Polygon Modelling
3D Representation
Wire frame
NURBS surface
Solid
Voxel
Mesh
Polygon mesh
Any polygon mesh can be convert to
triangle mesh
Can be rendered directly by graphic
hardware
Easy to compute
One format, all geometries
Facets and vectors
Facets and vectors
Normal vector a facet determine its
‘direction’
Normals point to the OUTSIDE
Most rendering software has ‘render backface’ option
For facets without normal vector, direction
determine by Right-hand rule
Euler Equation
V – E + F = 2
V – Vertex
E – Edge
F – Face
Polygon body must satisfy this relation
Try it on a cube
Features
Edges, holes, and genii
 Boundary edge – edge bounded by a single
triangle
 Hole – closed polygon of boundary edges
 Genus – ‘donuts’ of an object
 Physical object has neither boundary edge or
hole
 Most mesh formats has no build in check for
errors
 Similar to bitmap VS vector
Manifold
Polygon models with holes or naked
edges
The model is not ‘water-tight’ or ‘leaky’
Will not satisfy Euler Equation
OK for architectural, animation, etc.
Not acceptable for RP
Curve approximation
Curve approximation
Polygon models usually are only close
APPROXIMATION of physical object
The flatter, the more accurate
The more facets, the better
File Size Implication
File size directly proportional to number of
facet
Not related to physical size
Related to curvy/flat surface ratio
Related to number of small features
Related to resolution setting
Computation efficiency
Use native polygon model: eg. 3D Studio
Maintain internal polygon model for
rendering: eg. Rhinoceros
Meshes are also used for scientific
calculation
Hardware accelerated real-time smoothing
makes high quality renderings with coarse
models
Tessellation
Also called Triangulation or Polygonization
Conversion of NURBS surface or solid
model to polygon surface
The Large Carriage, by Xavier Veilhan,
Jean Nouvel & Renzo Piano, by Xavier Veilhan,
Applications
 Rapid prototyping
 Digital sculpting
 Rendering and Game
 Design collaboration