Simplification of Arbitrary Polyhedral Meshes

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.edu http//www.cs.utah.edu/ramse
y/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 Sanders 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 ?

B
B
B
A
A
A
A p - p B p - p
i-1 i i1 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
137950.950 0.990
0.999 0.9999
15
Threshold DifferencesRemove 15000 Polygons
0.00 minimum dot product 0.99 minimum dot
product
16
ResultsPercentage Search
Original 42 Edges
425 Edges
17
Results Simplification
870k polygons 370k
polygons
18
ResultsLOD Simplification
871k 378k 67k
19
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
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