Modeling 3D objects with

polygons

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 Why polygons?
 Simple mathematical description
 Standard 3D graphics primitive
 All graphics packages optimized for polygon
throughput
 Most 3D graphics algorithms assume a
polygon-based scene
 Common polygon algorithms implemented in
hardware
 In the end, everything (well, almost
everything) is a polygon
(C) Doug Bowman, Virginia Tech, 2008 2

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 Terminology
 Polygon soup: a
general set of
unstructured polygons
used to define a scene
 Polygonal mesh: a set
of connected polygons
that together form a
surface
(C) Doug Bowman, Virginia Tech, 2008 3

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 More terminology
 3D polygonal model: a 3D object made
up entirely of polygons
 3D polygonal modeling: the process of
building a 3D object by specifying the
polygons that make up that object
 NOTE: you can build a 3D polygonal model
without using 3D polygonal modeling!

(C) Doug Bowman, Virginia Tech, 2008 4

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 Methods of creating polygonal
meshes

 Build mesh by hand

(C) Doug Bowman, Virginia Tech, 2008 5

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 Methods of creating polygonal
meshes

 Tesselate a
theoretical smooth
surface
 Tesselation: the
process of creating a
polygonal
approximation from
a smooth surface

(C) Doug Bowman, Virginia Tech, 2008 6

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 Methods of creating polygonal
meshes
 Extrude a 2D
polygon, curve,
etc.
 Extrusion: the
process of moving
a 2D cross-section
through space to
create a 3D solid

(C) Doug Bowman, Virginia Tech, 2008 7

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 Methods of creating polygonal
meshes

 Revolve/sweep a 2D
polygon or curve
 Revolution: the
process of rotating a
2D cross-section about
an axis to create a 3D
solid

(C) Doug Bowman, Virginia Tech, 2008 8

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 Problems with polygonal
models
 They approximate smoothly curving
surfaces
 Tradeoff between realism and efficiency
 Lots of polygons: good approximation,
slow to process
 Few polygons: fast processing, poor
approximation

(C) Doug Bowman, Virginia Tech, 2008 9

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 Polygonal simplification
 Decrease the number of polygons without
sacrificing visual quality (meet polygon
budget)

30944 triangles 2502 triangles 621 triangles 251 triangles

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 Level of detail (LOD)
techniques
 LOD: change the
complexity of the
model/image
dynamically to
maintain real-time
performance
 Ex: use simplified
models when objects
are at a great distance
 “Popping” problem
(C) Doug Bowman, Virginia Tech, 2008 11

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 Texture substitution
 Textures
(“imposters”) can
cause objects to
appear much more
detailed than they
actually are
 Problem: when the
user is close
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 Rendering polygonal meshes
 Simply use traditional raster graphics
techniques
 Proper lighting depends on proper
normals
 Face normal: the normal to the plane in which
a polygon lies
 Vertex normal: the normal to the underlying
surface (being approximated by a polygonal
mesh) at a particular vertex

(C) Doug Bowman, Virginia Tech, 2008 13

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 Face normals vs. vertex
normals

(C) Doug Bowman, Virginia Tech, 2008 14

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 Practical polygonal modeling
 Modeling tools
 3D Studio Max
 Maya
 AutoCAD
 …
 File formats
 OBJ, DXF, 3DS, FLT, DWG, …

(C) Doug Bowman, Virginia Tech, 2008 15

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 Alternatives to polygonal
modeling
 As we noted, almost everything is a polygon
eventually, but the modeling process does
not have to be based on polygons
 Instead, we can model objects using smooth
higher-order surfaces, and only convert to
polygons in order to render
 Also, we can model volumes instead of
surfaces
 Next: modeling with curves/surfaces

(C) Doug Bowman, Virginia Tech, 2008 16

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