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A simple and efficient algorithm for finding the closest points between two convex polynomials is described. Data from numerous experiments tested on a broad set of convex polyhedra on R/sup 3/ show that the running time is roughly constant for finding closest points when nearest points are approximately known and is linear in total number of vertices if no special initialization is done. This algorithm can be used for collision detection, computation of the distance between two polyhedra in three-dimensional space, and other robotics problems. It forms the heart of the motion planning algorithm previously presented by the authors (Proc. IEEE ICRA, p.1554-9, 1990).>
Lin et al. (2002) studied this question.