Robust Repair of Polygonal Models

1. Robust Repair of Polygonal Models Tao Ju Rice University

2. Polygonal Models

3. Not Closed Closed Not Closed Closed Closed Model • Partitions the space into disjoint inside and outside volumes • Each polygon lies between inside and outside

4. Model Repair • Close polygonal models • Not just hole-filling • Challenges: • Models may contain complex errors • Models are often very big • Geometry features need to be preserved

5. Previous Work • Mesh-based model repair • Zippering [Turk and Levoy 1994] • Stitching [Barequet and Kumar 1997] • Progressive boundary decimation [Borodin et al. 2002] • Hole filling with fairing [Liepa 2003] • Scattered data reconstruction • Tangent plane estimation [Hoppe et al. 1992] • Level sets [Zhao and Osher 2002] • Radial basis functions [Turk and O’Brien 2002] • Partition-of-unity methods [Ohtake et al. 2003] • Moving least squares surfaces [Shen et al. 2004] • Context-based completion [Sharf et al. 2004]

6. Previous Work • Volumetric model repair • How to determine signs ? • How to generate surface ?

7. Previous Work • Volumetric model repair – Sign generation • Adaptive signed distances [Frisken et al. 2000] • Flood-filling [Oomes et al. 1997][Andujar et al. 2002] • Space carving [Curless and Levoy 1996] • Volumetric diffusion [Davis et al. 2002] • Parity count and ray stabbing [Nooruddin and Turk 2003] • Volumetric model repair – Contouring • Marching Cubes [Lorensen and Cline 1987] • Extended Marching Cubes [Kobbelt et al. 2001] • Dual Contouring [Ju et al. 2002]

8. Robust Model Repair • Robust • Closes arbitrary polygon soups • Efficient • Processes gigantic models on standard PCs • Accurate • Preserves surface quality • Simple !

9. “Dual Surface” Scan-convert Patch Contour Closed Dual Surface Algorithm in a Nutshell

11. Scan-conversion • Octree grid • Edges intersected with model • Top-down creation Memory-less octree construction Reliable and fast intersection tests

12. Dual Surface • Each face dual to an intersected octree edge Octree Edge Dual Face

13. Finding Holes • Boundary edges • Odd-valence edges • Closed dual surface No boundary edge • Set of boundary edges partitioned into cycles • Each cycle encloses a “hole”

14. Building a Patch • Build one patch for each cycle • Each quad dual to an octree edge • Patch boundary is the cycle • Divide-and-conquer! • Using octree

15. Integrating a Patch • Add a quad • If does not exist on the dual surface • Remove a quad • If already exists on the dual surface • Key: parity of edge valence

16. Integrating a Patch • Add a quad • If not already on the dual surface • Remove a quad • If already on the dual surface • Key: parity of edge valence

17. Sign Generation • Sign changes across dual surface • Flood-filling Dual Face Octree Signs

18. Contouring • Marching Cubes • Edge intersections • Rounded corners • Dual Contouring • Hermite data • Sharp features

19. Examples – CAD Model Input Model

20. Examples – CAD Model Dual Surface

21. Examples – CAD Model Closed Dual Surface

22. Examples – CAD Model Output (Marching Cubes)

23. Examples – CAD Model Output (Dual Contouring)

24. Examples - Bunny 1. Input 2. DS 4. Output 3. DS Closed Model Courtesy of the Stanford 3D Scanning Repository

25. Examples - Horse 1. Input 2. DS 4. Output 3. DS Closed Model Courtesy of the Stanford 3D Scanning Repository

26. Output Examples – David (at 1mm) Input Model Courtesy of the Digital Michelangelo Project

27. Performance • On PC with 1.5GHz CPU and 2GB memory

28. Conclusion • A simple, fast, and robust method to repair arbitrary polygon models • Future work • Remove topological noise • Improve the quality of hole filling • Repair using an adaptive grid • Special thanks to my advisor, Prof. Joe Warren, for his insights and support