1.
Optimized Continuous Collision Detection for Deformable Triangle Meshes
Marco Hutter and Arnulph Fuhrmann
WCSG’2007 – 30 January, 2007 – Plzen, Czech Republic
© 2003, Fraunhofer IGD

2. Overview Introduction Problem description Optimizations
Overview
Introduction
Problem description
Optimizations
Primitive Bounding Volumes
Optimized Continuous Collision Tests
Modification Marking
Conclusions & Discussion
© 2003, Fraunhofer IGD

3. Introduction Collision Detection Deformable Triangle Meshes
Introduction
Collision Detection
Physically based simulation
Deformable Triangle Meshes
Surfaces representing clothing & virtual garments
Multiple layers
Many collisions have to be resolved
Interactive simulation
Requires robustness and efficiency
© 2003, Fraunhofer IGD

4. Problem description Collision detection
Problem description
Collision detection
Bounding Volume Hierarchies [Klosowski 98],[Larsson 01]
Exact collision tests between primitives in leaves
Robust continuous collision detection [Govindaraju 05]
Computing the time when the collisions occur [Provot97]
Physical correctness
Treat collisions in correct (chronological) order [Bridson 02]
© 2003, Fraunhofer IGD

5. Optimizations Bounding Volume Hierarchies
Optimizations
Bounding Volume Hierarchies
Bounding Volumes usually for triangles
Two triangles: 9 edge/edge tests, 6 triangle/vertex tests
For objects in close proximity
Each triangle tested against 6 other triangles
 90 expensive collision tests
Many „false positives“
Efficient solutions for self-collisions (mainly curvature criteria)
One triangle BV on average intersects 6 other triangle BVs: 90 tests
Avoiding redundant tests: Still 60 tests
PVB: Reduction appx. about a factor of 6
Example: 5k Collisions, 160k tests, reduced to 22k tests
© 2003, Fraunhofer IGD

6. Optimizations Optimization:
Optimizations
Optimization:
Additional bounding volumes for edges and vertices
Slight memory overhead
Significantly reduces number of “false positives”
Efficient solutions for self-collisions (mainly curvature criteria)
One triangle BV on average intersects 6 other triangle BVs: 90 tests
Avoiding redundant tests: Still 60 tests
PVB: Reduction appx. about a factor of 6
Example: 5k Collisions, 160k tests, reduced to 22k tests
© 2003, Fraunhofer IGD

7. Optimizations Continuous collision tests
Optimizations
Continuous collision tests
Computing the time when the collision occurs
Edge-edge
Triangle-vertex
Checking 4 points for coplanarity
Compute coefficients and roots of 3rd degree polynomial from positions and velocities
© 2003, Fraunhofer IGD

8. Optimizations Continuous collision tests Optimized formula:
Optimizations
Continuous collision tests
Computationally expensive
Optimized formula:
© 2003, Fraunhofer IGD

9. Optimizations Iterative scheme for treating the collisions
Optimizations
Iterative scheme for treating the collisions
Correct chonological order
Take secondary collisions into account:
Optimization:
Marking the modified parts of the BVH in each iteration
Update and traverse only the marked parts
© 2003, Fraunhofer IGD

10. Conclusions Additional bounding volumes for primitives
Conclusions
Additional bounding volumes for primitives
Fewer false positives  less collision tests
Speedup of about 2,5 to 3
Easily applicable for all BVH-based algorithms
Optimized continuous collision tests
Small part of the total time, but saves many FLOPS
Marking the modified parts of the BVH
Much more efficient than complete update and traversal
Collision detection time less depends on number of primitives
Markierung der modifizierten Teile der BVH
Deutlich effizienter als vollständiges Update und Traversierung
© 2003, Fraunhofer IGD

11.
© 2003, Fraunhofer IGD

12.
Questions? Comments?
© 2003, Fraunhofer IGD