A maximal distance result of interest in robotic simulation

Given two hyper-rectangles inE ⁿ with sides having surface normals in the directions of the axes, and given a connected set in each 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 two connected sets. A result giving such a bound, necessary in branch and bound algorithms used for collision avoidance in robotic simulation, is stated and proved here.The work of the second and third authors was supported in part by the Natural Sciences and Engineering Research Council of Canada.