Polygon Modelling

3D Representation

Wire frameNURBS surfaceSolidVoxelMesh

Polygon mesh

Any polygon mesh can be convert to triangle mesh

Can be rendered directly by graphic hardware

Easy to computeOne format, all geometries

Facets and vectors

Facets and vectors

Normal vector a facet determine its ‘direction’

Normals point to the OUTSIDEMost rendering software has ‘render back-

face’ optionFor 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 relationTry 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 EquationOK 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 accurateThe more facets, the better

File Size Implication

File size directly proportional to number of facet

Not related to physical sizeRelated to curvy/flat surface ratioRelated to number of small featuresRelated to resolution setting

Computation efficiency

Use native polygon model: eg. 3D StudioMaintain internal polygon model for

rendering: eg. RhinocerosMeshes are also used for scientific

calculationHardware accelerated real-time smoothing

makes high quality renderings with coarse models

Tessellation

Also called Triangulation or PolygonizationConversion 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