (Feb 17, 2003): fixed custom range selection for 3D iso graphs; new build
system based on autoconf; new image reading code to import bitmaps as
400 Gmsh 4.11.1

post-processing views.

1.37 (Jan 25, 2003): generalized smoothing and cuts of post-processing views;
better Windows integration (solvers, external editors, etc.); small bug fixes.

1.36 (Nov 20, 2002): enhanced view duplication (one can now use "Duplicata
View[num]" in the input file); merged all option dialogs in a new general option
window; enhanced discoverability of the view option menus; new 3D point and line
display; many small bug fixes and enhancements ("Print" format in parser,
post-processing statistics, smooth normals, save window positions, restore
default options, etc.).

1.35 (Sep 11, 2002): graphical user interface upgraded to FLTK 1.1 (tooltips,
new file chooser with multiple selection, full keyboard navigation, cut/paste of
messages, etc.); colors can be now be directly assigned to mesh entities;
initial tensor visualization; new keyboard animation (right/left arrow for time
steps; up/down arrow for view cycling); new VRML output format for surface
meshes; new plugin for spherical elevation plots; new post-processing file
format (version 1.2) supporting quadrangles, hexahedra, prisms and pyramids;
transparency is now enabled by default for post-processing plots; many small bug
fixes (read mesh, ...).

1.34 (Feb 18, 2002): improved surface mesh of non-plane surfaces; fixed
orientation of elements in 2D anisotropic algorithm; minor user interface polish
and additions (mostly in post-processing options); various small bug fixes.

1.33 (Jan 24, 2002): new parameterizable solver interface (allowing up to 5

user-defined solvers); enhanced 2D aniso algorithm; 3D initial mesh speedup.

1.32 (Oct 04, 2001): new visibility browser; better floating point exception
checks; fixed infinite looping when merging meshes in project files; various
small clean ups (degenerate 2D extrusion, view->reload, ...).

1.31 (Nov 30, 2001): corrected ellipses; PostScript output update (better
shading, new combined PS/LaTeX output format); more interface polish; fixed
extra memory allocation in 2D meshes; Physical Volume handling in unv format;
various small fixes.

1.30 (Nov 16, 2001): interface polish; fix crash when extruding quadrangles.

1.29 (Nov 12, 2001): translations and rotations can now be combined in
extrusions; fixed coherence bug in Extrude Line; various small bug fixes and
additions.

1.28 (Oct 30, 2001): corrected the ’Using Progression’ attribute for tranfinite
meshes to actually match a real geometric progression; new Triangulate plugin;
new 2D graphs (space+time charts); better performance of geometrical
transformations (warning: the numbering of some automatically created entities
has changed); new text primitives in post-processing views (file format updated
to version 1.1); more robust mean plane computation and error checks; various
other small additions and clean-ups.
Appendix D: Version history 401

1.27 (Oct 05, 2001): added ability to extrude curves with Layers/Recombine
attributes; new PointSize/LineWidth options; fixed For/EndFor loops in included
files; fixed error messages (line numbers+file names) in loops and functions;
made the automatic removal of duplicate geometrical entities optional
(Geometry.AutoCoherence=0); various other small bug fixes and clean-ups.

1.26 (Sep 06, 2001): enhanced 2D anisotropic mesh generator (metric

intersections); fixed small bug in 3D initial mesh; added alternative syntax for
built-in functions (for GetDP compatibility); added line element display; Gmsh
now saves all the elements in the mesh if no physical groups are defined (or if
Mesh.SaveAll=1).

1.25 (Sep 01, 2001): fixed bug with mixed recombined/non-recombined extruded
meshes; Linux versions are now build with no optimization, due to bugs in gcc
2.95.X.

1.24 (Aug 30, 2001): fixed characteristic length interpolation for Splines;
fixed edge swapping bug in 3D initial mesh; fixed degenerated case in
geometrical extrusion (ruled surface with 3 borders); fixed generation of
degenerated hexahedra and prisms for recombined+extruded meshes; added BSplines
creation in the GUI; integrated Jonathan Shewchuk’s Triangle as an alternative
isotropic 2D mesh generator; added AngleSmoothNormals to control sharp edge
display with smoothed normals; fixed random crash for lighted 3D iso surfaces.

1.23 (Aug, 2001): fixed duplicate elements generation + non-matching tetrahedra

faces in 3D extruded meshes; better display of displacement maps; fixed
interactive ellipsis construction; generalized boundary operator; added new
explode option for post-processing views; enhanced link view behavior (to update
only the changed items); added new default plugins: Skin, Transform, Smooth;
fixed various other small bugs (mostly in the post-processing module and for
extruded meshes).

1.22 (Aug 03, 2001): fixed (yet another) bug for 2D mesh in the mean plane;
fixed surface coherence bug in extruded meshes; new double logarithmic scale,
saturate value and smoothed normals option for post-processing views; plugins
are now enabled by default; three new experimental statically linked plugins:
CutMap (extracts a given iso surface from a 3D scalar map), CutPlane (cuts a 3D
scalar map with a plane section), CutSphere (cuts a 3D scalar map with a
sphere); various other bug fixes, additions and clean-ups.

1.21 (Jul 25, 2001): fixed more memory leaks; added -opt command line option to
parse definitions directly from the command line; fixed missing screen refreshes
during contour/surface/volume selection; enhanced string manipulation functions
(Sprintf, StrCat, StrPrefix); many other small fixes and clean-ups.

1.20 (Jun 14, 2001): fixed various bugs (memory leaks, functions in included
files, solver command selection, ColorTable option, duplicate nodes in extruded
meshes (not finished yet), infinite loop on empty views, orientation of
recombined quadrangles, ...); reorganized the interface menus; added constrained
background mesh and mesh visibility options; added mesh quality histograms;
changed default mesh colors; reintegrated the old command-line extrusion mesh
generator.
402 Gmsh 4.11.1

1.19 (May 07, 2001): fixed seg. fault for scalar simplex post-processing; new
Solver menu; interface for GetDP solver through sockets; fixed multiple scale
alignment; added some options + full option descriptions.

1.18 (Apr 26, 2001): fixed many small bugs and incoherences in post-processing;
fixed broken background mesh in 1D mesh generation.

1.17 (Apr 17, 2001): corrected physical points saving; fixed parsing of DOS
files (carriage return problems); easier geometrical selections (cursor change);
plugin manager; enhanced variable arrays (sublist selection and affectation);
line loop check; New arrow display; reduced number of ’fatal’ errors + better
handling in interactive mode; fixed bug when opening meshes; enhanced File->Open
behavior for meshes and post-processing views.

1.16 (Feb 26, 2001): added single/double buffer selection (only useful for Unix
versions of Gmsh run from remote hosts without GLX); fixed a bug for recent
versions of the opengl32.dll on Windows, which caused OpenGL fonts not to show
up.

1.15 (Feb 23, 2001): added automatic visibility setting during entity selection;
corrected geometrical extrusion bug.

1.14 (Feb 17, 2001): corrected a few bugs in the GUI (most of them were
introduced in 1.13); added interactive color selection; made the option database
bidirectional (i.e. scripts now correctly update the GUI); default options can
now be saved and automatically reloaded at startup; made some changes to the
scripting syntax (PostProcessing.View[n] becomes View[n]; Offset0 becomes
OffsetX, etc.); corrected the handling of simple triangular surfaces with large
characteristic lengths in the 2D isotropic algorithm; added an ASCII to binary
post-processing view converter.

1.13 (Feb 09, 2001): added support for JPEG output on Windows.

1.12: corrected vector lines in the post-processing parsed format; corrected

animation on Windows; corrected file creation in scripts on Windows; direct
affectation of variable arrays.

1.11 (Feb 07, 2001): corrected included file loading problem.

1.10 (Feb 04, 2001): switched from Motif to FLTK for the GUI. Many small tweaks.

1.00 (Jan 15, 2001): added PPM and YUV output; corrected nested If/Endif;
Corrected several bugs for pixel output and enhanced GIF output (dithering,
transparency); slightly changed the post-processing file format to allow both
single and double precision numbers.

0.999 (Dec 20, 2000): added JPEG output and easy MPEG generation (see t8.geo in
the tutorial); clean up of export functions; small fixes; Linux versions are now
compiled with gcc 2.95.2, which should fix the problems encountered with
Mandrake 7.2.
Appendix D: Version history 403

0.998 (Dec 19, 2000): corrected bug introduced in 0.997 in the generation of the
initial 3D mesh.

0.997 (Dec 14, 2000): corrected bug in interactive surface/volume selection;

Added interactive symmetry; corrected geometrical extrusion with rotation in
degenerated or partially degenerated cases; corrected bug in 2D mesh when
meshing in the mean plane.

0.996: arrays of variables; enhanced Printf and Sprintf; Simplified options

(suppression of option arrays).

0.995 (Dec 11, 2000): totally rewritten geometrical database (performance has
been drastically improved for all geometrical transformations, and most notably
for extrusion). As a consequence, the internal numbering of geometrical entities
has changed: this will cause incompatibilities with old .geo files, and will
require a partial rewrite of your old .geo files if these files made use of
geometrical transformations. The syntax of the .geo file has also been
clarified. Many additions for scripting purposes. New extrusion mesh
generator. Preliminary version of the coupling between extruded and Delaunay
meshes. New option and procedural database. All interactive operations can be
scripted in the input files. See the last example in the tutorial for an
example. Many stability enhancements in the 2D and 3D mesh
algorithms. Performance boost of the 3D algorithm. Gmsh is still slow, but the
performance becomes acceptable. An average 1000 tetrahedra/second is obtained on
a 600Mhz computer for a mesh of one million tetrahedra. New anisotropic 2D mesh
algorithm. New (ASCII and binary) post-processing file format and clarified mesh
file format. New handling for interactive rotations (trackball mode). New
didactic interactive mesh construction (watch the Delaunay algorithm in real
time on complex geometries: that’s exciting ;-). And many, many bug fixes and
cleanups.

0.992 (Nov 13, 2000): corrected recombined extrusion; corrected ellipses; added
simple automatic animation of post-processing maps; fixed various bugs.

0.991 (Oct 24, 2000): fixed a serious allocation bug in 2D algorithm, which
caused random crashes. All users should upgrade to 0.991.

0.990: bug fix in non-recombined 3D transfinite meshes.

0.989 (Sep 01, 2000): added ability to reload previously saved meshes; some new
command line options; reorganization of the scale menu; GIF output.

0.987: fixed bug with smoothing (leading to the possible generation of erroneous
3d meshes); corrected bug for mixed 3D meshes; moved the ’toggle view link’
option to Opt->Postprocessing_Options.

0.986: fixed overlay problems; SGI version should now also run on 32 bits
machines; fixed small 3d mesh bug.

0.985: corrected colormap bug on HP, SUN, SGI and IBM versions; corrected small
initialization bug in postscript output.
404 Gmsh 4.11.1

0.984: corrected bug in display lists; added some options in Opt->General.

0.983: corrected some seg. faults in interactive mode; corrected bug in

rotations; changed default window sizes for better match with 1024x768 screens
(default X resources can be changed: see ex03.geo).

0.982: lighting for mesh and post-processing; corrected 2nd order mesh on non
plane surfaces; added example 13.
Appendix E: Copyright and credits 405

Appendix E Copyright and credits

Gmsh is copyright (C) 1997-2022

Christophe Geuzaine
<cgeuzaine at uliege.be>

and

Jean-Francois Remacle
<jean-francois.remacle at uclouvain.be>

Code contributions to Gmsh have been provided by David Colignon (colormaps),

Emilie Marchandise (old compound geometrical entities), Gaetan Bricteux (Gauss
integration and levelsets), Jacques Lechelle (DIFFPACK export), Jonathan
Lambrechts (mesh size fields, solver, Python wrappers), Jozef Vesely (old Tetgen
integration), Koen Hillewaert (high order elements, generalized periodic
meshes), Laurent Stainier (eigenvalue solvers, tensor display and help with
macOS port), Marc Ume (original list and tree code), Mark van Doesburg (old
OpenCASCADE face connection), Matt Gundry (Plot3d export), Matti Pellikka (cell
complex and homology solver), Nicolas Tardieu (help with Netgen integration),
Pascale Noyret (MED mesh IO), Pierre Badel (root finding and minimization), Ruth
Sabariego (pyramids), Stephen Guzik (old CGNS IO, old partitioning code),
Bastien Gorissen (parallel remote post-processing), Eric Bechet (solver), Gilles
Marckmann (camera and stero mode, X3D export), Ashish Negi (Netgen CAD healing),
Trevor Strickler (hybrid structured mesh coupling with pyramids), Amaury Johnen
(Bezier code, high-order element validity), Benjamin Ruard (old Java wrappers),
Maxime Graulich (iOS/Android port), Francois Henrotte (ONELAB metamodels),
Sebastian Eiser (PGF export), Alexis Salzman (compressed IO), Hang Si (TetGen/BR
boundary recovery code), Fernando Lorenzo (Tochnog export), Larry Price (Gambit
export), Anthony Royer (new partitioning code, MSH4 IO), Darcy Beurle (code
cleanup and performance improvements), Celestin Marot (HXT/tetMesh),
Pierre-Alexandre Beaufort (HXT/reparam), Zhidong Han (LSDYNA export), Ismail
Badia (hierarchical basis functions), Jeremy Theler (X3D export), Thomas
Toulorge (high order mesh optimizer, new CGNS IO), Max Orok (binary PLY), Marek
Wojciechowski (PyPi packaging), Maxence Reberol (automatic transfinite, quad
meshing tools), Michael Ermakov (Gambit export, Fortran API, TransfiniteTri),
Alex Krasner (X3D export), Giannis Nikiteas (Fortran API), Paul Sharp (Radioss
export). See comments in the sources for more information. If we forgot to list
your contributions please send us an email!

Thanks to the following folks who have contributed by providing fresh ideas on
theoretical or programming topics, who have sent patches, requests for changes
or improvements, or who gave us access to exotic machines for testing Gmsh: Juan
Abanto, Olivier Adam, Guillaume Alleon, Laurent Champaney, Pascal Dupuis,
Patrick Dular, Philippe Geuzaine, Johan Gyselinck, Francois Henrotte, Benoit
Meys, Nicolas Moes, Osamu Nakamura, Chad Schmutzer, Jean-Luc Fl’ejou, Xavier
Dardenne, Christophe Prud’homme, Sebastien Clerc, Jose Miguel Pasini, Philippe
Lussou, Jacques Kools, Bayram Yenikaya, Peter Hornby, Krishna Mohan Gundu,
Christopher Stott, Timmy Schumacher, Carl Osterwisch, Bruno Frackowiak, Philip
Kelleners, Romuald Conty, Renaud Sizaire, Michel Benhamou, Tom De Vuyst, Kris
Van den Abeele, Simon Vun, Simon Corbin, Thomas De-Soza, Marcus Drosson, Antoine
406 Gmsh 4.11.1

Dechaume, Jose Paulo Moitinho de Almeida, Thomas Pinchard, Corrado Chisari, Axel
Hackbarth, Peter Wainwright, Jiri Hnidek, Thierry Thomas, Konstantinos Poulios,
Laurent Van Miegroet, Shahrokh Ghavamian, Geordie McBain, Jose Paulo Moitinho de
Almeida, Guillaume Demesy, Wendy Merks-Swolfs, Cosmin Stefan Deaconu, Nigel
Nunn, Serban Georgescu, Julien Troufflard, Michele Mocciola, Matthijs Sypkens
Smit, Sauli Ruuska, Romain Boman, Fredrik Ekre, Mark Burton, Max Orok, Paul
Cristini, Isuru Fernando, Jose Paulo Moitinho de Almeida, Sophie Le Bras,
Alberto Escrig, Samy Mukadi, Peter Johnston, Bruno de Sousa Alves, Stefan
Bruens, Luca Verzeroli, Tristan Seidlhofer, Ding Jiaming, Joost Gevaert, Marcus
Calhoun-Lopez, Michel Zou, Sir Sunsheep, Mariano Forti, Walter Steffe, Nico
Schloemer, Simon Tournier, Alexandru Dadalau, Thomas Ulrich, Matthias Diener,
Jamie Border; Kenneth Jansen.

