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Efficient Polygonal Model Repair with Dual Surface Algorithm

This research presents a robust and efficient method for closing arbitrary polygonal models, preserving surface quality and geometric features. The Dual Surface Algorithm partitions the space into inside and outside volumes, allowing for seamless model repair. By integrating patches using octree-based techniques, holes are filled accurately and models are efficiently processed on standard PCs. The method is simple, accurate, and ensures the preservation of geometry features in large models. Future work includes improving hole-filling quality and using adaptive grids for repairs.

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Efficient Polygonal Model Repair with Dual Surface Algorithm

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  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

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

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

  12. 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”

  13. 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

  14. 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

  15. 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

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

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

  18. Examples – CAD Model Input Model

  19. Examples – CAD Model Dual Surface

  20. Examples – CAD Model Closed Dual Surface

  21. Examples – CAD Model Output (Marching Cubes)

  22. Examples – CAD Model Output (Dual Contouring)

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

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

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

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

  27. 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

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