Fast contact determination in dynamic environments

We present an efficient contact determination algorithm for objects undergoing rigid motion. The environment consists of polytopes and models described by algebraic sets. We extend an expected constant time collision detection algorithm between convex polytopes to concave polytopes and curved models. The algorithm makes use of hierarchical representations for concave polytopes and local, global methods for solving polynomial equations to determine possible contact points. We also propose techniques to reduce O(n²) pairwise intersection tests for a large environment of n objects. These algorithms work well in practice and give real time performance for most environments