FASTCD: Fracturing-Aware Stable Collision Detection

1. FASTCD: Fracturing-Aware Stable Collision Detection Jae-Pil Heo1, Joon-Kyung Seong1, Duksu Kim1, Miguel A. Otaduy2, Jeong-Mo Hong3, Min Tang4, and Sung-Eui Yoon1 1KAIST, 2URJC Madrid, 3Dongguk Univ, 4Zhejiang Univ. http://sglab.kaist.ac.kr/FASTCD

2. Collision Detection (CD) • Collision detection is an essential part of various applications • Physically-based simulation • Games • Robotics KAIST Hubo cloth simulation Quake 4

3. Inter- and Self- Collisions • Inter-collisions • Collisions between two objects • Self-collisions (intra-collisions) • Collisions betweendifferent parts of one object • Takes much longer computation time (~100x)than inter-collisions from Govindaraju’s work

4. CD for Fracturing Models • Fracturing • changes topology (connectivity) of a mesh  pre-computed information and acceleration structures become useless • places many objects in close proximity  CD cost is increasing • Fracturing is one of the most challenging scenarios of collision detection

5. Goals • Design a collision detection method that provides followings: • efficient performance for detecting inter- and self-collisions • stable performance with deforming models that have geometric and topological changes

6. Our Contributions • A novel culling method for self-collision detection, dual-cone method, which is suitable for fracturing models • A BVH selective restructuring method based on a novel cost estimation metric and a fast BVH construction technique for fracturing models

7. Benchmarks

8. Previous Work (1/2) • BVH update methods • Refit • [Teschner et al, 2005] • Reconstruction • [Wald et al, 2006] • Selective restructuring • [Larsson et al, 2006], [Yoon et al, 2006] • Selective restructuring for progressively fracturing models • [Otaduy et al, 2006] • Less attention to topology changing models

9. Previous Work (2/2) • Culling techniques for self-CD • Reduce redundant tests (low level culling) • [Curtis et al. 2008] • [Tang et al. 2010] • Easily combined with our method • Detect self-collision free regions (high level culling) • [Volino and Thalmann 1994] • [Tang et al, 2008] • [Sara et al, 2010] • Do not directly consider topology changes

10. Outline • Background • Dual-Cone Method • BVH Update Method • Comparison • Conclusion

11. Outline • Background • Dual-Cone Method • BVH Update Method • Comparison • Conclusion

12. Bounding Volume Hierarchies (BVHs) • Organize bounding volumes as a tree • Leaf nodes have triangles

13. BVH-based CD • BVH traversal BV overlap test A A X X B C Y Z Dequeue (A,X) Collision test pair queue

14. BVH-based CD • BVH traversal BV overlap test A X B C Y Z Dequeue Refine Self-CD (B,Y) (B,Z) (C,Y) (C,Y) (B,C) (Y,Z) Collision test pair queue What if “A” does not have any self-collisions?

15. Self-Collision Free Conditions[Volino and Thalmann 1994] SNC • surface is rather flat • Surface Normal Cone (SNC) bounds surface normals • apex angle of SNC α< 90º • Efficiently constructed and updated with BVHs [Provot 1997] • No self-intersection on projected contour( contour test ) • Quadratic time complexity • Dual-Cone method reduces this overhead α

16. Intuition of Dual-Cone Method • Consider the curvature of projected contour • Binormal: perpendicular to both surface normal and contour • Binormal Cone (BNC) bounds binormals • No self-intersection on contour axis angle of BNC β < 90º • Dual-Cone: SNC and BNC β Contour without self-intersection β Contour with self-intersection

17. Conservativeness of Dual-Cone • Dual-Cone method does not provide culling for a whole surface, since it is too conservative

18. Dual-Cone Method with BVH • Combine with BVH to provide practical culling • Ignore virtual contour • virtual contour: caused by bounding volume split (---) • Can bring counter-example • Did not miss any collisions in our complex benchmarks C C C C C: No Self-Collision (culling)

19. Dual-Cone Method • Dual-Cone • SNC: surface normal cone • BNC: binormal cone • Contour test can be replacedwith a test that whether axis of SNC is inside BNC or not C C

20. Result of Dual-Cone Method • Dynamic topology model • About 100x performance improvement at fracturing events prior method need pre-computations • Fixed topology model • Did not miss collisions • Comparable performance with “No Test”  Low culling overhead

21. Dual-Cone Method • Pros • Low culling overhead O(1) for each node [Provot 1997] • Efficiently constructed and updatedfor fracturing models • Cons • Approximate culling

22. Outline • Background • Dual-Cone Method • BVH Update Method • Comparison • Conclusion

23. Selective Restructuring of BVHs • As models deform, culling efficiency of their BVHs can be getting lower • should be restructured • How to determine efficiency of BVH? • LM metric : Overlap volume of sibling nodes [Larsson and Akenine-Möller 2006] • Our cost metric measures expected number of intersection tests ! Deform Restructuring

24. Cost Estimation Metric (1/2) • = expected # of intersection tests from node for self-collision detection • Recurrence formula • Replace with cost terms • No self-collision at  (Dual-Cone ) • Dual-Cone operator A n nL nR

25. Cost Estimation Metric (2/2) • Cost estimation metric for inter-collision detection [Yoon and Manocha 2006] • We approximate • Finally we obtain • Metric values can be computed in bottom-up BVH refitting process

26. Metric Validation • Estimated # of tests vs Observed # of tests • Linear Correlation : 0.71 • for various models ( 0.28 ~ 0.76 , average 0.48 )

27. Selective Restructuring using Our Metric compute CD Compute deform -restructure -update

28. Result of Selective Restructuring • LM metric : [Larsson and Akenine-Möller 2006] • Performance degradations at topological changes  unstable 252K triangles, dynamic topology

29. Fast BVH Construction Method • At a fracturing event, BVH for fractured part should be re-constructed • causes noticeable performance degradation • Propose BVH construction method based on grid and hashinginstead of typical NlogN methods • Constructed hierarchy haslow culling efficiency, but requires less construction time • Overall performance improved at fracturing events

30. Result of Fast BVH Construction • Performance degradations at fracturing events are reduced

31. Comparison (Continuous-CD) • 260x faster than T-CCD [Tang et al. 2008] at topology changes • Our method shows stable performance • Characteristics of benchmarks! 252K triangles, dynamic topology

32. Comparison (Discrete-CD) • 20x faster than optimized spatial hashing [Teschner et al, 2003] (S-Hash) • Stable performance 42~140K triangles, dynamic topology

33. Limitations • Dual-Cone method combined with BVHs is an approximate method • BVH selective restructuring method using our cost estimation metric does not guarantee to always improve the performance • Finalize with positive

34. Conclusion • Stable CD methods for fracturing models • Dual-cone culling method for self-collision detection • BVH selective-restructuring method using our cost estimation metric measuring estimated # of intersection tests • Fast BVH construction method that reduces performance degradations at fracturing events • 260x performance improvement at fracturing event over prior BVH based CD method • 20x performance improvement over optimized spatial hashing

35. Fracturing Benchmarks • Our fracturing benchmarks are at:http://sglab.kaist.ac.kr/models • Our project page:http://sglab.kaist.ac.kr/FASTCD

36. Acknowledgments • Members of Scalable Graphics Lab, KAIST • Anonymous reviewers • Funding agencies • MEST, NSFC, Spanish Dept. of Science and Innovation, BK, KAIST, IITA, KRF, MSRA, ADD, MKE, KSEF

37. Thanks for your attention. Any question or feedback?