1. Simplification of Arbitrary Polyhedral Meshes Shaun D. Ramsey* Martin Bertram Charles Hansen University of Utah University of Kaiserslautern University of Utah *Presented by Shaun D. Ramsey at CGIM 2003 ramsey()cs.utah.eduramsey()cs.utah.edu http://www.cs.utah.edu/~ramsey/research

2. Motivation  Model Size  Interactive/Hardware Rendering Editing  Modeling Programs  Transmission

3. Previous Work  Level of Detail (LOD)  Progressive Meshes (PM)  Edge Collapses  Triangulate Polygons From Sander’s Texture Mapped Progressive Meshes

4. The Process  Edge Selection  Vertex Selection  Edge Collapse

5. The Process  Edge Selection  Vertex Selection  Edge Collapse

6. The Process  Edge Selection  Vertex Selection  Edge Collapse

7. Edge Selection  For All Edges Compute Error  Choose Minimal Error  Error Metric Dot Product Test Add Threshold

8. Polygon Normals  Triangles  Quads  N-sided  A A A B B B A = p - p ; B = p - p i- 1 i i+ 1 i

9. Refined Edge Selection  Pre-computation  Random Selection  Single Selection

10. Vertex Selection  Half-edge  Full-edge

11. Vertex Selection  Half-edge  Full-edge

12. Collapse and Split

13. Options  Half or Full-edge Collapses  Changing the Error Metric  Error Threshold  Percent/Number of Edges Searched  Treat N-sided Polygons Differently

14. Threshold Differences – Maximum Simplification 256 1478 6492 13795 0.950 0.990 0.999 0.9999

15. Threshold Differences Remove 15000 Polygons 0.00 minimum dot product 0.99 minimum dot product

16. Results Percentage Search Original 42 Edges 425 Edges

17. Results Simplification ~870k polygons ~370k polygons

18. Results LOD Simplification 871k378k 67k

19. Results – Timing ModelOriginalSimplifiedTime (s) Dragon8714144858442.900 Bunny6945169584.110 Crocodile21590116953.670 Venus42547110.310 0.99 minimum dot product, search 1% of the mesh

20. Future Work  Selective Refinement  Multi-resolution Editing  Preservation of Feature Lines  Surface Parameterization  Surface Segmentation

21. Acknowledgements  Utah Graphics Group  Stanford Scanning Repository  Avalon