New distances for the separation and penetration of objects

Abstract

New quantitative measures for the separation and penetration of two convex objects are formulated. These measures, called separation and penetration growth distances, are closely related to traditional distance measures and share many of their desirable properties. The solution of a single optimization problem yields both the separation and penetration distances. For polytopal objects the optimization problem is a simple linear program whose computational time is O(m), where m is the number of linear inequalities required to specify the two polytopes. Numerical experiments with three dimensional polytopes demonstrate that the growth distances can be computed more rapidly than the traditional distances with a large advantage in the case of penetration distances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>