1. CS4995-1: ModelingPage 1 Modeling Polygonal and mesh representation Spline curves and patches Procedural modelling Geometry compression –Mesh simplification –Triangle strips and fans Level of Detail (LOD) Landscapes –Height fields –Fractals

2. CS4995-1: ModelingPage 2 Polygons ObjectSurfacesPolygons Vertices, Edges, Faces Vertex Edge Face

3. CS4995-1: ModelingPage 3 Polygonal Meshes

4. CS4995-1: ModelingPage 4 15 th c Mesh drawing A pen and ink drawing of a wireframe chalice ("Perspective Study of a Chalice"), done by Paolo Uccelloin 1430-1440, Florence, Italy.

5. CS4995-1: ModelingPage 5 Splines Cubic (Hermite) Spline –Points P1, P4 Tangent vectors R1, R4 –C(0) continuity Bezier Spline –Points P1, P4 Tangent vectors R1, R4 –Points form convex hull –C(0) continuity B-spline –Curve approximates points –C(0), C(1), C(2) continuity Interactive demo at http://www.siggraph.org/education/materials/HyperGraph/modeling/splines/demoprog/curve.html

6. CS4995-1: ModelingPage 6 Spline surfaces Cross-sections are splines Same continuity concerns as splines Control surface Control point Spline surface

7. CS4995-1: ModelingPage 7 Procedural modeling Architecture [pictures of many kinds of parts (roofs, windows, walls) and then completed building(s)] Plants (L-Systems) Patterns – procedurally generated tilings, brick, etc.

8. CS4995-1: ModelingPage 8 L-Systems ignore X# X will be ignored seed X rule F -> F F rule X -> F [+ X] F [+ X] - X delta 22.5 theta 90 leng 230 iter 6 ratio 2 x 0 y -230 red 0.0# color component between 0 and 1 green 0.6# blue 0.2#

9. CS4995-1: ModelingPage 9 L-Systems From PRUSINKIEWICZ

10. CS4995-1: ModelingPage 10 Geometry Compression Triangle strips and fans 1 2 3 4 5 6 7 8 9 10 12 13 14

11. CS4995-1: ModelingPage 11 Geometry Compression Mesh Simplification Vertex clustering Decimation Re-tiling –Use for computed meshes Wavelets

12. CS4995-1: ModelingPage 12 simplificati on A multi-resolution model obtained by simplification of the original model (in the top left corner). The number of triangles are respectively 96966, 13334, 3334 and 668. From the GTS library http://gts.sourceforge.net

13. CS4995-1: ModelingPage 13 Level of Detail http://gts.sourceforge.net/gallery/horse.mpeg

14. CS4995-1: ModelingPage 14 Landscapes Height fields Represent terrain as points at an altitude

15. CS4995-1: ModelingPage 15 Fractals

16. CS4995-1: ModelingPage 16 http://www.pandromeda.com Fractal image

17. CS4995-1: ModelingPage 17 Root World Room floor wall wall wall wall ceiling chair window texture light geo tex Scene Graph Directed acyclic graph (or tree) to organize and structure elements of a scene. –Allows clear and unambiguous scope of influence of scene parameters.