Determining the minimum translational distance between two convex polyhedra

Abstract

Given two objects we define the minimal translational distance (MTD) between them to be the length of the shortest relative translation that results in the objects being in contact. MTD is equivalent to the distance between two objects if the objects are not intersecting; however MTD is also defined for intersecting objects and it then gives a measure of penetration. We show that the computation of MTD can be recast as a configuration space problem, and describe an algorithm for computing MTD for convex polyhedra. This research was conducted under the McDonnell Douglas Independent Research and Development Program.