FASTCD: Fracturing-Aware Stable Collision Detection Jae-Pil Heo 1, Joon-Kyung Seong 1, Duksu Kim 1, Miguel A. Otaduy 2, Jeong-Mo Hong 3, Min Tang 4, and Sung-Eui Yoon 1 1 KAIST, 2 URJC Madrid, 3 Dongguk Univ, 4 Zhejiang Univ.

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

3 Inter- and Self- Collisions ●Inter-collisions ●Collisions between two objects ●Self-collisions (intra-collisions) ●Collisions between different 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 Cloth-BallExploding-DragonBreaking-Walls video # of topology changes 0 fixed topology 4 dynamic topology 8 dynamic topology complexity92K252K -> 252K42K -> 140K

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 A BC X YZ Collision test pair queue (A,X)(A,X) ●BVH traversal AX Dequeue BV overlap test

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

15 Self-Collision Free Conditions [Volino and Thalmann 1994] ●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 SNC 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 Contour with self-intersection Contour without self-intersection β β

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 CCC C: No Self-Collision (culling)

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

20 Result of Dual-Cone Method Contour TestMiss Collisions ?Culling RatioFPS No TestYes49%3.40 VT94No48%2.54 Dual-ConeNo46%3.24 ●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 updated for 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 nLnL nRnR n

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 CDCompute 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 hashing instead of typical NlogN methods ●Constructed hierarchy has low 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: ●Our project page:

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?