Naga K. Govindaraju, Stephane Redon, Ming C. Lin, Dinesh Manocha

1. Adapted from:CULLIDE: Interactive Collision Detection Between Complex Models in Large Environments using Graphics Hardware Naga K. Govindaraju, Stephane Redon, Ming C. Lin, Dinesh Manocha University of North Carolina at Chapel Hill

2. Collision Handling • Contact and collision between objects and between interactive tools with objects • Non-trivial to simulate collision, main problems are • Automatically report when collision happens • After collision detection, objects response in a natural way

3. Collision Handling • A wide range of techniques are used in collision detection on geometric models • Hierarchical trees formed with bounding boxes or spheres for efficient detect in different levels • Penetration depth should be reported to the handling process • The research issue for computational geometry and algorithms

4. Problem • Given a large environment with moving objects, • Compute overlapping objects • Overlapping triangles in each pair

5. Goal Interactive collision detectionbetween complex objects • Large number of objects • High primitive count • Non-convex objects • Open and closed objects

6. Non-rigid Motion • Deformable objects • Changing topology

7. Real-time Collision Detection using our Approach Complex breaking objects on a NVIDIA GeForce FX5800 Ultra GPU

8. Related Work • Object space techniques • Two phases • Broad phase – Compute object pairs in close proximity • Narrow phase – Check each pair for exact collision detection

9. Limitations of Object-space Techniques • Considerable pre-processing • Hard to achieve real-time performance on complex deformable models

10. Collision Detection using Graphics Hardware • Primitive rasterization – sorting in screen-space • Interference tests

11. Outline • Overview • Pruning Algorithm • Implementation and Results • Conclusions and Future Work

12. Outline • Overview • Pruning Algorithm • Implementation and Results • Conclusions and Future Work

13. Overview • Potentially Colliding Set (PCS) computation • Exact collision tests on the PCS

14. GPU based PCS computation Using CPU Algorithm Object LevelPruning Sub-objectLevelPruning Exact Tests

15. PCS Potentially Colliding Set (PCS)

16. Potentially Colliding Set (PCS) PCS

17. Outline • Problem Overview • Overview • Pruning Algorithm • Implementation and Results • Conclusions and Future Work

18. Algorithm Object LevelPruning Sub-object LevelPruning Exact Tests

19. Visibility Computations Lemma 1: An object O does not collide with a set of objects S if O is fully visible with respect to S • Utilize visibility for PCS computation

20. set S Object O Fully Visible Collision Detection using Visibility Computations

21. PCS Pruning Lemma 2: Given n objectsO1,O2,…,On , an object Oi does notbelong to PCS if it does notcollide with O1,…,Oi-1,Oi+1,…,On • Prune objects that do not collide

22. PCS Pruning O1 O2 … Oi-1 Oi Oi+1 … On-1 On O1 O2 … Oi-1OiOi+1 … On-1 On O1 O2 … Oi-1 Oi Oi+1 … On-1 On

23. PCS Pruning O1 O2 … Oi-1 Oi

24. PCS Pruning Oi Oi+1 … On-1 On

25. PCS Computation • Each object tested against all objects but itself • Naive algorithm is O(n2) • Linear time algorithm • Uses two pass rendering approach

26. Render PCS Computation: First Pass O1 O2 … Oi-1 Oi Oi+1 … On-1 On

27. Render Fully Visible? PCS Computation: First Pass O1

28. Render Yes. Does not collide withO1,O2,…,Oi-1 Fully Visible? PCS Computation: First Pass O1 O2 … Oi-1 Oi

29. Render Fully Visible? PCS Computation: First Pass O1 O2 … Oi-1 Oi Oi+1 … On-1 On

30. Render PCS Computation: Second Pass O1 O2 … Oi-1 Oi Oi+1 … On-1 On On

31. Render Fully Visible? PCS Computation: Second Pass On

32. Render Yes. Does not collide with Oi+1,…,On-1,On Fully Visible? PCS Computation: Second Pass Oi Oi+1 … On-1 On

33. Render Yes. Does not collide with O1,…,On-1,On PCS Computation: Second Pass O1 O2 … Oi-1 Oi Oi+1 … On-1 On Fully Visible?

34. Fully Visible Fully Visible PCS Computation O1 O2 … Oi-1 Oi Oi+1 … On-1 On

35. O1 O2 O3 … Oi-1 Oi Oi+1 … On-2 On-1 On PCS Computation O1 O3 … Oi-1 Oi+1 … On-1

36. Example O1 O2 O3 O4 Scene with 4 objectsO1and O2 collideO3, O4 do not collide Initial PCS = { O1,O2,O3,O4 }

37. First Pass Fully Visible Fully Visible Not Fully Visible O1 O3 Fully Visible O4 O1 O2 O3 O4 Order of rendering: O1 O4

38. Fully Visible Fully Visible Not Fully Visible O2 O3 Fully Visible O4 Second Pass O1 O2 O3 O4 Order of rendering: O4 O1

39. Fully Visible Fully Visible After two passes O1 O2 O3 O4

40. Potential Colliding Set O1 O2 PCS ={O1,O2}

41. Algorithm Object LevelPruning Sub-object LevelPruning Exact Tests

42. Overlap Localization • Each object is composed of sub-objects • We are given n objects O1,…,On • Compute sub-objects of an object Oi that overlap with sub-objects of other objects

43. Overlap Localization • Our solution • Test if each sub-object of Oi overlaps with sub-objects of O1,..Oi-1 • Test if each sub-object of Oi overlaps with sub-objects of Oi+1,...,On • Linear time algorithm • Extend the two pass approach

44. Potential Colliding Set O1 O2 PCS = {O1,O2}

45. Sub-objects O1 O2 PCS = sub-objects of {O1,O2}

46. First Pass Rendering order: Sub-objects of O1 O2

47. Fully Visible First Pass

48. Fully Visible First Pass

49. Fully Visible Fully Visible Not Fully Visible First Pass

50. Fully Visible Fully Visible Fully Visible First Pass