Computing the distance between general convex objects in three-dimensional space

Abstract

A methodology for computing the distance between objects in three-dimensional space is presented. The convex polytope is replaced by a general convex set, avoiding the errors caused by the usual polytope approximations and actually reducing the overall computational time. The basic algorithm is a simple extension of the polytope distance algorithm described by E.G. Gilbert et al. (1988). It utilizes the support mappings of the sets representing the objects. A calculus for evaluating these mappings that allows the extended algorithm to be applied to a rich family of nonpolytopal objects is presented. While the convergence of the algorithm is not finite, it is fast and an effective stopping condition that guarantees the accuracy of the numerical solution is available. Extensive numerical experiments support the claimed efficiency.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>