Fast Collision Detection between Geometric Models

We present an efficient algorithm for collision detection and contact determination between geometric models described by linear or curved boundaries and undergoing rigid motion. The set of models include surfaces described by rational spline patches or piecewise algebraic functions. In contrast to previous approaches, wefirst present a roughly constant time algorithm for collision detection between convex polytopes using coherence and local features. An extension using hiera.rchical representation to concave polytopes and a scheduling scheme to reduce the frequency of collision detection is also described. Finally we apply these algorithms along with properties of input models, local and global algebraic methods for solving polynomial equations and the geometric formulation of the problem to devise efficient algorithms for convex and concave curved objects. Additional