When generating meshes for FEM/FVM computations, sometimes your geometry is so simple that you don't need a complex mesh generator (like pygmsh, MeshPy, mshr, pygalmesh, dmsh), but something simple and fast that makes use of the structure of the domain. Enter meshzoo.
Install meshzoo from PyPI with
pip install meshzoo
on your machine and you're good to go.
All generators return the points as a (num_points, dim) float64 array and the
cells as a (num_cells, nodes_per_cell) int64 array.
import meshzoo
bary, cells = meshzoo.triangle(8)
# corners = np.array(
# [
# [0.0, -0.5 * numpy.sqrt(3.0), +0.5 * numpy.sqrt(3.0)],
# [1.0, -0.5, -0.5],
# ]
# )
# points = np.dot(corners, bary).T
# Process the mesh, e.g., write it to a file using meshio
# meshio.write_points_cells("triangle.vtk", points, {"triangle": cells})import meshzoo
import numpy as np
points, cells = meshzoo.rectangle_tri(
np.linspace(0.0, 1.0, 11),
np.linspace(0.0, 1.0, 11),
variant="zigzag", # or "up", "down", "center"
)
points, cells = meshzoo.rectangle_quad(
np.linspace(0.0, 1.0, 11),
np.linspace(0.0, 1.0, 11),
cell_type="quad4", # or "quad8", "quad9"
)meshzoo.ngon(4, 8) |
meshzoo.ngon(6, 8) |
meshzoo.ngon(9, 8) |
import meshzoo
points, cells = meshzoo.ngon(5, 11)meshzoo.disk(4, 8) |
meshzoo.disk(6, 8) |
meshzoo.disk(9, 8) |
The disk meshes are inflations of regular polygons.
import meshzoo
points, cells = meshzoo.disk(6, 11)
points, cells = meshzoo.disk_quad(10, cell_type="quad4") # or "quad8", "quad9"import meshzoo
import numpy as np
points, cells = meshzoo.annulus_tri(
np.linspace(0.5, 1.0, 6), # radii of the circles of points
40, # points per circle
variant="zigzag", # or "up", "down"
)
points, cells = meshzoo.annulus_quad(
np.linspace(0.5, 1.0, 6), 40, cell_type="quad4" # or "quad8", "quad9"
)The domain [-1, 1]^2 without the quadrant (0, 1]^2, with the re-entrant
corner at the origin.
import meshzoo
points, cells = meshzoo.lshape_tri(10, variant="zigzag") # or "up", "down", "center"
points, cells = meshzoo.lshape_quad(10, cell_type="quad4") # or "quad8", "quad9"import meshzoo
points, cells = meshzoo.moebius(num_twists=1, nl=60, nw=11)import meshzoo
points, cells = meshzoo.uv_sphere(num_points_per_circle=20, num_circles=10, radius=1.0)
points, tri, quad = meshzoo.geo_sphere(
num_points_per_circle=20, num_circles=10, radius=1.0
)Spheres can also be generated by refining the faces of platonic solids and then "inflating" them. meshzoo implements a few of them. The sphere generated from the icosahedron has the highest-quality (most equilateral) triangles.
All cells are oriented such that their normals point outwards.
meshzoo.tetra_sphere(10) |
meshzoo.octa_sphere(10) |
meshzoo.icosa_sphere(10) |
import meshzoo
points, cells = meshzoo.ball_tetra(10)
points, cells = meshzoo.ball_hexa(10)import meshzoo
points, cells = meshzoo.tube(length=1.0, radius=1.0, n=30)import meshzoo
points, cells = meshzoo.torus(
num_points_major=60, num_points_minor=20, major_radius=1.0, minor_radius=0.3
)import meshzoo
import numpy as np
points, cells = meshzoo.cube_tetra(
np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)
)
points, cells = meshzoo.cube_hexa(
np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)
)Any planar mesh can be extruded along the z-axis: triangles become wedges or tetrahedra, quadrilaterals become hexahedra. This gives, e.g., cylinders and pipes.
import meshzoo
import numpy as np
z = np.linspace(0.0, 2.0, 11)
points, tri = meshzoo.disk(6, 10)
points, wedges = meshzoo.extrude(points, tri, z) # cylinder
points, tets = meshzoo.extrude(points, tri, z, cell_type="tetra")
points, quads = meshzoo.annulus_quad(np.linspace(0.5, 1.0, 6), 40)
points, hexa = meshzoo.extrude(points, quads, z) # pipe