Special thanks to Bill Spitzak, Michael Sweet, Matthias Melcher, Greg Ercolano
and others for the Fast Light Tool Kit on which Gmsh’s GUI is based. See
http://www.fltk.org for more info on this excellent object-oriented,
cross-platform toolkit. Special thanks also to EDF for funding the original
OpenCASCADE and MED integration in 2006-2007. Gmsh development was also
financially supported by the PRACE project funded in part by the EU’s Horizon
2020 Research and Innovation programme (2014-2020) under grant agreement 823767.

The TetGen/BR code (src/mesh/tetgenBR.{cpp,h}) is copyright (c) 2016 Hang Si,

Weierstrass Institute for Applied Analysis and Stochatics. It is relicensed
under the terms of LICENSE.txt for use in Gmsh thanks to a Software License
Agreement between Weierstrass Institute for Applied Analysis and Stochastics and
GMESH SPRL.

The AVL tree code (src/common/avl.{cpp,h}) and the YUV image code
(src/graphics/gl2yuv.{cpp,h}) are copyright (C) 1988-1993, 1995 The Regents of
the University of California. Permission to use, copy, modify, and distribute
this software and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in supporting
documentation, and that the name of the University of California not be used in
advertising or publicity pertaining to distribution of the software without
specific, written prior permission. The University of California makes no
representations about the suitability of this software for any purpose. It is
provided "as is" without express or implied warranty.

The picojson code (src/common/picojson.h) is Copyright 2009-2010 Cybozu Labs,

Inc., Copyright 2011-2014 Kazuho Oku, All rights reserved. Redistribution and
use in source and binary forms, with or without modification, are permitted
provided that the following conditions are met: 1. Redistributions of source
code must retain the above copyright notice, this list of conditions and the
following disclaimer. 2. Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution. THIS
SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
Appendix E: Copyright and credits 407

(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;

LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The nanoflann code (src/numeric/nanoflann.hpp) is Copyright 2008-2009 Marius

Muja, 2008-2009 David G. Lowe, 2011-2016 Jose Luis Blanco. Redistribution and
use in source and binary forms, with or without modification, are permitted
provided that the following conditions are met: 1. Redistributions of source
code must retain the above copyright notice, this list of conditions and the
following disclaimer. 2. Redistributions in binary form must reproduce the
above copyright notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the distribution. THIS
SOFTWARE IS PROVIDED BY THE AUTHOR ‘‘AS IS’’ AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT
OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE.

The trackball code (src/graphics/Trackball.{cpp.h}) is copyright (C) 1993, 1994,

Silicon Graphics, Inc. ALL RIGHTS RESERVED. Permission to use, copy, modify, and
distribute this software for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that both the
copyright notice and this permission notice appear in supporting documentation,
and that the name of Silicon Graphics, Inc. not be used in advertising or
publicity pertaining to distribution of the software without specific, written
prior permission.

The GIF and PPM routines (src/graphics/gl2gif.cpp) are based on code copyright
(C) 1989, 1991, Jef Poskanzer. Permission to use, copy, modify, and distribute
this software and its documentation for any purpose and without fee is hereby
granted, provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in supporting
documentation. This software is provided "as is" without express or implied
warranty.

The colorbar widget (src/fltk/colorbarWindow.cpp) was inspired by code from the

Vis5d program for visualizing five dimensional gridded data sets, copyright (C)
1990-1995, Bill Hibbard, Brian Paul, Dave Santek, and Andre Battaiola.

The libOL code (src/common/libol1.{c,h}) is Copyright 2012-2018 - by Loc

Marchal / INRIA. This program is a free software. You can redistribute it
and/or modify it under the terms of the MIT License as published by the Open
Source Initiative.

The Fast & memory efficient hashtable based on robin hood hashing
408 Gmsh 4.11.1

(src/common/robin_hood.h) is Copyright (c) 2018-2020 Martin Ankerl and is

licensed under the MIT License.

In addition, this version of Gmsh may contain the following contributed,

optional codes in the contrib/ directory, each governed by their own license:

* contrib/ANN copyright (C) 1997-2005 University of Maryland and Sunil Arya and
David Mount;

* contrib/gmm copyright (C) 2002-2008 Yves Renard;

* contrib/hxt - Copyright (C) 2017-2020 - Universite catholique de Louvain;

* contrib/kbipack copyright (C) 2005 Saku Suuriniemi;

* contrib/MathEx based in part on the work of the SSCILIB Library, copyright (C)
2000-2003 Sadao Massago;

* contrib/metis written by George Karypis (karypis at cs.umn.edu), copyright (C)

1995-2013 Regents of the University of Minnesota;

* contrib/mpeg_encode copyright (c) 1995 The Regents of the University of

California;

* contrib/Netgen copyright (C) 1994-2004 Joachim Sch"oberl;

* contrib/bamg from Freefem++ copyright (C) Frederic Hecht;

* contrib/ALGLIB (C) Sergey Bochkanov (ALGLIB project);

* contrib/blossom copyright (C) 1995-1997 Bill Cook et al.;

* contrib/bamg from Freefem++ copyright (C) Frederic Hecht;

* contrib/voro++ from Voro++ Copyright (c) 2008, The Regents of the University
of California, through Lawrence Berkeley National Laboratory (subject to
receipt of any required approvals from the U.S. Dept. of Energy). All rights
reserved;

* contrib/zipper from MiniZip - Copyright (c) 1998-2010 - by Gilles Vollant -

version 1.1 64 bits from Mathias Svensson.

Check the configuration options to see which have been enabled.

Appendix F: License 409

Appendix F License
Gmsh is provided under the terms of the GNU General Public License
(GPL), Version 2 or later, with the following exception:

The copyright holders of Gmsh give you permission to combine Gmsh

with code included in the standard release of Netgen (from Joachim
Sch"oberl), METIS (from George Karypis at the University of
Minnesota), OpenCASCADE (from Open CASCADE S.A.S) and ParaView
(from Kitware, Inc.) under their respective licenses. You may copy
and distribute such a system following the terms of the GNU GPL for
Gmsh and the licenses of the other code concerned, provided that
you include the source code of that other code when and as the GNU
GPL requires distribution of source code.

Note that people who make modified versions of Gmsh are not
obligated to grant this special exception for their modified
versions; it is their choice whether to do so. The GNU General
Public License gives permission to release a modified version
without this exception; this exception also makes it possible to
release a modified version which carries forward this exception.

End of exception.

GNU GENERAL PUBLIC LICENSE

Version 2, June 1991

Copyright (C) 1989, 1991 Free Software Foundation, Inc.

51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

Preamble

The licenses for most software are designed to take away your
freedom to share and change it. By contrast, the GNU General Public
License is intended to guarantee your freedom to share and change free
software--to make sure the software is free for all its users. This
General Public License applies to most of the Free Software
Foundation’s software and to any other program whose authors commit to
using it. (Some other Free Software Foundation software is covered by
the GNU Library General Public License instead.) You can apply it to
your programs, too.

When we speak of free software, we are referring to freedom, not

price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
this service if you wish), that you receive source code or can get it
if you want it, that you can change the software or use pieces of it
in new free programs; and that you know you can do these things.

To protect your rights, we need to make restrictions that forbid

410 Gmsh 4.11.1

anyone to deny you these rights or to ask you to surrender the rights.
These restrictions translate to certain responsibilities for you if you
distribute copies of the software, or if you modify it.

For example, if you distribute copies of such a program, whether

gratis or for a fee, you must give the recipients all the rights that
you have. You must make sure that they, too, receive or can get the
source code. And you must show them these terms so they know their
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We protect your rights with two steps: (1) copyright the software, and
(2) offer you this license which gives you legal permission to copy,
distribute and/or modify the software.

Also, for each author’s protection and ours, we want to make certain
that everyone understands that there is no warranty for this free
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want its recipients to know that what they have is not the original, so
that any problems introduced by others will not reflect on the original
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Finally, any free program is threatened constantly by software

patents. We wish to avoid the danger that redistributors of a free
program will individually obtain patent licenses, in effect making the
program proprietary. To prevent this, we have made it clear that any
patent must be licensed for everyone’s free use or not licensed at all.

The precise terms and conditions for copying, distribution and

modification follow.

GNU GENERAL PUBLIC LICENSE

TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

0. This License applies to any program or other work which contains

a notice placed by the copyright holder saying it may be distributed
under the terms of this General Public License. The "Program", below,
refers to any such program or work, and a "work based on the Program"
means either the Program or any derivative work under copyright law:
that is to say, a work containing the Program or a portion of it,
either verbatim or with modifications and/or translated into another
language. (Hereinafter, translation is included without limitation in
the term "modification".) Each licensee is addressed as "you".

Activities other than copying, distribution and modification are not

covered by this License; they are outside its scope. The act of
running the Program is not restricted, and the output from the Program
is covered only if its contents constitute a work based on the
Program (independent of having been made by running the Program).
Whether that is true depends on what the Program does.

1. You may copy and distribute verbatim copies of the Program’s

source code as you receive it, in any medium, provided that you
Appendix F: License 411

conspicuously and appropriately publish on each copy an appropriate

copyright notice and disclaimer of warranty; keep intact all the
notices that refer to this License and to the absence of any warranty;
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You may charge a fee for the physical act of transferring a copy, and
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2. You may modify your copy or copies of the Program or any portion
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These requirements apply to the modified work as a whole. If

identifiable sections of that work are not derived from the Program,
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this License, whose permissions for other licensees extend to the
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Thus, it is not the intent of this section to claim rights or contest

your rights to work written entirely by you; rather, the intent is to
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In addition, mere aggregation of another work not based on the Program

with the Program (or with a work based on the Program) on a volume of
a storage or distribution medium does not bring the other work under
the scope of this License.
412 Gmsh 4.11.1

3. You may copy and distribute the Program (or a work based on it,
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a) Accompany it with the complete corresponding machine-readable

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to distribute corresponding source code. (This alternative is
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The source code for a work means the preferred form of the work for
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If distribution of executable or object code is made by offering

access to copy from a designated place, then offering equivalent
access to copy the source code from the same place counts as
distribution of the source code, even though third parties are not
compelled to copy the source along with the object code.

4. You may not copy, modify, sublicense, or distribute the Program

except as expressly provided under this License. Any attempt
otherwise to copy, modify, sublicense or distribute the Program is
void, and will automatically terminate your rights under this License.
However, parties who have received copies, or rights, from you under
this License will not have their licenses terminated so long as such
parties remain in full compliance.

5. You are not required to accept this License, since you have not
signed it. However, nothing else grants you permission to modify or
distribute the Program or its derivative works. These actions are
prohibited by law if you do not accept this License. Therefore, by
modifying or distributing the Program (or any work based on the
Appendix F: License 413

Program), you indicate your acceptance of this License to do so, and

all its terms and conditions for copying, distributing or modifying
the Program or works based on it.

6. Each time you redistribute the Program (or any work based on the
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This section is intended to make thoroughly clear what is believed to

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8. If the distribution and/or use of the Program is restricted in

certain countries either by patents or by copyrighted interfaces, the
original copyright holder who places the Program under this License
may add an explicit geographical distribution limitation excluding
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countries not thus excluded. In such case, this License incorporates
the limitation as if written in the body of this License.
414 Gmsh 4.11.1

9. The Free Software Foundation may publish revised and/or new versions
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OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGES.

END OF TERMS AND CONDITIONS

How to Apply These Terms to Your New Programs

If you develop a new program, and you want it to be of the greatest

possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.

To do so, attach the following notices to the program. It is safest

Appendix F: License 415

to attach them to the start of each source file to most effectively

convey the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.

<one line to give the program’s name and a brief idea of what it does.>
Copyright (C) <year> <name of author>

This program is free software; you can redistribute it and/or modify

it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,

but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

Also add information on how to contact you by electronic and paper mail.

If the program is interactive, make it output a short notice like this

when it starts in an interactive mode:

Gnomovision version 69, Copyright (C) year name of author

Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type ‘show w’.
This is free software, and you are welcome to redistribute it
under certain conditions; type ‘show c’ for details.

The hypothetical commands ‘show w’ and ‘show c’ should show the appropriate
parts of the General Public License. Of course, the commands you use may
be called something other than ‘show w’ and ‘show c’; they could even be
mouse-clicks or menu items--whatever suits your program.

You should also get your employer (if you work as a programmer) or your
school, if any, to sign a "copyright disclaimer" for the program, if
necessary. Here is a sample; alter the names:

Yoyodyne, Inc., hereby disclaims all copyright interest in the program

‘Gnomovision’ (which makes passes at compilers) written by James Hacker.

