Maximal distance for robotic simulation: The convex case (Q1091953)

Given two hyper-rectangles in \(E^ n\) with sides having surface normals in the directions of the axes, each containing a set that touches all 2n sides of its containing hyper-rectangle, it is important to have an easily calculated upper bound on the distance between the sets, for use in a branch and bound algorithm applicable in collision avoidance in robotic simulation. In another paper by the authors and G. Hurteau [``A maximal distance result of interest in robotic simulation'', Appl. Math. Opt., to appear], such a bound was given under the hypothesis that the sets are connected. Here, we consider the case where the sets are convex.