1. Polygon Modelling

2. 3D Representation Wire frame NURBS surface Solid Voxel Mesh

3. 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

4. Facets and vectors

5. Normal vector a facet determine its ‘direction’ Normals point to the OUTSIDE Most rendering software has ‘render back- face’ option For facets without normal vector, direction determine by Right-hand rule

6. Euler Equation V – E + F = 2  V – Vertex  E – Edge  F – Face Polygon body must satisfy this relation Try it on a cube

7. Features

8. 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

9. 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

10. Curve approximation

11. Polygon models usually are only close APPROXIMATION of physical object The flatter, the more accurate The more facets, the better

12. 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

13. 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

14. Tessellation Also called Triangulation or Polygonization Conversion of NURBS surface or solid model to polygon surface

15. The Large Carriage, by Xavier Veilhan, Jean Nouvel & Renzo Piano, by Xavier Veilhan,

16. Applications Rapid prototyping Digital sculpting Rendering and Game Design collaboration