<signature of Ty Coon>, 1 April 1989

Ty Coon, President of Vice

This General Public License does not permit incorporating your program into
proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Library General
Public License instead of this License.
Concept index 417

Concept index

2 F
2D plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 FAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
File format, mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
File formats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
3 File, comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3D plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Frequently asked questions . . . . . . . . . . . . . . . . . . . . . . 375
Functions, built-in . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

A
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
G
API . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 General commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Geometry, boolean operations . . . . . . . . . . . . . . . . . . . 107
Geometry, difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
B Geometry, extrusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Background mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Geometry, fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Binary operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Geometry, intersection . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Bindings, keyboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Geometry, scripting commands . . . . . . . . . . . . . . . . . . 102
Bindings, mouse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Geometry, transformations . . . . . . . . . . . . . . . . . . . . . . 108
Boolean operations, geometry . . . . . . . . . . . . . . . . . . . 107 Geometry, union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Bugs, reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Graphical user interface . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
C
Changelog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 H
Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Command-line options . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 History, versions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Commands, general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Concepts, index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
I
Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Index, concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Index, syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Contributors, list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Copyright . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3, 405 Internet address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Curves, elementary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Issues, reporting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Curves, physical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
K
D Keyboard, shortcuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Developer, information . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Keywords, index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Download . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
L
E License . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3, 409
Elementary curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Elementary points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Elementary surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Elementary volumes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Evaluation order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 M
Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Macros, user-defined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Expressions, affectation . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mesh size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Expressions, color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Mesh, background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Expressions, definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Mesh, element size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Expressions, floating point . . . . . . . . . . . . . . . . . . . . . . . 89 Mesh, extrusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Expressions, identifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mesh, file format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
Expressions, lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Mesh, scripting commands . . . . . . . . . . . . . . . . . . . . . . 111
Expressions, string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Mesh, transfinite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Extrusion, geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Mouse, actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Extrusion, mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 MSH4 file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
418 Gmsh 4.11.1

N Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Nodes, ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Running Gmsh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Numbers, real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
S
O Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Scripting commands, geometry . . . . . . . . . . . . . . . . . . 102
Operator precedence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Scripting commands, Mesh . . . . . . . . . . . . . . . . . . . . . . 111
Operators, definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Scripting commands, Post-processing . . . . . . . . . . . . 117
Options, command line . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Shortcuts, keyboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Options, post-processing . . . . . . . . . . . . . . . . . . . . . . . . 280
Size, elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Order, evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Surfaces, elementary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Surfaces, physical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
P Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Syntax, index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Physical curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Physical points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Physical surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 T
Physical volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Ternary operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Transfinite, mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Plugins, post-processing . . . . . . . . . . . . . . . . . . . . . . . . . 317 Transformations, geometry . . . . . . . . . . . . . . . . . . . . . . 108
Points, elementary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Points, physical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Post-processing plugins . . . . . . . . . . . . . . . . . . . . . . . . . 317
Post-processing, options . . . . . . . . . . . . . . . . . . . . . . . . . 280
Post-processing, scripting commands . . . . . . . . . . . . 117 U
Precedence, operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Unary operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Programming, API . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Programming, notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
V
Versions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Q Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Questions, frequently asked . . . . . . . . . . . . . . . . . . . . . 375 Volumes, elementary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Volumes, physical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

R
Real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 W
Reporting bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Web site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Syntax index 419

Syntax index

! -ignore_periocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -info . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
!= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -link int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-listen string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-log filename . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
% -match . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
% . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -merge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-minterpreter string . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
& -new . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-nodb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
&& . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
-noenv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-nolocale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
( -nopopup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-nt int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
-numsubedges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-o file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
* -open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-optimize[_netgen] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -optimize_ho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
*= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 -optimize_threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-option file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
+ -order int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-part int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -part_[no_]ghosts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -part_[no_]physicals . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
+= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 -part_[no_]topo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-part_split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
- -part_topo_pro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-part_weight [tri,quad,tet,hex,pri,pyr,trih]
- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93, 94 int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-, -parse_and_exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 -pid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 -preserve_numbering_msh2 . . . . . . . . . . . . . . . . . . . . . . 84
-= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 -pyinterpreter string . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 -rand value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-1, -2, -3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 -reclassify angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-a, -g, -m, -s, -p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 -refine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-algo string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 -reparam angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-aniso_max value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-barycentric_refine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-save . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-bg file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-save_all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-bgm file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-save_parametric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-save_topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-camera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-setnumber name value . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-setstring name value . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-clcurv value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-smooth int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-clextend value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-smooth_ratio value . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-clmax value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-stereo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-clmin value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-string "string" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-clscale value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
-swapangle value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-combine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-theme string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
-convert files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-tol value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-cpu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-display string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 -v int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-epslc1d value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 -version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-fontsize int . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 -watch pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-format string . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
-gamepad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
-help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 /
-help_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
-ho_[min,max,nlayers] . . . . . . . . . . . . . . . . . . . . . . . . . 84 /*, */ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
420 Gmsh 4.11.1

// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Background Mesh View[expression ]; . . . . . . . . . . . 118

/= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
Bezier ( expression ) = { expression-list };
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
: Bezier Surface ( expression ) = {
: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 expression-list }; . . . . . . . . . . . . . . . . . . . . . . . 104
boolean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
BooleanDifference ( expression ) = {
< boolean-list } { boolean-list }; . . . . . . . . 108
< . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 BooleanDifference { boolean-list } {
< Recursive > Color color-expression { boolean-list } . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
<Physical> Point | Curve | Surface | Volume { BooleanFragments { boolean-list } {
expression-list-or-all }; ... } . . . . . . . . . 116 boolean-list } . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
< Recursive > Delete { <Physical> Point | Curve | BooleanIntersection ( expression ) = {
Surface | Volume { expression-list-or-all boolean-list } { boolean-list }; . . . . . . . . 108
}; ... }. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 BooleanIntersection { boolean-list } {
< Recursive > Hide { <Physical> Point | Curve | boolean-list } . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Surface | Volume { expression-list-or-all BooleanUnion ( expression ) = { boolean-list } {
}; ... }. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 boolean-list }; . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
< Recursive > Show { <Physical> Point | Curve | BooleanUnion { boolean-list } { boolean-list }
Surface | Volume { expression-list-or-all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
}; ... }. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Boundary { transform-list } . . . . . . . . . . . . . . . . . . 109
<= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 BoundaryLayer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
BoundingBox { expression, expression,
expression, expression, expression,
= expression }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 BoundingBox; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
== . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
Box ( expression ) = { expression-list }; . . . . 105
BSpline ( expression ) = { expression-list };
> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 BSpline Surface ( expression ) = {
>= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 expression-list }; . . . . . . . . . . . . . . . . . . . . . . . 104
build-in-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
?
? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 C
Call string | string-expression ; . . . . . . . . . . . . . 96
Ceil ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
^ Chamfer { expression-list } { expression-list }
^ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 { expression-list } { expression-list }
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Circle ( expression ) = { expression,
| expression, expression <, ...> }; . . . . . . . 103
|| . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 ClassifySurfaces { expression , expression ,
expression < , expression > }; . . . . . . . . . . . 116
Coherence Mesh; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
A Coherence; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Abort; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Cohomology ( { expression-list } ) { {
Acos ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 expression-list } , { expression-list } };
AdaptMesh { expression-list } { expression-list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
} { { expression-list < , ... > } }; . . . . . . 114 color-option = color-expression ; . . . . . . . . . . . . . 99
Affine { expression-list } { transform-list } Combine ElementsByViewName; . . . . . . . . . . . . . . . . . . 118
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Combine ElementsFromAllViews | Combine Views;
Alias View[expression ]; . . . . . . . . . . . . . . . . . . . . . . 117 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
AliasWithOptions View[expression ];. . . . . . . . . . 118 Combine ElementsFromVisibleViews; . . . . . . . . . . . 118
Asin ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Combine TimeStepsByViewName | Combine
Atan ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 TimeSteps; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Atan2 ( expression, expression ) . . . . . . . . . . . . . . 95 Combine TimeStepsFromAllViews; . . . . . . . . . . . . . . 118
AttractorAnisoCurve . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Combine TimeStepsFromVisibleViews; . . . . . . . . . . 118
AutomaticMeshSizeField . . . . . . . . . . . . . . . . . . . . . . . 299 CombinedBoundary { transform-list } . . . . . . . . . 109
Compound Curve | Surface {
expression-list-or-all } ; . . . . . . . . . . . . . . . 117
B Compound Spline | BSpline ( expression ) = {
Background Field = expression ; . . . . . . . . . . . . . . . 111 expression-list } Using expression ; . . . . 103
Syntax index 421

Cone ( expression ) = { expression-list }; . . 105 Extrude { { expression-list }, { expression-list

Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 }, { expression-list }, expression } {
Coordinates Surface expression ; . . . . . . . . . . . . . 111 extrude-list layers } . . . . . . . . . . . . . . . . . . . . 112
CopyOptions View[expression, expression ]; . . 118 Extrude { { expression-list }, { expression-list
Cos ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 }, expression } { extrude-list } . . . . . . . . . 106
Cosh ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Extrude { { expression-list }, { expression-list
Cpu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 }, expression } { extrude-list layers }
CreateDir string-expression ;. . . . . . . . . . . . . . . . . . 99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
CreateGeometry < { <Physical> Point | Curve | Extrude { expression-list } { extrude-list }
Surface | Volume { expression-list-or-all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
}; ... } > ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Extrude { expression-list } { extrude-list
CreateTopology < { expression , expression } > ; layers } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Extrude { extrude-list } . . . . . . . . . . . . . . . . . . . . . . 106
Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Extrude { extrude-list } Using Wire {
Curve Loop ( expression ) = { expression-list }; expression-list }. . . . . . . . . . . . . . . . . . . . . . . . . 107
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Extrude { Surface { expression-list }; layers <
Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Using Index[expr ]; > < Using View[expr ]; > <
Cylinder ( expression ) = { expression-list }; ScaleLastLayer; > } . . . . . . . . . . . . . . . . . . . . . . . 113
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
F
D Fabs ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
DefineConstant[ string = { Field[expression ] = string ; . . . . . . . . . . . . . . . . . . 111
expression |string-expression, Field[expression ].string = string-expression |
onelab-options } <, ...>]; . . . . . . . . . . . . . . . . 99 expression | expression-list ; . . . . . . . . . . . 111
DefineConstant[ string = Fillet { expression-list } { expression-list } {
expression |string-expression <, ...>]; . . 99 expression-list }. . . . . . . . . . . . . . . . . . . . . . . . . 107
Delete Embedded { <Physical> Point | Curve | Floor ( expression ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Surface | Volume { expression-list-or-all Fmod ( expression, expression ) . . . . . . . . . . . . . . . 95
}; ... }. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 For ( expression : expression ) . . . . . . . . . . . . . . . 96
Delete Empty Views; . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 For ( expression : expression : expression )
Delete Model; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Delete Options; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 For string In { expression : expression :
Delete Physicals; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 expression } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
For string In { expression : expression } . . . . 96
Delete string ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Frustum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Delete Variables; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Delete View[expression ]; . . . . . . . . . . . . . . . . . . . . . 118
Dilate { { expression-list }, { expression, G
expression, expression } } { transform-list
} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 General.AbortOnError . . . . . . . . . . . . . . . . . . . . . . . . . 223
General.AlphaBlending . . . . . . . . . . . . . . . . . . . . . . . . 223
Dilate { { expression-list }, expression } {
transform-list } . . . . . . . . . . . . . . . . . . . . . . . . . . 108 General.Antialiasing . . . . . . . . . . . . . . . . . . . . . . . . . 223
General.ArrowHeadRadius . . . . . . . . . . . . . . . . . . . . . . 223
Disk ( expression ) = { expression-list }; . . 104
General.ArrowStemLength . . . . . . . . . . . . . . . . . . . . . . 223
Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
General.ArrowStemRadius . . . . . . . . . . . . . . . . . . . . . . 223
Draw; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
General.Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
General.AxesAutoPosition . . . . . . . . . . . . . . . . . . . . . 223
General.AxesForceValue . . . . . . . . . . . . . . . . . . . . . . . 223
E General.AxesFormatX . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Ellipse ( expression ) = { expression, General.AxesFormatY . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
expression, expression <, ...> }; . . . . . . . 103 General.AxesFormatZ . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Else . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 General.AxesLabelX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
ElseIf ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . 97 General.AxesLabelY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
EndFor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 General.AxesLabelZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
EndIf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 General.AxesMaxX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Euclidian Coordinates ; . . . . . . . . . . . . . . . . . . . . . . . 111 General.AxesMaxY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Exit; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 General.AxesMaxZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Exp ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 General.AxesMikado . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Extend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 General.AxesMinX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
ExternalProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 General.AxesMinY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
extrude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 General.AxesMinZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Extrude { { expression-list }, { expression-list General.AxesTicsX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
}, { expression-list }, expression } { General.AxesTicsY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
extrude-list } . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 General.AxesTicsZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
422 Gmsh 4.11.1

General.AxesValueMaxX . . . . . . . . . . . . . . . . . . . . . . . . 224 General.DetachedMenu . . . . . . . . . . . . . . . . . . . . . . . . . 229

General.AxesValueMaxY . . . . . . . . . . . . . . . . . . . . . . . . 224 General.DetachedProcess . . . . . . . . . . . . . . . . . . . . . . 229
General.AxesValueMaxZ . . . . . . . . . . . . . . . . . . . . . . . . 224 General.Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
General.AxesValueMinX . . . . . . . . . . . . . . . . . . . . . . . . 225 General.DisplayBorderFactor . . . . . . . . . . . . . . . . . 229
General.AxesValueMinY . . . . . . . . . . . . . . . . . . . . . . . . 225 General.DoubleBuffer . . . . . . . . . . . . . . . . . . . . . . . . . 229
General.AxesValueMinZ . . . . . . . . . . . . . . . . . . . . . . . . 225 General.DrawBoundingBoxes . . . . . . . . . . . . . . . . . . . . 229
General.BackgroundGradient. . . . . . . . . . . . . . . . . . . 225 General.ErrorFileName . . . . . . . . . . . . . . . . . . . . . . . . 221
General.BackgroundImage3D . . . . . . . . . . . . . . . . . . . . 225 General.ExecutableFileName. . . . . . . . . . . . . . . . . . . 221
General.BackgroundImageFileName . . . . . . . . . . . . . 220 General.ExpertMode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
General.BackgroundImageHeight . . . . . . . . . . . . . . . 225 General.ExtraHeight . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
General.BackgroundImagePage . . . . . . . . . . . . . . . . . 225 General.ExtraPositionX . . . . . . . . . . . . . . . . . . . . . . . 229
General.BackgroundImagePositionX . . . . . . . . . . . . 225 General.ExtraPositionY . . . . . . . . . . . . . . . . . . . . . . . 230
General.BackgroundImagePositionY . . . . . . . . . . . . 225 General.ExtraWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
General.BackgroundImageWidth . . . . . . . . . . . . . . . . 225 General.FastRedraw . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
General.BoundingBoxSize . . . . . . . . . . . . . . . . . . . . . . 226 General.FieldHeight . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
General.BuildInfo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 General.FieldPositionX . . . . . . . . . . . . . . . . . . . . . . . 230
General.BuildOptions . . . . . . . . . . . . . . . . . . . . . . . . . 220 General.FieldPositionY . . . . . . . . . . . . . . . . . . . . . . . 230
General.Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.FieldWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
General.CameraAperture . . . . . . . . . . . . . . . . . . . . . . . 226 General.FileChooserPositionX . . . . . . . . . . . . . . . . 230
General.CameraEyeSeparationRatio . . . . . . . . . . . . 226 General.FileChooserPositionY . . . . . . . . . . . . . . . . 230
General.CameraFocalLengthRatio . . . . . . . . . . . . . . 226 General.FileName . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
General.Clip0A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.FltkColorScheme . . . . . . . . . . . . . . . . . . . . . . 230
General.Clip0B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.FltkRefreshRate . . . . . . . . . . . . . . . . . . . . . . 230
General.Clip0C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.FltkTheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
General.Clip0D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.FontSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
General.Clip1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.GraphicsFont . . . . . . . . . . . . . . . . . . . . . . . . . 221
General.Clip1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.GraphicsFontEngine. . . . . . . . . . . . . . . . . . . 221
General.Clip1C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 General.GraphicsFontSize . . . . . . . . . . . . . . . . . . . . . 231
General.Clip1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.GraphicsFontSizeTitle . . . . . . . . . . . . . . . 231
General.Clip2A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.GraphicsFontTitle . . . . . . . . . . . . . . . . . . . . 221
General.Clip2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.GraphicsHeight . . . . . . . . . . . . . . . . . . . . . . . 231
General.Clip2C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.GraphicsPositionX . . . . . . . . . . . . . . . . . . . . 231
General.Clip2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.GraphicsPositionY . . . . . . . . . . . . . . . . . . . . 231
General.Clip3A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.GraphicsWidth . . . . . . . . . . . . . . . . . . . . . . . . 231
General.Clip3B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.HighOrderToolsPositionX . . . . . . . . . . . . . 231
General.Clip3C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.HighOrderToolsPositionY . . . . . . . . . . . . . 231
General.Clip3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.HighResolutionGraphics . . . . . . . . . . . . . . 231
General.Clip4A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.InitialModule . . . . . . . . . . . . . . . . . . . . . . . . 231
General.Clip4B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.InputScrolling . . . . . . . . . . . . . . . . . . . . . . . 231
General.Clip4C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 General.Light0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.Clip4D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light0W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.Clip5A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light0X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.Clip5B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light0Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.Clip5C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light0Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.Clip5D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.ClipFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light1W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.ClipOnlyDrawIntersectingVolume . . . . . 228 General.Light1X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.ClipOnlyVolume . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light1Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.ClipPositionX . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light1Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.ClipPositionY . . . . . . . . . . . . . . . . . . . . . . . . 228 General.Light2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
General.ClipWholeElements . . . . . . . . . . . . . . . . . . . . 228 General.Light2W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.AmbientLight. . . . . . . . . . . . . . . . . . . 241 General.Light2X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 General.Light2Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.Background . . . . . . . . . . . . . . . . . . . . . 241 General.Light2Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.BackgroundGradient . . . . . . . . . . . . 241 General.Light3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.DiffuseLight. . . . . . . . . . . . . . . . . . . 242 General.Light3W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.Foreground . . . . . . . . . . . . . . . . . . . . . 241 General.Light3X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.SmallAxes . . . . . . . . . . . . . . . . . . . . . . 241 General.Light3Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.SpecularLight . . . . . . . . . . . . . . . . . 242 General.Light3Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.Color.Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 General.Light4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.ColorScheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 General.Light4W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
General.ConfirmOverwrite . . . . . . . . . . . . . . . . . . . . . 229 General.Light4X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
General.ContextPositionX . . . . . . . . . . . . . . . . . . . . . 229 General.Light4Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
General.ContextPositionY . . . . . . . . . . . . . . . . . . . . . 229 General.Light4Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
General.DefaultFileName . . . . . . . . . . . . . . . . . . . . . . 220 General.Light5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Syntax index 423

