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Simplification of Arbitrary Polyhedral Meshes: 

Simplification of Arbitrary Polyhedral Meshes *Presented by Shaun D. Ramsey at CGIM 2003 ramsey()cs.utah.edu http://www.cs.utah.edu/~ramsey/research

Motivation: 

Motivation Model Size Interactive/Hardware Rendering Editing Modeling Programs Transmission

Previous Work: 

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

The Process: 

The Process Edge Selection Vertex Selection Edge Collapse

The Process: 

The Process Edge Selection Vertex Selection Edge Collapse

The Process: 

The Process Edge Selection Vertex Selection Edge Collapse

Edge Selection: 

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

Polygon Normals: 

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: 

Refined Edge Selection Pre-computation Random Selection Single Selection

Vertex Selection: 

Vertex Selection Half-edge Full-edge

Vertex Selection: 

Vertex Selection Half-edge Full-edge

Collapse and Split: 

Collapse and Split

Options: 

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 – Maximum Simplification 256 1478 6492 13795 0.950 0.990 0.999 0.9999

Threshold Differences Remove 15000 Polygons: 

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

Results Percentage Search: 

Results Percentage Search Original 42 Edges 425 Edges

Results Simplification: 

Results Simplification ~870k polygons ~370k polygons

Results LOD Simplification: 

Results LOD Simplification 871k 378k 67k

Results – Timing: 

Results – Timing 0.99 minimum dot product, search 1% of the mesh

Future Work: 

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

Acknowledgements: 

Acknowledgements Utah Graphics Group Stanford Scanning Repository Avalon