Collision and Proximity Queries
Dinesh Manocha
Department of Computer Science
University of North Carolina
dm@cs.unc.edu
Proximity Queries
Collision
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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
d
Closest Points & Separation Distance
GDC’03
Penetration Depth
Problem Domain Specifications
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Model Representations
– polyhedra (convex vs. non-convex vs. soups)
– CSG, implicits, parametrics, point-clouds
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Type of Queries
– discrete vs. continuous query
– distance vs. penetration computation
– estimated time to collision
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Simulation Environments
– pairwise vs. n-body
– static vs. dynamic
– rigid vs. deformable
Applications
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Robot motion planning
Simulation of (dis-)assembly tasks
Tolerance verification
Simulation-based design
Ergonomics analysis
Haptic rendering
Physics-based modeling and simulation
History
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Studied over 4 decades in
Computational Geometry
Robotics & Automation
Simulated Environments
Computer Animation
Physically-based Modeling
Earlier work: 1970s and 1980s
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Algorithms for 2D & 3D intersection
computation
 Collision checking and avoidance
1990’s: considerable momentum
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Distance computation between convex polytopes
(Gilbert et al. 1998; Lin & Canny’91)
 Bounding volume hierarchies (sphere-trees,
OBBTrees, k-DOP trees, Shelltrees)
 N-body collision checking (sweep-and-prune,
grid-based methods)
 Collision systems for rigid models (I-Collide,
RAPID, V-Collide, SOLID, QuickCD, PQP,….)
1990’s: considerable momentum

Distance computation between convex polytopes
(Gilbert et al. 1998; Lin & Canny’91)
 Bounding volume hierarchies (sphere-trees,
OBBTrees, k-DOP trees, Shelltrees)
 N-body collision checking (sweep-and-prune,
grid-based methods)
 Collision systems for rigid models (I-Collide,
RAPID, V-Collide, SOLID, QuickCD, PQP,….)
1990’s: considerable momentum

Collision and contact computations for Physicsbased simulation (Baraff’92; Lin’93; Mirtich’95)
1990’s: considerable momentum
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Collision checking for virtual environments
(Cohen et al.’95)
1990’s: considerable momentum
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Haptic rendering (Gregory et al.’98; H-Collide)
Last 10-12 years
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Novel algorithms
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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
 Development of Physics engines
Focus of this Course
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Recent research on collision and proximity
queries
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Implementation in Game Physics libraries
Recent Research
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Continuous collision detection and penetration
depth queries (Young Kim)
 Algorithms for deformable, breaking and volume
meshes (Sungeui Yoon)
 Acceleration using GPU parallelism (Dinesh
Manocha)
Game Physics Simulation
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Bullet Physics Library (Erwin Coumans)
 NVIDIA PHYSX (Richard Tonge)