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

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

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

The Process  Edge Selection  Vertex Selection  Edge Collapse

The Process  Edge Selection  Vertex Selection  Edge Collapse

The Process  Edge Selection  Vertex Selection  Edge Collapse

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

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

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

Vertex Selection  Half-edge  Full-edge

Vertex Selection  Half-edge  Full-edge

Collapse and Split

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

Threshold Differences – Maximum Simplification

Threshold Differences Remove Polygons 0.00 minimum dot product 0.99 minimum dot product

Results Percentage Search Original 42 Edges 425 Edges

Results Simplification ~870k polygons ~370k polygons

Results LOD Simplification 871k378k 67k

Results – Timing ModelOriginalSimplifiedTime (s) Dragon Bunny Crocodile Venus minimum dot product, search 1% of the mesh

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

Acknowledgements  Utah Graphics Group  Stanford Scanning Repository  Avalon