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Interactive Continuous Collision Detection for Polygon Soups

Interactive Continuous Collision Detection for Polygon Soups. Xin Huang 11/20/2007. Introduction. Discrete CD Miss collision between sampled time instances Continuous Collision Detection (CCD). Introduction. Continuous Collision Detection (CCD) Consider continuous motion

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Interactive Continuous Collision Detection for Polygon Soups

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  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. Application in Assembly Maintainability: extract the part, • there are many non-manifold parts in the robot 12,236 vertices11,569 triangles Obstacle 16,781 vertices15,197 triangles 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 upperbound of TOC by repeatedly advancing A by dt towardB 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. U d 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

  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 underscrew motions. In: ACM Conference on Solid Modeling and Applications(2003) • Larsen, E., Gottschalk, S., Lin, M., Manocha, D.: Fast proximityqueries with swept sphere volumes. Tech. Rep. TR99-018, Departmentof Computer Science, University of North Carolina (1999) • Schwarzer, F., Saha, M., Latombe, J.C.: Exact collision checkingof robot paths. In: Workshop on Algorithmic Foundations ofRobotics (WAFR) (2002)

  27. References • Lin, M., Manocha, D.: Collision and proximity queries. In: Handbookof Discrete and Computational Geometry (2003) • Mirtich, B.: Timewarp rigid body simulation. SIGGRAPH 00Conference Proceedings pp. 193–200 (2000) • Mirtich, B.V.: Impulse-based dynamic simulation of rigid bodysystems. Ph.D. thesis, University of California, Berkeley (1996) • Redon, S., Kheddar, A., Coquillart, S.: Fast continuous collisiondetection between rigid bodies. Proc. of Eurographics (ComputerGraphics 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)

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