Collision and Proximity Queries Dinesh Manocha Department of

Collision and Proximity Queries Dinesh Manocha Department of Computer Science University of North Carolina dm@cs. unc. edu

Proximity Queries Collision l. A procedure to compute the spatial relation between objects.

Proximity Queries Geometric reasoning of spatial relationships among objects (in a dynamic environment) Collision Detection Contact Points & Normals d Closest Points & Separation Distance GDC’ 03 d Penetration Depth

Problem Domain Specifications l Model Representations – polyhedra (convex vs. non-convex vs. soups) – CSG, implicits, parametrics, point-clouds l Type of Queries – discrete vs. continuous query – distance vs. penetration computation – estimated time to collision l Simulation Environments – pairwise vs. n-body – static vs. dynamic – rigid vs. deformable

Applications l l l l Robot motion planning Simulation of (dis-)assembly tasks Tolerance verification Simulation-based design Ergonomics analysis Haptic rendering Physics-based modeling and simulation

History l l l Studied over 4 decades in Computational Geometry Robotics & Automation Simulated Environments Computer Animation Physically-based Modeling

Earlier work: 1970 s and 1980 s Algorithms for 2 D & 3 D intersection computation l Collision checking and avoidance l

1990’s: considerable momentum Distance computation between convex polytopes (Gilbert et al. 1998; Lin & Canny’ 91) l Bounding volume hierarchies (sphere-trees, OBBTrees, k-DOP trees, Shelltrees) l N-body collision checking (sweep-and-prune, grid -based methods) l Collision systems for rigid models (I-Collide, RAPID, V-Collide, SOLID, Quick. CD, PQP, …. ) l

1990’s: considerable momentum Distance computation between convex polytopes (Gilbert et al. 1998; Lin & Canny’ 91) l Bounding volume hierarchies (sphere-trees, OBBTrees, k-DOP trees, Shelltrees) l N-body collision checking (sweep-and-prune, grid -based methods) l Collision systems for rigid models (I-Collide, RAPID, V-Collide, SOLID, Quick. CD, PQP, …. ) l

1990’s: considerable momentum l Collision and contact computations for Physicsbased simulation (Baraff’ 92; Lin’ 93; Mirtich’ 95)

1990’s: considerable momentum l Collision checking for virtual environments (Cohen et al. ’ 95)

1990’s: considerable momentum l Haptic rendering (Gregory et al. ’ 98; H-Collide)

Last 10 -12 years l Novel algorithms – – Discrete vs. continuous collision detection Penetration depth computation Deformable models Self-collisions and breaking objects Utilize the parallelism in multi-core CPUs and many-core GPUs l Development of Physics engines l

Focus of this Course l Recent research on collision and proximity queries l Implementation in Game Physics libraries

Recent Research Continuous collision detection and penetration depth queries (Young Kim) l Algorithms for deformable, breaking and volume meshes (Sungeui Yoon) l Acceleration using GPU parallelism (Dinesh Manocha) l

Game Physics Simulation Bullet Physics Library (Erwin Coumans) l NVIDIA PHYSX (Richard Tonge) l