1. Interactive Continuous Collision Detection for Polygon Soups Xin Huang 11/20/2007

2. Introduction Discrete CD –Miss collision between sampled time instances Continuous Collision Detection (CCD)

3. Introduction Continuous Collision Detection (CCD) –Consider continuous motion –Report first time of contact (TOC) Well applied in –Cloth simulation –Rigid body Dynamics –Local planning

4. Motivation CCD in Local Planning –CCD is used to check collision along the interpolating trajectory between two free nearby samples –Perform the CCD query for samples near contact space is vital in local planning

5. Related work (1) Schwarzer [2002]: Exact collision checking  Use adaptive bisection approach  Can be used for polygon soups  Calculate un-directional motion bound  Work not well when separation distance is very small

6. Related work (2) [Redon 2002]  Use interval arithmetic to compute the motion bound  Continuous OBB test  Work not well when the motion has large rotation  Does not perform adaptive bisection, suffer from a large number of bisection steps when objects are far apart

7. Related work (3) [Zhang 06]: Extend conservative advancement  Compute continuous motion by linear interpolating  Perform hierarchy advancement based on convex hull tree  Benefit from motion coherence supported by swift++  As reported, perform more efficiently than [Redon 2002]

8. Challenge Exact CCD –Small separation distance [Redon 2002] –Large Rotation [Zhang 06] –Polygon soups –High number of convex pieces

9. Disassembly Plan (D-Plan) Efficient collision free path computation CAD/CAM models –non-manifold or polygon soups with no connectivity or topology information –have tight spaces and multiple narrow passages in configuration spaces

10. Some challenging benchmarks 200K+ polygons

11. 12,236 vertices 11,569 triangles Obstacle Robot 16,781 vertices 15,197 triangles Application in Assembly Maintainability: extract the part, there are many non-manifold parts in the robot

12. Goal Perform fast continuous collision detection for polygon soups in local planning for part disassembly

13. Main Approaches Perform conservative advancement (CA) for polygon soups Directional motion bound computation Hierarchical CA for BVH Explore motion coherence to accelerate

14. Conservative Advancement CA for Convex Polytopes –computes an upper bound of TOC by repeatedly advancing A by dt toward B while avoiding collision –When close enough, if TOC<1, then report collision; else report collision free

15. Conservative Advancement CA for non-convex objects –Convex decomposition –Assume the closed mesh CA for polygon soups –Using SSV based on PQP –Compute the motion bound for SSV –Compute the motion bound for triangle –Can process polygon soups

16. Directional motion bound computation Calculate linear motion interpolation –: U = V + W*R Project the motion along the direction of the closest distance d Compute the directional motion for BV and Triangle in Leaf BV d U

17. Hierarchical CA for BVH Bound volume traversal trees –Given two BVHs (HA, HB), starting from the root nodes, recursively perform pairwise TOC computation –If TOC(na, nb) < TOCcurrent, the recursive traversal continues; otherwise it stops

18. Explore motion coherence Temporal coherence in contact space sampling and constraint motion Motion coherence during each step of CA Compute the initial TOC according to the closest features stored in last iteration

19. Explore motion coherence Further benefit motion coherence by exploring local tree containing the closest features The initial small TOC will help culling many BV pair Tests and Triangle pair test

20. Algorithm 1. Build the Bound Volume traversal tree for object A and B 2. Compute the initial TOC using local tree motion coherence 3. Traverse the BVH tree to compute TOC 4. If the current node in traversal tree is leaf node, compute the distance and directional motion bound between the two triangles to calculate TOC 5. If the current node is not leaf node, go to step 3 to traverse its child node if the TOC of the two BV is less than current minimal TOC 6.Advance the object A by TOC until TOC > 1 or distance between the two objects is less than threshold 7. Return TOC

21. Demo

22. Experiments analysis The alpha model (1K triangles)

23. Experiments analysis Test motion coherence No motion coherence Enable motion coherence

24. Conclusion Implement the CCD for polygon soups using conservative advancement  Perform the hierarchy conservative advancement for polygon soups based on PQP  Calculate the directional motion bound for SSV using linear interpolating  Explore motion coherence

25. Future work Compute the motion bound for constrained motion Perform continuous collision detection for sliding motion

26. References Xinyu Zhang, Minkyoung Lee, Young J. Kim: Interactive continuous collision detection for non-convex polyhedra. The Visual Computer 22(9-11): 749- 760 (2006) Gottschalk, S., Lin, M., Manocha, D.: OBB-Tree: A hierarchical structure for rapid interference detection. In: H. Rushmeier (ed.) SIGGRAPH 96 Conference Proceedings, Annual Conference Series, pp. 171–180. ACM SIGGRAPH, Addison Wesley (1996). Kim, B., Rossignac, J.: Collision prediction for polyhedra under screw motions. In: ACM Conference on Solid Modeling and Applications (2003) Larsen, E., Gottschalk, S., Lin, M., Manocha, D.: Fast proximity queries with swept sphere volumes. Tech. Rep. TR99-018, Department of Computer Science, University of North Carolina (1999) Schwarzer, F., Saha, M., Latombe, J.C.: Exact collision checking of robot paths. In: Workshop on Algorithmic Foundations of Robotics (WAFR) (2002)

27. References Lin, M., Manocha, D.: Collision and proximity queries. In: Handbook of Discrete and Computational Geometry (2003) Mirtich, B.: Timewarp rigid body simulation. SIGGRAPH 00 Conference Proceedings pp. 193–200 (2000) Mirtich, B.V.: Impulse-based dynamic simulation of rigid body systems. Ph.D. thesis, University of California, Berkeley (1996) Redon, S., Kheddar, A., Coquillart, S.: Fast continuous collision detection between rigid bodies. Proc. of Eurographics (Computer Graphics Forum) (2002) Xinyu Zhang, Stephane Redon, Minkyoung Lee, Young J. Kim: Continuous collision detection for articulated models using Taylor models and temporal culling. ACM Trans. Graph. 26(3): 15 (2007)