General.Light5W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 General.ShininessExponent . . . . . . . . . . . . . . . . . . . . 238

General.Light5X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 General.ShowMessagesOnStartup . . . . . . . . . . . . . . . 239
General.Light5Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 General.ShowModuleMenu . . . . . . . . . . . . . . . . . . . . . . . 239
General.Light5Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 General.ShowOptionsOnStartup . . . . . . . . . . . . . . . . 239
General.LineWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 General.SmallAxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
General.ManipulatorPositionX . . . . . . . . . . . . . . . . 234 General.SmallAxesPositionX. . . . . . . . . . . . . . . . . . . 239
General.ManipulatorPositionY . . . . . . . . . . . . . . . . 234 General.SmallAxesPositionY. . . . . . . . . . . . . . . . . . . 239
General.MaxX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.SmallAxesSize . . . . . . . . . . . . . . . . . . . . . . . . 239
General.MaxY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.StatisticsPositionX . . . . . . . . . . . . . . . . . 239
General.MaxZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.StatisticsPositionY . . . . . . . . . . . . . . . . . 239
General.MenuHeight . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.Stereo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
General.MenuPositionX . . . . . . . . . . . . . . . . . . . . . . . . 235 General.SystemMenuBar . . . . . . . . . . . . . . . . . . . . . . . . 239
General.MenuPositionY . . . . . . . . . . . . . . . . . . . . . . . . 235 General.Terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.MenuWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.TextEditor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
General.MessageFontSize . . . . . . . . . . . . . . . . . . . . . . 235 General.TmpFileName . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
General.MessageHeight . . . . . . . . . . . . . . . . . . . . . . . . 235 General.Tooltips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.MinX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.Trackball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.MinY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.TrackballHyperbolicSheet . . . . . . . . . . . . 240
General.MinZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 General.TrackballQuaternion0 . . . . . . . . . . . . . . . . 240
General.MouseHoverMeshes . . . . . . . . . . . . . . . . . . . . . 236 General.TrackballQuaternion1 . . . . . . . . . . . . . . . . 240
General.MouseInvertZoom . . . . . . . . . . . . . . . . . . . . . . 236 General.TrackballQuaternion2 . . . . . . . . . . . . . . . . 240
General.MouseSelection . . . . . . . . . . . . . . . . . . . . . . . 236 General.TrackballQuaternion3 . . . . . . . . . . . . . . . . 240
General.NativeFileChooser . . . . . . . . . . . . . . . . . . . . 236 General.TranslationX . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.NonModalWindows . . . . . . . . . . . . . . . . . . . . . . 236 General.TranslationY . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.NoPopup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 General.TranslationZ . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.NumThreads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 General.VectorType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
General.OptionsFileName . . . . . . . . . . . . . . . . . . . . . . 221 General.Verbosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
General.OptionsPositionX . . . . . . . . . . . . . . . . . . . . . 236 General.Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
General.OptionsPositionY . . . . . . . . . . . . . . . . . . . . . 236 General.VisibilityPositionX . . . . . . . . . . . . . . . . . 241
General.Orthographic . . . . . . . . . . . . . . . . . . . . . . . . . 236 General.VisibilityPositionY . . . . . . . . . . . . . . . . . 241
General.PluginHeight . . . . . . . . . . . . . . . . . . . . . . . . . 237 General.WatchFilePattern . . . . . . . . . . . . . . . . . . . . . 223
General.PluginPositionX . . . . . . . . . . . . . . . . . . . . . . 236 General.ZoomFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
General.PluginPositionY . . . . . . . . . . . . . . . . . . . . . . 237 Geometry.AutoCoherence . . . . . . . . . . . . . . . . . . . . . . . 247
General.PluginWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Geometry.Clip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
General.PointSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Geometry.Color.Curves . . . . . . . . . . . . . . . . . . . . . . . . 254
General.PolygonOffsetAlwaysOn . . . . . . . . . . . . . . . 237 Geometry.Color.HighlightOne . . . . . . . . . . . . . . . . . 254
General.PolygonOffsetFactor . . . . . . . . . . . . . . . . . 237 Geometry.Color.HighlightTwo . . . . . . . . . . . . . . . . . 254
General.PolygonOffsetUnits. . . . . . . . . . . . . . . . . . . 237 Geometry.Color.HighlightZero . . . . . . . . . . . . . . . . 254
General.ProgressMeterStep . . . . . . . . . . . . . . . . . . . . 237 Geometry.Color.Normals . . . . . . . . . . . . . . . . . . . . . . . 255
General.QuadricSubdivisions . . . . . . . . . . . . . . . . . 237 Geometry.Color.Points . . . . . . . . . . . . . . . . . . . . . . . . 254
General.RecentFile0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Geometry.Color.Projection . . . . . . . . . . . . . . . . . . . . 255
General.RecentFile1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Geometry.Color.Selection . . . . . . . . . . . . . . . . . . . . . 254
General.RecentFile2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Geometry.Color.Surfaces . . . . . . . . . . . . . . . . . . . . . . 254
General.RecentFile3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Geometry.Color.Tangents . . . . . . . . . . . . . . . . . . . . . . 254
General.RecentFile4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.Color.Volumes . . . . . . . . . . . . . . . . . . . . . . . 254
General.RecentFile5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.CopyMeshingMethod. . . . . . . . . . . . . . . . . . . 247
General.RecentFile6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.CurveLabels . . . . . . . . . . . . . . . . . . . . . . . . . 247
General.RecentFile7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
General.RecentFile8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.CurveSelectWidth . . . . . . . . . . . . . . . . . . . . 247
General.RecentFile9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.CurveType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
General.RotationCenterGravity . . . . . . . . . . . . . . . 238 Geometry.CurveWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
General.RotationCenterX . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.DoubleClickedCurveCommand . . . . . . . . . 246
General.RotationCenterY . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.DoubleClickedEntityTag . . . . . . . . . . . . . 248
General.RotationCenterZ . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.DoubleClickedPointCommand . . . . . . . . . 246
General.RotationX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Geometry.DoubleClickedSurfaceCommand . . . . . . . 246
General.RotationY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Geometry.DoubleClickedVolumeCommand . . . . . . . . 247
General.RotationZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Geometry.ExactExtrusion . . . . . . . . . . . . . . . . . . . . . . 248
General.SaveOptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.ExtrudeReturnLateralEntities . . . . . . 248
General.SaveSession . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.ExtrudeSplinePoints . . . . . . . . . . . . . . . . 248
General.ScaleX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.HighlightOrphans . . . . . . . . . . . . . . . . . . . . 248
General.ScaleY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.LabelType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
General.ScaleZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
General.ScriptingLanguages. . . . . . . . . . . . . . . . . . . 222 Geometry.LightTwoSide . . . . . . . . . . . . . . . . . . . . . . . . 248
General.SessionFileName . . . . . . . . . . . . . . . . . . . . . . 222 Geometry.MatchGeomAndMesh . . . . . . . . . . . . . . . . . . . . 248
General.Shininess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 Geometry.MatchMeshScaleFactor . . . . . . . . . . . . . . . 248
424 Gmsh 4.11.1

Geometry.MatchMeshTolerance . . . . . . . . . . . . . . . . . 249 gmsh/fltk/isAvailable . . . . . . . . . . . . . . . . . . . . . . . . 210

Geometry.Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/lock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Geometry.NumSubEdges . . . . . . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/openTreeItem . . . . . . . . . . . . . . . . . . . . . . . 212
Geometry.OCCAutoEmbed . . . . . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/run. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Geometry.OCCAutoFix . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/selectElements . . . . . . . . . . . . . . . . . . . . . 211
Geometry.OCCBooleanPreserveNumbering . . . . . . . 249 gmsh/fltk/selectEntities . . . . . . . . . . . . . . . . . . . . . 211
Geometry.OCCBoundsUseStl . . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/selectViews . . . . . . . . . . . . . . . . . . . . . . . . 211
Geometry.OCCDisableStl . . . . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/setCurrentWindow. . . . . . . . . . . . . . . . . . . 211
Geometry.OCCExportOnlyVisible . . . . . . . . . . . . . . . 250 gmsh/fltk/setStatusMessage. . . . . . . . . . . . . . . . . . . 212
Geometry.OCCFixDegenerated. . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/showContextWindow . . . . . . . . . . . . . . . . . 212
Geometry.OCCFixSmallEdges . . . . . . . . . . . . . . . . . . . . 249 gmsh/fltk/splitCurrentWindow . . . . . . . . . . . . . . . . 211
Geometry.OCCFixSmallFaces . . . . . . . . . . . . . . . . . . . . 250 gmsh/fltk/unlock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
Geometry.OCCImportLabels . . . . . . . . . . . . . . . . . . . . . 250 gmsh/fltk/update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Geometry.OCCMakeSolids . . . . . . . . . . . . . . . . . . . . . . . 250 gmsh/fltk/wait . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Geometry.OCCParallel . . . . . . . . . . . . . . . . . . . . . . . . . 250 gmsh/graphics/draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
Geometry.OCCSafeUnbind . . . . . . . . . . . . . . . . . . . . . . . 250 gmsh/initialize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Geometry.OCCScaling . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 gmsh/isInitialized . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Geometry.OCCSewFaces . . . . . . . . . . . . . . . . . . . . . . . . . 250 gmsh/logger/get . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Geometry.OCCTargetUnit . . . . . . . . . . . . . . . . . . . . . . . 247 gmsh/logger/getCpuTime . . . . . . . . . . . . . . . . . . . . . . . 218
Geometry.OCCThruSectionsDegree . . . . . . . . . . . . . . 250 gmsh/logger/getLastError . . . . . . . . . . . . . . . . . . . . . 218
Geometry.OCCUnionUnify . . . . . . . . . . . . . . . . . . . . . . . 250 gmsh/logger/getWallTime . . . . . . . . . . . . . . . . . . . . . . 217
Geometry.OCCUseGenericClosestPoint . . . . . . . . . 251 gmsh/logger/start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Geometry.OffsetX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/logger/stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Geometry.OffsetY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/logger/write . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Geometry.OffsetZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/merge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Geometry.OldCircle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/model/add . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Geometry.OldNewReg . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/model/addDiscreteEntity . . . . . . . . . . . . . . . . 133
Geometry.OldRuledSurface . . . . . . . . . . . . . . . . . . . . . 251 gmsh/model/addPhysicalGroup . . . . . . . . . . . . . . . . . 130
Geometry.OrientedPhysicals. . . . . . . . . . . . . . . . . . . 251 gmsh/model/geo/addBezier . . . . . . . . . . . . . . . . . . . . . 171
Geometry.PipeDefaultTrihedron . . . . . . . . . . . . . . . 247 gmsh/model/geo/addBSpline . . . . . . . . . . . . . . . . . . . . 171
Geometry.PointLabels . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/model/geo/addCircleArc . . . . . . . . . . . . . . . . . 170
Geometry.Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 gmsh/model/geo/addCompoundBSpline. . . . . . . . . . . 172
Geometry.PointSelectSize . . . . . . . . . . . . . . . . . . . . . 251 gmsh/model/geo/addCompoundSpline . . . . . . . . . . . . 172
Geometry.PointSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addCurveLoop . . . . . . . . . . . . . . . . . 172
Geometry.PointType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addCurveLoops . . . . . . . . . . . . . . . . 173
Geometry.ReparamOnFaceRobust . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addEllipseArc . . . . . . . . . . . . . . . . 170
Geometry.ScalingFactor . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addGeometry. . . . . . . . . . . . . . . . . . . 174
Geometry.SnapPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addLine . . . . . . . . . . . . . . . . . . . . . . . 170
Geometry.SnapX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addPhysicalGroup . . . . . . . . . . . . . 179
Geometry.SnapY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addPlaneSurface . . . . . . . . . . . . . . 173
Geometry.SnapZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addPoint . . . . . . . . . . . . . . . . . . . . . . 170
Geometry.SurfaceLabels . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addPointOnGeometry. . . . . . . . . . . 174
Geometry.Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addPolyline. . . . . . . . . . . . . . . . . . . 171
Geometry.SurfaceType . . . . . . . . . . . . . . . . . . . . . . . . . 252 gmsh/model/geo/addSpline . . . . . . . . . . . . . . . . . . . . . 171
Geometry.Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/addSurfaceFilling . . . . . . . . . . . . 173
Geometry.Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/addSurfaceLoop . . . . . . . . . . . . . . . 173
Geometry.ToleranceBoolean . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/addVolume . . . . . . . . . . . . . . . . . . . . . 174
Geometry.Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/copy . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Geometry.TransformXX . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/dilate . . . . . . . . . . . . . . . . . . . . . . . . 177
Geometry.TransformXY . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/extrude . . . . . . . . . . . . . . . . . . . . . . . 174
Geometry.TransformXZ . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/extrudeBoundaryLayer . . . . . . . . 176
Geometry.TransformYX . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/getMaxTag . . . . . . . . . . . . . . . . . . . . . 178
Geometry.TransformYY . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/mesh/setAlgorithm . . . . . . . . . . . . 181
Geometry.TransformYZ . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/mesh/setRecombine . . . . . . . . . . . . 181
Geometry.TransformZX . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/mesh/setReverse . . . . . . . . . . . . . . 181
Geometry.TransformZY . . . . . . . . . . . . . . . . . . . . . . . . . 253 gmsh/model/geo/mesh/setSize . . . . . . . . . . . . . . . . . 179
Geometry.TransformZZ . . . . . . . . . . . . . . . . . . . . . . . . . 254 gmsh/model/geo/mesh/setSizeFromBoundary . . . . 181
Geometry.VolumeLabels . . . . . . . . . . . . . . . . . . . . . . . . 254 gmsh/model/geo/mesh/setSmoothing . . . . . . . . . . . . 181
Geometry.Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 gmsh/model/geo/mesh/setTransfiniteCurve . . . . 180
gmsh/clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 gmsh/model/geo/mesh/setTransfiniteSurface
gmsh/finalize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 ............................................ 180
gmsh/fltk/awake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 gmsh/model/geo/mesh/setTransfiniteVolume . . 180
gmsh/fltk/closeTreeItem . . . . . . . . . . . . . . . . . . . . . . 212 gmsh/model/geo/mirror . . . . . . . . . . . . . . . . . . . . . . . . 177
gmsh/fltk/finalize . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 gmsh/model/geo/remove . . . . . . . . . . . . . . . . . . . . . . . . 178
gmsh/fltk/initialize . . . . . . . . . . . . . . . . . . . . . . . . . 209 gmsh/model/geo/removeAllDuplicates . . . . . . . . . 178
Syntax index 425

