Computing the distance between smooth objects in three dimensional space

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