A fast growth distance algorithm for incremental motions

A fast algorithm is presented for computing the growth distance between a pair of convex objects in three-dimensional space. The growth distance is a measure of both separation and penetration between objects. When the objects are polytopes represented by their faces, the growth distance is determined by the solution of a Linear Program (LP). This article presents a new approach to the solution of the LP. Under appropriate conditions, the computational time is very small and does not depend on the total number of faces of the objects. Compared to the existing algorithm for growth distance, there is a time reduction of several orders of magnitude. This increase in speed is achieved by exploiting two resources: adjacency of the object faces and the computational coherence induced by incremental motions of the objects. Computational experiments show that the performance of the algorithm is in the same range as the fastest codes for the computation of the Euclidean separation distance.