Direct Sampling on Surfaces for High Quality Remeshing

1. Direct Sampling on Surfaces for High Quality Remeshing Yan Fu Bingfeng Zhou fuyan@icst.pku.edu.cn cczbf@pku.edu.cn Peking University Presenter: XiaoXiao Hou

2. Motivation • Triangle meshes • Prevalent form of 3D model representation • Quality of meshes • Geometry • Connectivity • Remeshing • Isotropic Sampling

3. Previous work • Parametrization-based remeshing • Parametrization • Local [Eck et al.1995] • Global [Gu2002] • Sampling • Uniform sampling [Lee1998] • Importance Sampling [Alliez2002]

4. Previous work • Sampling Directly on Mesh Surface • Greedy approaches [Gabriel2005, Boissonnat2003] • Delaunay/Voronoi Criteria • Relaxation-based approaches [Turk 1992, Alliez2003] • Expel and attract force

5. Surface Sampling on Triangle Meshes • Directly sampling on mesh surface • Poisson-Disk sampling • Dart-Throwing • Expellant Disk：R • Fast Poisson-Disk sampling[Dunbar2006] • Available boundary：2R • Confined to 2D and uniform • How to sample 3D mesh surface?

6. Surface Sampling on Triangle Meshes • Flow chart of Poisson-Disk Sampling on 2-Manifold Triangle Meshes no Find an initial sample p0 Compute the available boundary of p0 Get a new sample ，and re-compute the available boundary Update available boundary Compute the available boundary of p0 Is AB NULL yes End

7. Surface Sampling on Triangle Meshes • Uniform sampling • Available boundary • Isoline with distance of 2R • Exact Isoline Extraction • Based on fast MMP algorithm [Surazhsky2005] • Represented with continuous curves

8. Surface Sampling on Triangle Meshes • Updating Available Boundary • The arcs are arranged in clock-wise order • Compute the intersection between Bnew and Bwhole • Keep/Discard Decision • The arc that does not lies in the Bwhole Keep • Stable & fast • The arc where new sample lies on Discard • Stable & fast • Local parametrization: line & Bnew intersection • Odd : Keep • Even: Discard

9. Surface Sampling on Triangle Meshes

10. Surface Sampling on Triangle Meshes • Adaptive Poisson-Disk Sampling • Radius of expellant disk • Available boundary • The set of the nearest points that can be used as the next sample • Property of Available boundary • Conic curves

11. Surface Sampling on Triangle Meshes • Experimental results

12. Surface Sampling on Triangle Meshes • Experimental results

13. Application 1——Object distribution • Object Distribution

14. Application 2——Texture mapping

15. Progressive sampling • 2D

16. Progressive sampling • Experimental results

17. High-Quality Remeshing • Remeshing • 3D Delaunay • Topology errors

18. High-Quality Remeshing • Remeshing • 3D Delaunay • Topology errors • Utilize topology information of the original mesh • Mutual Tessellation • Remove the original vertices • Guarantee topology consistence

19. p1 p2 c1 c6 p c2 p’ p6 p3 c3 c5 c4 p5 p4 High-Quality Remeshing • Location Optimization • Centroidal Voronoi Tessellation [Du2002] • Move each vertex to the center of CVT • Several iterations • Connectivity Optimization • Edge flip

20. High-Quality Remeshing

21. High-Quality Remeshing • Remesh the result of boolean operation + Adaptive Uniform

22. High-Quality Remeshing • Comparison • Models with different genus and complexity

23. High-Quality Remeshing • Comparison

24. High-Quality Remeshing • Feature preservation • Feature extraction[Jiao2002] • Continuous • Robust • Feature Re-sampling

25. High-Quality Remeshing • Experimental results Remeshed Original

26. Summary • Direct Poisson-Disk sampling on Triangle meshes • Uniform • Adaptive • Application • Object distribution • Texture mapping • Progressive mapping • High-quality remeshing

27. Thank you!