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.edu

http://www.cs.utah.edu/~ramsey/research

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

AA

BBB

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

256 1478 6492 137950.950 0.990 0.999 0.9999

Threshold DifferencesRemove 15000 Polygons

0.00 minimum dot product 0.99 minimum dot product

ResultsPercentage Search

Original 42 Edges 425 Edges

Results Simplification

~870k polygons ~370k polygons

ResultsLOD Simplification

871k 378k 67k

Results – Timing

Model Original Simplified Time (s)

Dragon 871414 48584 42.900

Bunny 69451 6958 4.110

Crocodile 21590 11695 3.670

Venus 4254 711 0.310

0.99 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