gmsh/model/geo/removePhysicalGroups . . . . . . . . 179 gmsh/model/mesh/field/setAsBackgroundMesh

gmsh/model/geo/revolve . . . . . . . . . . . . . . . . . . . . . . . 175 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
gmsh/model/geo/rotate . . . . . . . . . . . . . . . . . . . . . . . . 176 gmsh/model/mesh/field/setAsBoundaryLayer . . 169
gmsh/model/geo/setMaxTag . . . . . . . . . . . . . . . . . . . . . 178 gmsh/model/mesh/field/setNumber . . . . . . . . . . . . . 168
gmsh/model/geo/splitCurve . . . . . . . . . . . . . . . . . . . . 178 gmsh/model/mesh/field/setNumbers . . . . . . . . . . . . 169
gmsh/model/geo/symmetrize . . . . . . . . . . . . . . . . . . . . 177 gmsh/model/mesh/field/setString . . . . . . . . . . . . . 168
gmsh/model/geo/synchronize. . . . . . . . . . . . . . . . . . . 179 gmsh/model/mesh/generate . . . . . . . . . . . . . . . . . . . . . 140
gmsh/model/geo/translate . . . . . . . . . . . . . . . . . . . . . 176 gmsh/model/mesh/getAllEdges . . . . . . . . . . . . . . . . . 153
gmsh/model/geo/twist . . . . . . . . . . . . . . . . . . . . . . . . . 175 gmsh/model/mesh/getAllFaces . . . . . . . . . . . . . . . . . 154
gmsh/model/getAdjacencies . . . . . . . . . . . . . . . . . . . . 132 gmsh/model/mesh/getBarycenters . . . . . . . . . . . . . . 155
gmsh/model/getAttribute . . . . . . . . . . . . . . . . . . . . . . 139 gmsh/model/mesh/getBasisFunctions. . . . . . . . . . . 151
gmsh/model/getAttributeNames . . . . . . . . . . . . . . . . 139 gmsh/model/mesh/getBasisFunctionsOrientation
gmsh/model/getBoundary . . . . . . . . . . . . . . . . . . . . . . . 132 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
gmsh/model/getBoundingBox . . . . . . . . . . . . . . . . . . . . 132 gmsh/model/mesh/getBasisFunctionsOrientation
gmsh/model/getClosestPoint. . . . . . . . . . . . . . . . . . . 137 ForElement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
gmsh/model/getColor . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 gmsh/model/mesh/getDuplicateNodes. . . . . . . . . . . 164
gmsh/model/getCurrent . . . . . . . . . . . . . . . . . . . . . . . . 128 gmsh/model/mesh/getEdges . . . . . . . . . . . . . . . . . . . . . 152
gmsh/model/getCurvature . . . . . . . . . . . . . . . . . . . . . . 135 gmsh/model/mesh/getElement. . . . . . . . . . . . . . . . . . . 146
gmsh/model/getDerivative . . . . . . . . . . . . . . . . . . . . . 135 gmsh/model/mesh/getElementByCoordinates . . . . 146
gmsh/model/getDimension . . . . . . . . . . . . . . . . . . . . . . 133 gmsh/model/mesh/getElementEdgeNodes . . . . . . . . 156
gmsh/model/getEntities . . . . . . . . . . . . . . . . . . . . . . . 129 gmsh/model/mesh/getElementFaceNodes . . . . . . . . 156
gmsh/model/getEntitiesForPhysicalGroup . . . . . 130 gmsh/model/mesh/getElementProperties . . . . . . . 147
gmsh/model/getEntitiesInBoundingBox . . . . . . . . 132 gmsh/model/mesh/getElementQualities . . . . . . . . 148
gmsh/model/getEntityName . . . . . . . . . . . . . . . . . . . . . 129 gmsh/model/mesh/getElements . . . . . . . . . . . . . . . . . 145
gmsh/model/getFileName . . . . . . . . . . . . . . . . . . . . . . . 129 gmsh/model/mesh/getElementsByCoordinates . . 146
gmsh/model/getNormal . . . . . . . . . . . . . . . . . . . . . . . . . 136 gmsh/model/mesh/getElementsByType. . . . . . . . . . . 148
gmsh/model/getNumberOfPartitions . . . . . . . . . . . . 134 gmsh/model/mesh/getElementType . . . . . . . . . . . . . . 147
gmsh/model/getParametrization . . . . . . . . . . . . . . . 136 gmsh/model/mesh/getElementTypes . . . . . . . . . . . . . 147
gmsh/model/getParametrizationBounds . . . . . . . . 137 gmsh/model/mesh/getEmbedded . . . . . . . . . . . . . . . . . 161
gmsh/model/getParent . . . . . . . . . . . . . . . . . . . . . . . . . 134 gmsh/model/mesh/getFaces . . . . . . . . . . . . . . . . . . . . . 153
gmsh/model/getPartitions . . . . . . . . . . . . . . . . . . . . . 134 gmsh/model/mesh/getGhostElements . . . . . . . . . . . . 156
gmsh/model/getPhysicalGroups . . . . . . . . . . . . . . . . 130 gmsh/model/mesh/getIntegrationPoints . . . . . . . 149
gmsh/model/getPhysicalGroupsForEntity . . . . . . 130 gmsh/model/mesh/getJacobian . . . . . . . . . . . . . . . . . 150
gmsh/model/getPhysicalName. . . . . . . . . . . . . . . . . . . 131 gmsh/model/mesh/getJacobians . . . . . . . . . . . . . . . . 150
gmsh/model/getPrincipalCurvatures. . . . . . . . . . . 136 gmsh/model/mesh/getKeys . . . . . . . . . . . . . . . . . . . . . . 154
gmsh/model/getSecondDerivative . . . . . . . . . . . . . . 135 gmsh/model/mesh/getKeysForElement. . . . . . . . . . . 154
gmsh/model/getType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 gmsh/model/mesh/getKeysInformation . . . . . . . . . 155
gmsh/model/getValue . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 gmsh/model/mesh/getLastEntityError . . . . . . . . . 141
gmsh/model/getVisibility . . . . . . . . . . . . . . . . . . . . . 138 gmsh/model/mesh/getLastNodeError . . . . . . . . . . . . 141
gmsh/model/isInside . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 gmsh/model/mesh/getLocalCoordinatesInElement
gmsh/model/list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
gmsh/model/mesh/addEdges . . . . . . . . . . . . . . . . . . . . . 154 gmsh/model/mesh/getMaxElementTag . . . . . . . . . . . . 148
gmsh/model/mesh/addElements . . . . . . . . . . . . . . . . . 149 gmsh/model/mesh/getMaxNodeTag . . . . . . . . . . . . . . . 144
gmsh/model/mesh/addElementsByType. . . . . . . . . . . 149 gmsh/model/mesh/getNode . . . . . . . . . . . . . . . . . . . . . . 143
gmsh/model/mesh/addFaces . . . . . . . . . . . . . . . . . . . . . 154 gmsh/model/mesh/getNodes . . . . . . . . . . . . . . . . . . . . . 142
gmsh/model/mesh/addHomologyRequest . . . . . . . . . 166 gmsh/model/mesh/getNodesByElementType . . . . . . 143
gmsh/model/mesh/addNodes . . . . . . . . . . . . . . . . . . . . . 144 gmsh/model/mesh/getNodesForPhysicalGroup . . 144
gmsh/model/mesh/affineTransform . . . . . . . . . . . . . 142 gmsh/model/mesh/getNumberOfKeys . . . . . . . . . . . . . 155
gmsh/model/mesh/classifySurfaces . . . . . . . . . . . . 165 gmsh/model/mesh/getNumberOfOrientations . . . . 152
gmsh/model/mesh/clear . . . . . . . . . . . . . . . . . . . . . . . . 142 gmsh/model/mesh/getPeriodic . . . . . . . . . . . . . . . . . 163
gmsh/model/mesh/clearHomologyRequests . . . . . . 166 gmsh/model/mesh/getPeriodicKeys . . . . . . . . . . . . . 163
gmsh/model/mesh/computeCrossField. . . . . . . . . . . 166 gmsh/model/mesh/getPeriodicNodes . . . . . . . . . . . . 163
gmsh/model/mesh/computeHomology . . . . . . . . . . . . . 166 gmsh/model/mesh/getSizes . . . . . . . . . . . . . . . . . . . . . 157
gmsh/model/mesh/createEdges . . . . . . . . . . . . . . . . . 153 gmsh/model/mesh/importStl . . . . . . . . . . . . . . . . . . . . 163
gmsh/model/mesh/createFaces . . . . . . . . . . . . . . . . . 153 gmsh/model/mesh/optimize . . . . . . . . . . . . . . . . . . . . . 140
gmsh/model/mesh/createGeometry . . . . . . . . . . . . . . 165 gmsh/model/mesh/partition . . . . . . . . . . . . . . . . . . . . 140
gmsh/model/mesh/createTopology . . . . . . . . . . . . . . 165 gmsh/model/mesh/preallocateBarycenters . . . . . 155
gmsh/model/mesh/embed . . . . . . . . . . . . . . . . . . . . . . . . 161 gmsh/model/mesh/preallocateBasisFunctions
gmsh/model/mesh/field/add . . . . . . . . . . . . . . . . . . . . 167 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
gmsh/model/mesh/field/getNumber . . . . . . . . . . . . . 168 gmsh/model/mesh/preallocateElementsByType
gmsh/model/mesh/field/getNumbers . . . . . . . . . . . . 169 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
gmsh/model/mesh/field/getString . . . . . . . . . . . . . 168 gmsh/model/mesh/preallocateJacobians . . . . . . . 150
gmsh/model/mesh/field/getType . . . . . . . . . . . . . . . 168 gmsh/model/mesh/rebuildElementCache . . . . . . . . 144
gmsh/model/mesh/field/list. . . . . . . . . . . . . . . . . . . 167 gmsh/model/mesh/rebuildNodeCache . . . . . . . . . . . . 144
gmsh/model/mesh/field/remove . . . . . . . . . . . . . . . . 167 gmsh/model/mesh/reclassifyNodes . . . . . . . . . . . . . 145
426 Gmsh 4.11.1

gmsh/model/mesh/recombine . . . . . . . . . . . . . . . . . . . . 141 gmsh/model/occ/addWire . . . . . . . . . . . . . . . . . . . . . . . 185

