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.>

A methodology for computing the distance between smooth objects in three-dimensional space is presented. The convex polytope, which is the basic solid modeling tool of prior developments, is replaced by a general convex set. This permits the direct treatment of objects with curved surfaces, eliminating the errors caused by polytope approximations. The computational procedure is a simple extension of the efficient distance algorithm described by E.G. Gilbert et al. (1988). While the convergence of the algorithm is not finite, it is fast and an effective stopping condition is available. Procedures for treating a rich family of smooth objects are given. Extensive numerical experiments support the claimed efficiency.>