CS 326A: Motion Planning ai.stanford.edu/~latombe/cs326/2007/index.htm Collision Detection and Distance Computation

Two Main Approaches  Hierarchical bounding volume hierarchies (pre-computation)  Feature tracking (pairs of closest features)

 Enclose objects into bounding volumes (spheres or boxes)  Check the bounding volumes first Bounding Volume Hierarchy Method

 Enclose objects into bounding volumes (spheres or boxes)  Check the bounding volumes first  Decompose an object into two Bounding Volume Hierarchy Method

BVH in 3D

Collision Detection Methods  Bounding Volume Hierarchy (BVH) methods: Good for few moving objects with complex geometry  Feature-Tracking methods: Good for few objects with moderate geometric complexity

Probabilistic Roadmaps Few moving objects, but complex geometry

Static vs. Dynamic Collision Checking C-space

Combining Bounding Volume and Feature Tracking Methods  S.A. Ehmann and M.C. Lin. Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition. Proc Eurographics, Vol. 20, No. 3, pp ,  Use BVH to quickly identify close pairs of polyhedra  Use feature-tracking to check these pairs

Combining Bounding Volume and Feature Tracking Methods  T.Y. Li and J.S. Chen Incremental 3D Collision Detection with Hierarchical Data Structures,Proc. ACM Symp. on Virtual Reality Software and Technology, p , Taipei, Taiwan

Collision Detection Methods  Bounding Volume Hierarchy (BVH) methods: good for few moving objects with complex geometry  Feature-Tracking methods: Good for few objects with moderate geometric complexity  Grid method: Good for many simple moving objects of about the same size (e.g., many moving discs/balls with similar radii)

Crowd Simulation Many moving objects, but simple geometry (discs) Need to also compute distances (vision, sounds)

Grid Method d  Subdivide space into a regular grid cubic of square bins  Index each object in a bin

Grid Method d Running time is proportional to number of moving objects