gmsh/model/mesh/refine . . . . . . . . . . . . . . . . . . . . . . . 141 gmsh/model/occ/affineTransform . . . . . . . . . . . . . . 196
gmsh/model/mesh/relocateNodes . . . . . . . . . . . . . . . 145 gmsh/model/occ/chamfer . . . . . . . . . . . . . . . . . . . . . . . 193
gmsh/model/mesh/removeConstraints. . . . . . . . . . . 161 gmsh/model/occ/convertToNURBS . . . . . . . . . . . . . . . 197
gmsh/model/mesh/removeDuplicateElements . . . . 164 gmsh/model/occ/copy . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
gmsh/model/mesh/removeDuplicateNodes . . . . . . . 164 gmsh/model/occ/cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
gmsh/model/mesh/removeEmbedded . . . . . . . . . . . . . . 161 gmsh/model/occ/dilate . . . . . . . . . . . . . . . . . . . . . . . . 195
gmsh/model/mesh/removeSizeCallback . . . . . . . . . 158 gmsh/model/occ/extrude . . . . . . . . . . . . . . . . . . . . . . . 192
gmsh/model/mesh/renumberElements . . . . . . . . . . . . 162 gmsh/model/occ/fillet . . . . . . . . . . . . . . . . . . . . . . . . 193
gmsh/model/mesh/renumberNodes . . . . . . . . . . . . . . . 162 gmsh/model/occ/fragment . . . . . . . . . . . . . . . . . . . . . . 194
gmsh/model/mesh/reorderElements . . . . . . . . . . . . . 162 gmsh/model/occ/fuse . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
gmsh/model/mesh/reverse . . . . . . . . . . . . . . . . . . . . . . 142 gmsh/model/occ/getBoundingBox . . . . . . . . . . . . . . . 199
gmsh/model/mesh/setAlgorithm . . . . . . . . . . . . . . . . 160 gmsh/model/occ/getCenterOfMass . . . . . . . . . . . . . . 199
gmsh/model/mesh/setCompound . . . . . . . . . . . . . . . . . 160 gmsh/model/occ/getCurveLoops . . . . . . . . . . . . . . . . 199
gmsh/model/mesh/setNode . . . . . . . . . . . . . . . . . . . . . . 143 gmsh/model/occ/getEntities. . . . . . . . . . . . . . . . . . . 198
gmsh/model/mesh/setOrder . . . . . . . . . . . . . . . . . . . . . 141 gmsh/model/occ/getEntitiesInBoundingBox . . . . 198
gmsh/model/mesh/setOutwardOrientation . . . . . . 160 gmsh/model/occ/getMass . . . . . . . . . . . . . . . . . . . . . . . 199
gmsh/model/mesh/setPeriodic . . . . . . . . . . . . . . . . . 162 gmsh/model/occ/getMatrixOfInertia. . . . . . . . . . . 200
gmsh/model/mesh/setRecombine . . . . . . . . . . . . . . . . 159 gmsh/model/occ/getMaxTag . . . . . . . . . . . . . . . . . . . . . 200
gmsh/model/mesh/setReverse. . . . . . . . . . . . . . . . . . . 159 gmsh/model/occ/getSurfaceLoops . . . . . . . . . . . . . . 199
gmsh/model/mesh/setSize . . . . . . . . . . . . . . . . . . . . . . 157 gmsh/model/occ/healShapes . . . . . . . . . . . . . . . . . . . . 197
gmsh/model/mesh/setSizeAtParametricPoints gmsh/model/occ/importShapes . . . . . . . . . . . . . . . . . 197
............................................ 157 gmsh/model/occ/importShapesNativePointer . . 198
gmsh/model/mesh/setSizeCallback . . . . . . . . . . . . . 157 gmsh/model/occ/intersect . . . . . . . . . . . . . . . . . . . . . 194
gmsh/model/mesh/setSizeFromBoundary . . . . . . . . 160 gmsh/model/occ/mesh/setSize . . . . . . . . . . . . . . . . . 201
gmsh/model/mesh/setSmoothing . . . . . . . . . . . . . . . . 159 gmsh/model/occ/mirror . . . . . . . . . . . . . . . . . . . . . . . . 196
gmsh/model/mesh/setTransfiniteAutomatic . . . . 159 gmsh/model/occ/remove . . . . . . . . . . . . . . . . . . . . . . . . 196
gmsh/model/mesh/setTransfiniteCurve . . . . . . . . 158 gmsh/model/occ/removeAllDuplicates . . . . . . . . . 197
gmsh/model/mesh/setTransfiniteSurface . . . . . . 158 gmsh/model/occ/revolve . . . . . . . . . . . . . . . . . . . . . . . 192
gmsh/model/mesh/setTransfiniteVolume . . . . . . . 158 gmsh/model/occ/rotate . . . . . . . . . . . . . . . . . . . . . . . . 195
gmsh/model/mesh/setVisibility . . . . . . . . . . . . . . . 164 gmsh/model/occ/setMaxTag . . . . . . . . . . . . . . . . . . . . . 200
gmsh/model/mesh/splitQuadrangles . . . . . . . . . . . . 164 gmsh/model/occ/symmetrize . . . . . . . . . . . . . . . . . . . . 196
gmsh/model/mesh/tetrahedralize . . . . . . . . . . . . . . 167 gmsh/model/occ/synchronize. . . . . . . . . . . . . . . . . . . 200
gmsh/model/mesh/triangulate . . . . . . . . . . . . . . . . . 167 gmsh/model/occ/translate . . . . . . . . . . . . . . . . . . . . . 195
gmsh/model/mesh/unpartition . . . . . . . . . . . . . . . . . 140 gmsh/model/remove . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
gmsh/model/occ/addBezier . . . . . . . . . . . . . . . . . . . . . 184 gmsh/model/removeAttribute. . . . . . . . . . . . . . . . . . . 139
gmsh/model/occ/addBezierFilling . . . . . . . . . . . . . 187 gmsh/model/removeEntities . . . . . . . . . . . . . . . . . . . . 133
gmsh/model/occ/addBezierSurface . . . . . . . . . . . . . 188 gmsh/model/removeEntityName . . . . . . . . . . . . . . . . . 133
gmsh/model/occ/addBox . . . . . . . . . . . . . . . . . . . . . . . . 189 gmsh/model/removePhysicalGroups . . . . . . . . . . . . . 131
gmsh/model/occ/addBSpline . . . . . . . . . . . . . . . . . . . . 184 gmsh/model/removePhysicalName . . . . . . . . . . . . . . . 131
gmsh/model/occ/addBSplineFilling . . . . . . . . . . . . 187 gmsh/model/reparametrizeOnSurface. . . . . . . . . . . 137
gmsh/model/occ/addBSplineSurface . . . . . . . . . . . . 187 gmsh/model/setAttribute . . . . . . . . . . . . . . . . . . . . . . 139
gmsh/model/occ/addCircle . . . . . . . . . . . . . . . . . . . . . 183 gmsh/model/setColor . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
gmsh/model/occ/addCircleArc . . . . . . . . . . . . . . . . . 182 gmsh/model/setCoordinates . . . . . . . . . . . . . . . . . . . . 139
gmsh/model/occ/addCone . . . . . . . . . . . . . . . . . . . . . . . 190 gmsh/model/setCurrent . . . . . . . . . . . . . . . . . . . . . . . . 128
gmsh/model/occ/addCurveLoop . . . . . . . . . . . . . . . . . 185 gmsh/model/setEntityName . . . . . . . . . . . . . . . . . . . . . 129
gmsh/model/occ/addCylinder. . . . . . . . . . . . . . . . . . . 190 gmsh/model/setFileName . . . . . . . . . . . . . . . . . . . . . . . 129
gmsh/model/occ/addDisk . . . . . . . . . . . . . . . . . . . . . . . 186 gmsh/model/setPhysicalName. . . . . . . . . . . . . . . . . . . 131
gmsh/model/occ/addEllipse . . . . . . . . . . . . . . . . . . . . 183 gmsh/model/setTag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
gmsh/model/occ/addEllipseArc . . . . . . . . . . . . . . . . 183 gmsh/model/setVisibility . . . . . . . . . . . . . . . . . . . . . 138
gmsh/model/occ/addLine . . . . . . . . . . . . . . . . . . . . . . . 182 gmsh/model/setVisibilityPerWindow. . . . . . . . . . . 138
gmsh/model/occ/addPipe . . . . . . . . . . . . . . . . . . . . . . . 192 gmsh/onelab/clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
gmsh/model/occ/addPlaneSurface . . . . . . . . . . . . . . 186 gmsh/onelab/get . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
gmsh/model/occ/addPoint . . . . . . . . . . . . . . . . . . . . . . 182 gmsh/onelab/getChanged . . . . . . . . . . . . . . . . . . . . . . . 216
gmsh/model/occ/addRectangle . . . . . . . . . . . . . . . . . 185 gmsh/onelab/getNames . . . . . . . . . . . . . . . . . . . . . . . . . 214
gmsh/model/occ/addSphere . . . . . . . . . . . . . . . . . . . . . 189 gmsh/onelab/getNumber . . . . . . . . . . . . . . . . . . . . . . . . 215
gmsh/model/occ/addSpline . . . . . . . . . . . . . . . . . . . . . 184 gmsh/onelab/getString . . . . . . . . . . . . . . . . . . . . . . . . 215
gmsh/model/occ/addSurfaceFilling . . . . . . . . . . . . 186 gmsh/onelab/run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
gmsh/model/occ/addSurfaceLoop . . . . . . . . . . . . . . . 188 gmsh/onelab/set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
gmsh/model/occ/addThickSolid . . . . . . . . . . . . . . . . 191 gmsh/onelab/setChanged . . . . . . . . . . . . . . . . . . . . . . . 216
gmsh/model/occ/addThruSections . . . . . . . . . . . . . . 191 gmsh/onelab/setNumber . . . . . . . . . . . . . . . . . . . . . . . . 215
gmsh/model/occ/addTorus . . . . . . . . . . . . . . . . . . . . . . 191 gmsh/onelab/setString . . . . . . . . . . . . . . . . . . . . . . . . 215
gmsh/model/occ/addTrimmedSurface . . . . . . . . . . . . 188 gmsh/open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
gmsh/model/occ/addVolume . . . . . . . . . . . . . . . . . . . . . 189 gmsh/option/getColor . . . . . . . . . . . . . . . . . . . . . . . . . 127
gmsh/model/occ/addWedge . . . . . . . . . . . . . . . . . . . . . . 190 gmsh/option/getNumber . . . . . . . . . . . . . . . . . . . . . . . . 126
Syntax index 427

gmsh/option/getString . . . . . . . . . . . . . . . . . . . . . . . . 127 L
gmsh/option/setColor . . . . . . . . . . . . . . . . . . . . . . . . . 127 Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
gmsh/option/setNumber . . . . . . . . . . . . . . . . . . . . . . . . 126 Line ( expression ) = { expression, expression
gmsh/option/setString . . . . . . . . . . . . . . . . . . . . . . . . 127 }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
gmsh/parser/clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Log ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
gmsh/parser/getNames . . . . . . . . . . . . . . . . . . . . . . . . . 213 Log10 ( expression ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
gmsh/parser/getNumber . . . . . . . . . . . . . . . . . . . . . . . . 213 LonLat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
gmsh/parser/getString . . . . . . . . . . . . . . . . . . . . . . . . 213
gmsh/parser/parse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
gmsh/parser/setNumber . . . . . . . . . . . . . . . . . . . . . . . . 213 M
gmsh/parser/setString . . . . . . . . . . . . . . . . . . . . . . . . 213 Macro string | string-expression . . . . . . . . . . . . . 96
gmsh/plugin/run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 MathEval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
gmsh/plugin/setNumber . . . . . . . . . . . . . . . . . . . . . . . . 208 MathEvalAniso. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
gmsh/plugin/setString . . . . . . . . . . . . . . . . . . . . . . . . 208 Max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
gmsh/view/add. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Max ( expression, expression ) . . . . . . . . . . . . . . . . 95
gmsh/view/addAlias . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 MaxEigenHessian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
gmsh/view/addHomogeneousModelData. . . . . . . . . . . 202 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
gmsh/view/addListData . . . . . . . . . . . . . . . . . . . . . . . . 203 Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
gmsh/view/addListDataString . . . . . . . . . . . . . . . . . 204 Merge string-expression ; . . . . . . . . . . . . . . . . . . . . . 100
gmsh/view/addModelData . . . . . . . . . . . . . . . . . . . . . . . 202 Mesh expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
gmsh/view/combine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Mesh.Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
gmsh/view/getHomogeneousModelData. . . . . . . . . . . 203 Mesh.Algorithm3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
gmsh/view/getIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Mesh.AlgorithmSwitchOnFailure . . . . . . . . . . . . . . . 255
gmsh/view/getListData . . . . . . . . . . . . . . . . . . . . . . . . 203 Mesh.AllowSwapAngle . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
gmsh/view/getListDataStrings . . . . . . . . . . . . . . . . 204 Mesh.AngleSmoothNormals . . . . . . . . . . . . . . . . . . . . . . 255
gmsh/view/getModelData . . . . . . . . . . . . . . . . . . . . . . . 202 Mesh.AngleToleranceFacetOverlap . . . . . . . . . . . . . 255
gmsh/view/getTags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Mesh.AnisoMax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
gmsh/view/option/copy . . . . . . . . . . . . . . . . . . . . . . . . 207 Mesh.BdfFieldFormat . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Mesh.Binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
gmsh/view/option/getColor . . . . . . . . . . . . . . . . . . . . 207
Mesh.BoundaryLayerFanElements . . . . . . . . . . . . . . . 256
gmsh/view/option/getNumber. . . . . . . . . . . . . . . . . . . 206
Mesh.CgnsConstructTopology. . . . . . . . . . . . . . . . . . . 256
gmsh/view/option/getString. . . . . . . . . . . . . . . . . . . 207
Mesh.CgnsExportCPEX0045 . . . . . . . . . . . . . . . . . . . . . . 256
gmsh/view/option/setColor . . . . . . . . . . . . . . . . . . . . 207
Mesh.CgnsExportStructured . . . . . . . . . . . . . . . . . . . . 256
gmsh/view/option/setNumber. . . . . . . . . . . . . . . . . . . 206
Mesh.CgnsImportIgnoreBC . . . . . . . . . . . . . . . . . . . . . . 256
gmsh/view/option/setString. . . . . . . . . . . . . . . . . . . 207 Mesh.CgnsImportIgnoreSolution . . . . . . . . . . . . . . . 256
gmsh/view/probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Mesh.CgnsImportOrder . . . . . . . . . . . . . . . . . . . . . . . . . 256
gmsh/view/remove . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Mesh.Clip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
gmsh/view/setInterpolationMatrices . . . . . . . . . 204 Mesh.Color.Eight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
gmsh/view/setVisibilityPerWindow . . . . . . . . . . . . 206 Mesh.Color.Eighteen . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
gmsh/view/write . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 Mesh.Color.Eleven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
gmsh/write . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Mesh.Color.Fifteen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
GMSH_MAJOR_VERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mesh.Color.Five . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
GMSH_MINOR_VERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mesh.Color.Four . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
GMSH_PATCH_VERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mesh.Color.Fourteen . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Mesh.Color.Hexahedra . . . . . . . . . . . . . . . . . . . . . . . . . 273
Mesh.Color.Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Mesh.Color.Nine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
H Mesh.Color.Nineteen . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
HealShapes; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Mesh.Color.Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Hide { : } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Mesh.Color.NodesSup . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Homology ( { expression-list } ) { { Mesh.Color.Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
expression-list } , { expression-list } }; Mesh.Color.One . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Mesh.Color.Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Hypot ( expression, expression ) . . . . . . . . . . . . . . 95 Mesh.Color.Pyramids . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Mesh.Color.Quadrangles . . . . . . . . . . . . . . . . . . . . . . . 273
Mesh.Color.Seven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
I Mesh.Color.Seventeen . . . . . . . . . . . . . . . . . . . . . . . . . 275
Mesh.Color.Six . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
If ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Mesh.Color.Sixteen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Include string-expression ; . . . . . . . . . . . . . . . . . . . 101 Mesh.Color.Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Intersect Curve { expression-list } Surface { Mesh.Color.Ten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
expression } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Mesh.Color.Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . 273
IntersectAniso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 Mesh.Color.Thirteen . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Mesh.Color.Three . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
428 Gmsh 4.11.1

