Fast Collision Detection for Deformable Models using Representative-Triangles

1. Fast Collision Detection for Deformable Models using Representative-Triangles By Sean Curtis, Rasmus Tamstorf and Dinesh Manocha Presented by Marcus Parker http://gamma.cs.unc.edu/RTRI

2. Collision Detection • Triangulated models • Vertices, edges, faces • Discrete collision detection (CD) • 6 elementary tests • Continuous collision detection (CCD) • 15 elementary tests • Culling efficiency

3. Contributions • Approach applies to both CD and CCD • Feature-based hierarchies • Leaf nodes of (BVH) are features • Representative-Triangles (R-Triangles) • BVH of AABBs • Cloth simulation and N-body collisions

4. Related Work • Bounding Volume Hierarchies (BVH) • Recomputed for each frame for deformable models • Feature-Based Collision Detection • Largely limited to rigid models • Continuous Collision Detection

5. Terminology • Feature – vertex, edge, face • Contact – collision between feature pairs • Vertex-face (VF) and edge-edge (EE) for CCD • Edge-face for CD • Culling Efficiency – number of false positive elementary tests • Duplicate Elementary Tests

6. Feature-Based Hierarchies • Uses set of independent BVHs • one BVH for each feature type • Improves Culling Efficiency • Culling normally on triangles instead of features • Each feature represented only once in corresponding hierarchy

7. Representative-Triangles • Benefits of feature based hierarches, cost of single hierarchy • Contains basic structural data plus • Feature assignments • Feature bounding volumes • Every feature is assigned to exactly ONE incident triangle

8. Improved Culling Efficiency • R-Triangles replicate functionality of a feature-based hierarchy • Only test if triangles represent compatible feature pairs • EE or VF • BVs are linked to their R-Triangles eliminates duplicate BV-overlap tests

9. Eliminating Duplicate Queries • For each compatible feature pair, the corresponding test is dispatched once • Proof based on 3 properties: • I: Every vertex and edge must be represented by a triangle (triangles represent their own faces) • II: Every vertex and edge can be assigned to no more than one triangle • III: If a feature is assigned to a triangle, then it must be incident to that triangle

10. Optimal Representation • Assignment schema – which features are assigned to which triangles • Maximal schema – feature assignments result in largest number of unassigned triangles • Uniform schema – each triangle has the same number of assigned features • Optimal assignment schema is possible locally but not globally

12. Implementation • Assign features to triangles via a greedy algorithm • Representation encoded in 4 bits • Upper 2 for vertices, lower 2 for edges • Processing Candidate Triangle Pairs • Element BV Type – AABBs • Memory Requirements

13. Results • Benchmarks • N-body balls, Cloth Ball, Princess, Flamenco • Compared against 3 other algorithms for query time and number of elementary tests

14. Analysis/Limitations • Duplicate queries eliminated without excessive cost • Along with culling, provides increase in performance • False positive percentage still over 90%

15. Future Work • Integration into Simulation • Element Bounding Volumes • Use OBBs or kDOPs instead of AABBs • Dynamic Representative Reassignment