Mesh.Color.Triangles . . . . . . . . . . . . . . . . . . . . . . . . . 273 Mesh.MeshSizeMin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Mesh.Color.Trihedra . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Mesh.MetisAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Mesh.Color.Twelve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Mesh.MetisEdgeMatching . . . . . . . . . . . . . . . . . . . . . . . 262
Mesh.Color.Two . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Mesh.MetisMaxLoadImbalance. . . . . . . . . . . . . . . . . . . 262
Mesh.Color.Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Mesh.MetisMinConn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Mesh.ColorCarousel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Mesh.MetisObjective . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Mesh.CompoundClassify . . . . . . . . . . . . . . . . . . . . . . . . 256 Mesh.MetisRefinementAlgorithm . . . . . . . . . . . . . . . 262
Mesh.CompoundMeshSizeFactor . . . . . . . . . . . . . . . . . 257 Mesh.MinimumCircleNodes . . . . . . . . . . . . . . . . . . . . . . 262
Mesh.CpuTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.MinimumCurveNodes . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.CreateTopologyMsh2 . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.MinimumElementsPerTwoPi . . . . . . . . . . . . . . . . 263
Mesh.CrossFieldClosestPoint . . . . . . . . . . . . . . . . . 270 Mesh.MinimumLineNodes . . . . . . . . . . . . . . . . . . . . . . . . 262
Mesh.DrawSkinOnly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.MshFileVersion . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.Dual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbHexahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.ElementOrder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbNodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.Explode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbPartitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.FirstElementTag . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbPrisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.FirstNodeTag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbPyramids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
Mesh.FlexibleTransfinite . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbQuadrangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Mesh.NbTetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.Hexahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.NbTriangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderCurveOuterBL. . . . . . . . . . . . . . . . . . . 259 Mesh.NbTrihedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderDistCAD . . . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.NewtonConvergenceTestXYZ . . . . . . . . . . . . . . . 264
Mesh.HighOrderFastCurvingNewAlgo . . . . . . . . . . . . 259 Mesh.NodeLabels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderFixBoundaryNodes . . . . . . . . . . . . . . 258 Mesh.Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderIterMax . . . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.NodeSize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderMaxAngle . . . . . . . . . . . . . . . . . . . . . . . 259 Mesh.NodeType. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderMaxInnerAngle . . . . . . . . . . . . . . . . . 259 Mesh.Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderMaxRho . . . . . . . . . . . . . . . . . . . . . . . . . 259 Mesh.NumSubEdges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
Mesh.HighOrderNumLayers . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.OldInitialDelaunay2D . . . . . . . . . . . . . . . . . . . . 265
Mesh.HighOrderOptimize . . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.Optimize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Mesh.HighOrderPassMax . . . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.OptimizeNetgen . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Mesh.HighOrderPeriodic . . . . . . . . . . . . . . . . . . . . . . . 258 Mesh.OptimizeThreshold . . . . . . . . . . . . . . . . . . . . . . . 265
Mesh.HighOrderPoissonRatio. . . . . . . . . . . . . . . . . . . 258 Mesh.PartitionConvertMsh2 . . . . . . . . . . . . . . . . . . . . 266
Mesh.HighOrderPrimSurfMesh. . . . . . . . . . . . . . . . . . . 259 Mesh.PartitionCreateGhostCells . . . . . . . . . . . . . . 266
Mesh.HighOrderSavePeriodic. . . . . . . . . . . . . . . . . . . 258 Mesh.PartitionCreatePhysicals . . . . . . . . . . . . . . . 266
Mesh.HighOrderThresholdMax. . . . . . . . . . . . . . . . . . . 259 Mesh.PartitionCreateTopology . . . . . . . . . . . . . . . . 266
Mesh.HighOrderThresholdMin. . . . . . . . . . . . . . . . . . . 259 Mesh.PartitionHexWeight . . . . . . . . . . . . . . . . . . . . . . 265
Mesh.IgnoreParametrization. . . . . . . . . . . . . . . . . . . 259 Mesh.PartitionLineWeight . . . . . . . . . . . . . . . . . . . . . 265
Mesh.IgnorePeriodicity . . . . . . . . . . . . . . . . . . . . . . . 259 Mesh.PartitionOldStyleMsh2. . . . . . . . . . . . . . . . . . . 266
Mesh.LabelSampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionPrismWeight . . . . . . . . . . . . . . . . . . . . 265
Mesh.LabelType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionPyramidWeight . . . . . . . . . . . . . . . . . 265
Mesh.LcIntegrationPrecision . . . . . . . . . . . . . . . . . 260 Mesh.PartitionQuadWeight . . . . . . . . . . . . . . . . . . . . . 265
Mesh.Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionSplitMeshFiles . . . . . . . . . . . . . . . . 266
Mesh.LightLines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionTetWeight . . . . . . . . . . . . . . . . . . . . . . 265
Mesh.LightTwoSide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionTopologyFile. . . . . . . . . . . . . . . . . . . 266
Mesh.LineLabels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionTrihedronWeight . . . . . . . . . . . . . . . 265
Mesh.Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PartitionTriWeight . . . . . . . . . . . . . . . . . . . . . . 265
Mesh.LineWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.PreserveNumberingMsh2. . . . . . . . . . . . . . . . . . . 266
Mesh.MaxIterDelaunay3D . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Mesh.MaxNumThreads1D . . . . . . . . . . . . . . . . . . . . . . . . . 260 Mesh.Pyramids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Mesh.MaxNumThreads2D . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.QuadqsRemeshingBoldness . . . . . . . . . . . . . . . . 267
Mesh.MaxNumThreads3D . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.QuadqsScalingOnTriangulation. . . . . . . . . . . 267
Mesh.MaxRetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.QuadqsSizemapMethod . . . . . . . . . . . . . . . . . . . . . 266
Mesh.MedFileMinorVersion . . . . . . . . . . . . . . . . . . . . . 263 Mesh.QuadqsTopologyOptimizationMethods . . . . . 267
Mesh.MedImportGroupsOfNodes . . . . . . . . . . . . . . . . . 263 Mesh.Quadrangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MedSingleModel . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Mesh.QualityInf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MeshOnlyEmpty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.QualitySup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MeshOnlyVisible . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.QualityType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MeshSizeExtendFromBoundary . . . . . . . . . . . . . 261 Mesh.RadiusInf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MeshSizeFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.RadiusSup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MeshSizeFromCurvature. . . . . . . . . . . . . . . . . . . 261 Mesh.RandomFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
Mesh.MeshSizeFromCurvatureIsotropic . . . . . . . . 262 Mesh.RandomFactor3D . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
Mesh.MeshSizeFromParametricPoints. . . . . . . . . . . 262 Mesh.RandomSeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
Mesh.MeshSizeFromPoints . . . . . . . . . . . . . . . . . . . . . . 262 Mesh.ReadGroupsOfElements . . . . . . . . . . . . . . . . . . . . 268
Mesh.MeshSizeMax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Mesh.RecombinationAlgorithm . . . . . . . . . . . . . . . . . 268
Syntax index 429

Mesh.Recombine3DAll . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 newp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Mesh.Recombine3DConformity. . . . . . . . . . . . . . . . . . . 269 newreg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Mesh.Recombine3DLevel . . . . . . . . . . . . . . . . . . . . . . . . 268 news . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Mesh.RecombineAll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 newsl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Mesh.RecombineMinimumQuality . . . . . . . . . . . . . . . . 268 newv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Mesh.RecombineNodeRepositioning . . . . . . . . . . . . . 268 NonBlockingSystemCall string-expression ; . . . 101
Mesh.RecombineOptimizeTopology . . . . . . . . . . . . . . 268 number-option *= expression ; . . . . . . . . . . . . . . . . . . 99
Mesh.RefineSteps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 number-option += expression ; . . . . . . . . . . . . . . . . . . 99
Mesh.Renumber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 number-option -= expression ; . . . . . . . . . . . . . . . . . . 99
Mesh.ReparamMaxTriangles . . . . . . . . . . . . . . . . . . . . . 269 number-option /= expression ; . . . . . . . . . . . . . . . . . . 99
Mesh.SaveAll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 number-option = expression ; . . . . . . . . . . . . . . . . . . . 99
Mesh.SaveElementTagType . . . . . . . . . . . . . . . . . . . . . . 269
Mesh.SaveGroupsOfElements . . . . . . . . . . . . . . . . . . . . 269
Mesh.SaveGroupsOfNodes . . . . . . . . . . . . . . . . . . . . . . . 269 O
Mesh.SaveParametric . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Octree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Mesh.SaveTopology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
OnelabRun ( string-expression <,
Mesh.SaveWithoutOrphans . . . . . . . . . . . . . . . . . . . . . . 270
string-expression > ) . . . . . . . . . . . . . . . . . . . . 101
Mesh.ScalingFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
operator-binary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Mesh.SecondOrderIncomplete. . . . . . . . . . . . . . . . . . . 270
operator-ternary-left . . . . . . . . . . . . . . . . . . . . . . . . . 93
Mesh.SecondOrderLinear . . . . . . . . . . . . . . . . . . . . . . . 270
operator-ternary-right . . . . . . . . . . . . . . . . . . . . . . . . 93
Mesh.SmoothCrossField . . . . . . . . . . . . . . . . . . . . . . . . 270
operator-unary-left . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Mesh.Smoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
operator-unary-right . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Mesh.SmoothNormals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
OptimizeMesh string-expression ; . . . . . . . . . . . . . 114
Mesh.SmoothRatio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Mesh.StlAngularDeflection . . . . . . . . . . . . . . . . . . . . 270
Mesh.StlLinearDeflection . . . . . . . . . . . . . . . . . . . . . 271
Mesh.StlLinearDeflectionRelative . . . . . . . . . . . . 271
P
Mesh.StlOneSolidPerSurface. . . . . . . . . . . . . . . . . . . 271 Param . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Mesh.StlRemoveDuplicateTriangles . . . . . . . . . . . . 271 Parametric Surface ( expression ) = "string "
Mesh.SubdivisionAlgorithm . . . . . . . . . . . . . . . . . . . . 271 "string " "string "; . . . . . . . . . . . . . . . . . . . . . . . 110
Mesh.SurfaceEdges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 PartitionMesh expression ; . . . . . . . . . . . . . . . . . . . . 115
Mesh.SurfaceFaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 Periodic Curve { expression-list } = {
Mesh.SurfaceLabels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 expression-list } ; . . . . . . . . . . . . . . . . . . . . . . . 115
Mesh.SwitchElementTags . . . . . . . . . . . . . . . . . . . . . . . 271 Periodic Curve | Surface { expression-list } = {
Mesh.Tangents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 expression-list } Affine | Translate {
Mesh.Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 expression-list } ; . . . . . . . . . . . . . . . . . . . . . . . 115
Mesh.ToleranceEdgeLength . . . . . . . . . . . . . . . . . . . . . 272 Periodic Curve | Surface { expression-list } = {
Mesh.ToleranceInitialDelaunay . . . . . . . . . . . . . . . 272 expression-list } Rotate { expression-list
Mesh.ToleranceReferenceElement . . . . . . . . . . . . . . 272 }, { expression-list }, expression } ; . . 115
Mesh.TransfiniteTri . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Periodic Surface expression { expression-list }
Mesh.Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 = expression { expression-list } ; . . . . . . 115
Mesh.Trihedra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Physical Curve ( expression | string-expression
Mesh.UnvStrictFormat . . . . . . . . . . . . . . . . . . . . . . . . . 272 <, expression > ) <+|->= { expression-list
Mesh.VolumeEdges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Mesh.VolumeFaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Physical Point ( expression | string-expression
Mesh.VolumeLabels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 <, expression > ) <+|->= { expression-list
Mesh.Voronoi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Mesh.ZoneDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Physical Surface ( expression |
MeshAlgorithm Surface { expression-list } = string-expression <, expression > ) <+|->= {
expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 expression-list }; . . . . . . . . . . . . . . . . . . . . . . . 105
MeshSize { expression-list } = expression ; . . 111 Physical Volume ( expression |
MeshSizeFromBoundary Surface { expression-list string-expression <, expression > ) <+|->= {
} = expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 expression-list }; . . . . . . . . . . . . . . . . . . . . . . . 106
Min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Min ( expression, expression ) . . . . . . . . . . . . . . . . 95 Plane Surface ( expression ) = { expression-list
MinAniso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Modulo ( expression, expression ) . . . . . . . . . . . . . 95 Plugin (string ) . Run; . . . . . . . . . . . . . . . . . . . . . . . . 118
MPI_Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Plugin (string ) . string = expression |
MPI_Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 string-expression ; . . . . . . . . . . . . . . . . . . . . . . . 119
Plugin(AnalyseMeshQuality). . . . . . . . . . . . . . . . . . . 317
Plugin(Annotate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
N Plugin(BoundaryAngles) . . . . . . . . . . . . . . . . . . . . . . . 318
newc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Plugin(Bubbles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
newcl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Plugin(Crack). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
NewModel; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Plugin(Curl) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
430 Gmsh 4.11.1

Plugin(CurvedBndDist) . . . . . . . . . . . . . . . . . . . . . . . . 320 PostProcessing.CombineCopyOptions. . . . . . . . . . . 281

Plugin(CutBox) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 PostProcessing.CombineRemoveOriginal . . . . . . . 281
Plugin(CutGrid) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 PostProcessing.DoubleClickedGraphPointCommand
Plugin(CutMesh) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Plugin(CutParametric) . . . . . . . . . . . . . . . . . . . . . . . . 322 PostProcessing.DoubleClickedGraphPointX . . . . 281
Plugin(CutPlane) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 PostProcessing.DoubleClickedGraphPointY . . . . 281
Plugin(CutSphere) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 PostProcessing.DoubleClickedView . . . . . . . . . . . . 281
Plugin(DiscretizationError) . . . . . . . . . . . . . . . . . 323 PostProcessing.ForceElementData . . . . . . . . . . . . . 281
Plugin(Distance) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 PostProcessing.ForceNodeData . . . . . . . . . . . . . . . . 281
Plugin(Divergence) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 PostProcessing.Format . . . . . . . . . . . . . . . . . . . . . . . . 281
Plugin(Eigenvalues) . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 PostProcessing.GraphPointCommand . . . . . . . . . . . . 280
Plugin(Eigenvectors) . . . . . . . . . . . . . . . . . . . . . . . . . 324 PostProcessing.GraphPointX. . . . . . . . . . . . . . . . . . . 281
Plugin(ExtractEdges) . . . . . . . . . . . . . . . . . . . . . . . . . 325 PostProcessing.GraphPointY. . . . . . . . . . . . . . . . . . . 281
Plugin(ExtractElements) . . . . . . . . . . . . . . . . . . . . . . 325 PostProcessing.HorizontalScales . . . . . . . . . . . . . 282
Plugin(FieldFromAmplitudePhase) . . . . . . . . . . . . . 325 PostProcessing.Link . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
Plugin(GaussPoints) . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 PostProcessing.NbViews . . . . . . . . . . . . . . . . . . . . . . . 282
Plugin(Gradient) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 PostProcessing.Plugins . . . . . . . . . . . . . . . . . . . . . . . 282
Plugin(HarmonicToTime) . . . . . . . . . . . . . . . . . . . . . . . 326 PostProcessing.SaveInterpolationMatrices . . 282
Plugin(HomologyComputation) . . . . . . . . . . . . . . . . . 327 PostProcessing.SaveMesh . . . . . . . . . . . . . . . . . . . . . . 282
Plugin(HomologyPostProcessing) . . . . . . . . . . . . . . 327 PostProcessing.Smoothing . . . . . . . . . . . . . . . . . . . . . 282
Plugin(Integrate) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 PostView . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Plugin(Invisible) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Print string-expression ; . . . . . . . . . . . . . . . . . . . . . 101
Plugin(Isosurface) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Print.Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(Lambda2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Print.CompositeWindows . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(LongitudeLatitude) . . . . . . . . . . . . . . . . . . . . 330 Print.DeleteTemporaryFiles. . . . . . . . . . . . . . . . . . . 242
Plugin(MakeSimplex) . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Print.EpsBestRoot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(MathEval) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Print.EpsCompress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(MeshSizeFieldView) . . . . . . . . . . . . . . . . . . . . 332 Print.EpsLineWidthFactor . . . . . . . . . . . . . . . . . . . . . 243
Plugin(MeshSubEntities) . . . . . . . . . . . . . . . . . . . . . . 332 Print.EpsOcclusionCulling . . . . . . . . . . . . . . . . . . . . 243
Plugin(MeshVolume) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 Print.EpsPointSizeFactor . . . . . . . . . . . . . . . . . . . . . 243
Plugin(MinMax) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 Print.EpsPS3Shading . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(ModifyComponents) . . . . . . . . . . . . . . . . . . . . . 333 Print.EpsQuality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(ModulusPhase) . . . . . . . . . . . . . . . . . . . . . . . . . 334 Print.Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(NearestNeighbor) . . . . . . . . . . . . . . . . . . . . . . 335 Print.GeoLabels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(NearToFarField) . . . . . . . . . . . . . . . . . . . . . . . 334 Print.GeoOnlyPhysicals . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(NewView) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Print.GifDither . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(Particles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Print.GifInterlace . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Plugin(Probe). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 Print.GifSort. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Remove) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Print.GifTransparent . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Scal2Tens) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Print.Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Scal2Vec) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Print.JpegQuality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(ShowNeighborElements) . . . . . . . . . . . . . . . . 338 Print.JpegSmoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(SimplePartition) . . . . . . . . . . . . . . . . . . . . . . 338 Print.Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(Skin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Print.ParameterCommand . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(Smooth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Print.ParameterFirst . . . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(SpanningTree) . . . . . . . . . . . . . . . . . . . . . . . . . 339 Print.ParameterLast . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(SphericalRaise) . . . . . . . . . . . . . . . . . . . . . . . 339 Print.ParameterSteps . . . . . . . . . . . . . . . . . . . . . . . . . 242
Plugin(StreamLines) . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Print.PgfExportAxis . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Summation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Print.PgfHorizontalBar . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Tetrahedralize) . . . . . . . . . . . . . . . . . . . . . . . 341 Print.PgfTwoDim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Transform) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Print.PostDisto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Plugin(Triangulate) . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Print.PostElement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(VoroMetal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Print.PostElementary . . . . . . . . . . . . . . . . . . . . . . . . . 244
Plugin(Warp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Print.PostEta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Point ( expression ) = { expression, expression, Print.PostGamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
expression <, expression > }; . . . . . . . . . . . . 102 Print.PostSICN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Point | Curve { expression-list } In Surface { Print.PostSIGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
expression }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Print.TexAsEquation . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Point | Curve | Surface { expression-list } In Print.TexForceFontSize . . . . . . . . . . . . . . . . . . . . . . . 245
Volume { expression }; . . . . . . . . . . . . . . . . . . . . 115 Print.Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
PointsOf { transform-list } . . . . . . . . . . . . . . . . . . 109 Print.TexWidthInMm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
PostProcessing.AnimationCycle . . . . . . . . . . . . . . . 280 Print.Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
PostProcessing.AnimationDelay . . . . . . . . . . . . . . . 280 Print.X3dColorize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
PostProcessing.AnimationStep . . . . . . . . . . . . . . . . 280 Print.X3dCompatibility . . . . . . . . . . . . . . . . . . . . . . . 245
PostProcessing.Binary . . . . . . . . . . . . . . . . . . . . . . . . 281 Print.X3dEdges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Syntax index 431

Print.X3dPrecision . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Solver.AutoCheck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

Print.X3dRemoveInnerBorders . . . . . . . . . . . . . . . . . 245 Solver.AutoLoadDatabase . . . . . . . . . . . . . . . . . . . . . . 279
Print.X3dSurfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Solver.AutoMergeFile . . . . . . . . . . . . . . . . . . . . . . . . . 280
Print.X3dTransparency . . . . . . . . . . . . . . . . . . . . . . . . 246 Solver.AutoMesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Print.X3dVertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Solver.AutoSaveDatabase . . . . . . . . . . . . . . . . . . . . . . 279
Print.X3dVolumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 Solver.AutoShowLastStep . . . . . . . . . . . . . . . . . . . . . . 280
Printf ( string-expression , expression-list ) Solver.AutoShowViews . . . . . . . . . . . . . . . . . . . . . . . . . 280
> string-expression ; . . . . . . . . . . . . . . . . . . . . . 100 Solver.Executable0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Printf ( string-expression , expression-list ) Solver.Executable1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
>> string-expression ; . . . . . . . . . . . . . . . . . . . . 100 Solver.Executable2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Printf ( string-expression <, expression-list > Solver.Executable3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
); . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Solver.Executable4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Solver.Executable5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Solver.Executable6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
R Solver.Executable7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Rand ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Solver.Executable8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Recombine Surface { expression-list-or-all } < = Solver.Executable9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
expression >; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Solver.Extension0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
RecombineMesh; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Solver.Extension1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Rectangle ( expression ) = { expression-list }; Solver.Extension2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Solver.Extension3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
RefineMesh; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Solver.Extension4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
RelocateMesh Point | Curve | Surface { Solver.Extension5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
expression-list-or-all }; . . . . . . . . . . . . . . . 114 Solver.Extension6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
RenumberMeshElements; . . . . . . . . . . . . . . . . . . . . . . . . 116 Solver.Extension7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
RenumberMeshNodes; . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Solver.Extension8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
ReorientMesh Volume { expression-list } ; . . . 117 Solver.Extension9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Restrict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Solver.Name0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Solver.Name1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Solver.Name2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
ReverseMesh Curve | Surface {
Solver.Name3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
expression-list-or-all } ; . . . . . . . . . . . . . . . 117
Solver.Name4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Rotate { { expression-list }, { expression-list
Solver.Name5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
}, expression } { transform-list } . . . . . . 108
Solver.Name6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Round ( expression ). . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Solver.Name7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Ruled ThruSections ( expression ) = {
Solver.Name8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
expression-list }; . . . . . . . . . . . . . . . . . . . . . . . 106
Solver.Name9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Ruled ThruSections { expression-list } . . . . . . 107
Solver.OctaveInterpreter . . . . . . . . . . . . . . . . . . . . . 278
Solver.Plugins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Solver.PythonInterpreter . . . . . . . . . . . . . . . . . . . . . 278
S Solver.RemoteLogin0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Save string-expression ; . . . . . . . . . . . . . . . . . . . . . . 117 Solver.RemoteLogin1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Save View[expression ] string-expression ; . . . 119 Solver.RemoteLogin2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
SendToServer View[expression ] Solver.RemoteLogin3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
string-expression ; . . . . . . . . . . . . . . . . . . . . . . . 119 Solver.RemoteLogin4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
SetChanged; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Solver.RemoteLogin5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
SetCurrentWindow expression ; . . . . . . . . . . . . . . . . 100 Solver.RemoteLogin6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
SetFactory(string-expression ); . . . . . . . . . . . . . . 101 Solver.RemoteLogin7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
SetMaxTag Point | Curve | Surface | Volume ( Solver.RemoteLogin8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Solver.RemoteLogin9 . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
SetName string-expression ; . . . . . . . . . . . . . . . . . . . 101 Solver.ShowInvisibleParameters . . . . . . . . . . . . . . 280
SetNumber( string-expression , expression ); Solver.SocketName . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Solver.Timeout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
SetOrder expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Sphere ( expression ) = { expression-list };
SetString( string-expression , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
string-expression ); . . . . . . . . . . . . . . . . . . . . . . 99 Sphere | PolarSphere ( expression ) =
ShapeFromFile( string-expression ); . . . . . . . . . 100 {expression, expression }; . . . . . . . . . . . . . . . 110
Show { : } . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Spline ( expression ) = { expression-list };
Sin ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Sinh ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Split Curve { expression } Point {
Sleep expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 expression-list }. . . . . . . . . . . . . . . . . . . . . . . . . 109
Smoother Surface { expression-list } = SplitCurrentWindowHorizontal expression ; . . . 100
expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 SplitCurrentWindowVertical expression ; . . . . . 100
Solver.AlwaysListen . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Sqrt ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Solver.AutoArchiveOutputFiles . . . . . . . . . . . . . . . 279 string *= expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . 98
432 Gmsh 4.11.1

string += { expression-list }; . . . . . . . . . . . . . . . . 98 U
string += expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . 98 UnsplitWindow; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
string -= { expression-list }; . . . . . . . . . . . . . . . . 98
string -= expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . 98
string /= expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . 98 V
string = { }; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 View "string " { string < ( expression-list ) > {
string = expression ; . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 expression-list }; ... }; . . . . . . . . . . . . . . . . 119
string = string-expression ; . . . . . . . . . . . . . . . . . . . 99 View.AbscissaRangeType . . . . . . . . . . . . . . . . . . . . . . . 285
string [ { expression-list } ] *= { View.AdaptVisualizationGrid . . . . . . . . . . . . . . . . . 285
expression-list };. . . . . . . . . . . . . . . . . . . . . . . . . 98 View.AngleSmoothNormals . . . . . . . . . . . . . . . . . . . . . . 285
string [ { expression-list } ] += { View.ArrowSizeMax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
expression-list };. . . . . . . . . . . . . . . . . . . . . . . . . 98 View.ArrowSizeMin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
string [ { expression-list } ] -= { View.Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
expression-list };. . . . . . . . . . . . . . . . . . . . . . . . . 98 View.AutoPosition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
string [ { expression-list } ] /= { View.Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
expression-list };. . . . . . . . . . . . . . . . . . . . . . . . . 99 View.AxesAutoPosition . . . . . . . . . . . . . . . . . . . . . . . . 285
string [ { expression-list } ] = { View.AxesFormatX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
expression-list };. . . . . . . . . . . . . . . . . . . . . . . . . 98 View.AxesFormatY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
string-option = string-expression ; . . . . . . . . . . . 99 View.AxesFormatZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
string [] += Str( string-expression-list ) ; View.AxesLabelX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 View.AxesLabelY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
string [] = { expression-list }; . . . . . . . . . . . . . . . 98 View.AxesLabelZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
string [] = Str( string-expression-list ) ; . . . 99 View.AxesMaxX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Structured . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 View.AxesMaxY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
Surface ( expression ) = { expression-list } < View.AxesMaxZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
In Sphere { expression }, Using Point { View.AxesMikado . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
expression-list } >;. . . . . . . . . . . . . . . . . . . . . . 104 View.AxesMinX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Surface Loop ( expression ) = { expression-list View.AxesMinY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
} < Using Sewing >; . . . . . . . . . . . . . . . . . . . . . . . . 104 View.AxesMinZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Symmetry { expression-list } { transform-list } View.AxesTicsX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 View.AxesTicsY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
SyncModel; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 View.AxesTicsZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
SystemCall string-expression ; . . . . . . . . . . . . . . . 101 View.Boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
View.CenterGlyphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
View.Clip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
T View.Closed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
View.Color.Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Tan ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 View.Color.Background2D . . . . . . . . . . . . . . . . . . . . . . 297
Tanh ( expression ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 View.Color.Hexahedra . . . . . . . . . . . . . . . . . . . . . . . . . 296
Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 View.Color.Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
ThruSections ( expression ) = { expression-list View.Color.Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
}; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 View.Color.Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
ThruSections { expression-list } . . . . . . . . . . . . . 107 View.Color.Prisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Torus ( expression ) = { expression-list }; View.Color.Pyramids . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 View.Color.Quadrangles . . . . . . . . . . . . . . . . . . . . . . . 296
TotalMemory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 View.Color.Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Transfinite Curve { expression-list-or-all } = View.Color.Tetrahedra . . . . . . . . . . . . . . . . . . . . . . . . 296
expression < Using Progression | Bump View.Color.Text2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
expression >; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 View.Color.Text3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Transfinite Surface { expression-list-or-all } View.Color.Triangles . . . . . . . . . . . . . . . . . . . . . . . . . 296
< = { expression-list } > < Left | Right | View.Color.Trihedra . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Alternate | AlternateRight | AlternateLeft View.ColormapAlpha . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
> ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 View.ColormapAlphaPower . . . . . . . . . . . . . . . . . . . . . . 287
Transfinite Volume { expression-list } < = { View.ColormapBeta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
expression-list } > ; . . . . . . . . . . . . . . . . . . . . . 114 View.ColormapBias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 View.ColormapCurvature . . . . . . . . . . . . . . . . . . . . . . . 287
TransformMesh { expression-list } { View.ColormapInvert . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
transform-list };. . . . . . . . . . . . . . . . . . . . . . . . . 114 View.ColormapNumber . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
TransformMesh { expression-list }; . . . . . . . . . . 114 View.ColormapRotation . . . . . . . . . . . . . . . . . . . . . . . . 287
TransfQuadTri { expression-list } ;. . . . . . . . . . 114 View.ColormapSwap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Translate { expression-list } { transform-list View.ColorTable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 View.ComponentMap0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
View.ComponentMap1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
View.ComponentMap2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Syntax index 433

View.ComponentMap3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.NormalRaise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292

View.ComponentMap4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.Normals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
View.ComponentMap5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.OffsetX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
View.ComponentMap6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.OffsetY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
View.ComponentMap7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.OffsetZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
View.ComponentMap8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.PointSize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
View.CustomAbscissaMax . . . . . . . . . . . . . . . . . . . . . . . 288 View.PointType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
View.CustomAbscissaMin . . . . . . . . . . . . . . . . . . . . . . . 288 View.PositionX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.CustomMax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.PositionY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.CustomMin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 View.RaiseX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DisplacementFactor . . . . . . . . . . . . . . . . . . . . . . 288 View.RaiseY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DoubleClickedCommand . . . . . . . . . . . . . . . . . . . . 283 View.RaiseZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawHexahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.RangeType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawLines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.SaturateValues . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawPrisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.ScaleType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawPyramids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.ShowElement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawQuadrangles . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.ShowScale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
View.DrawScalars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.ShowTime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.DrawSkinOnly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.SmoothNormals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.DrawStrings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.Stipple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.DrawTensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.Stipple0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.DrawTetrahedra . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.Stipple1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.DrawTriangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.Stipple2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.DrawTrihedra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 View.Stipple3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.DrawVectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.Stipple4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.Explode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.Stipple5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.ExternalView . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.Stipple6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.FakeTransparency . . . . . . . . . . . . . . . . . . . . . . . . 290 View.Stipple7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.FileName. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 View.Stipple8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.ForceNumComponents . . . . . . . . . . . . . . . . . . . . . . 290 View.Stipple9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
View.Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 View.Tangents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.GeneralizedRaiseFactor . . . . . . . . . . . . . . . . . 290 View.TargetError . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.GeneralizedRaiseView . . . . . . . . . . . . . . . . . . . . 290 View.TensorType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.GeneralizedRaiseX . . . . . . . . . . . . . . . . . . . . . . . 283 View.Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.GeneralizedRaiseY . . . . . . . . . . . . . . . . . . . . . . . 283 View.TimeStep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.GeneralizedRaiseZ . . . . . . . . . . . . . . . . . . . . . . . 283 View.TransformXX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.GlyphLocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.TransformXY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 View.TransformXZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
View.Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.TransformYX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.IntervalsType . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.TransformYY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 View.TransformYZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.LightLines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.TransformZX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.LightTwoSide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.TransformZY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.LineType. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.TransformZZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.LineWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.Max . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.UseGeneralizedRaise . . . . . . . . . . . . . . . . . . . . . 295
View.MaxRecursionLevel . . . . . . . . . . . . . . . . . . . . . . . 291 View.VectorType . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.MaxVisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.Visible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.MaxX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 View.Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
View.MaxY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Volume ( expression ) = { expression-list };
View.MaxZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 ............................................ 105
View.Min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
View.MinVisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
View.MinX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 W
View.MinY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Warning|Error ( string-expression <,
View.MinZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 expression-list > ); . . . . . . . . . . . . . . . . . . . . . . 100
View.Name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 Wedge ( expression ) = { expression-list };
View.NbIso . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
View.NbTimeStep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 Wire ( expression ) = { expression-list }; . . 103