Exact Collision Detection for Scaled Convex Polyhedral Objects

This paper addresses the following collision detection problem: determine the collision status for a pair of stationary convex polyhedral objects whose allowed deformation is uniform but arbitrary scaling of vertices within given upper and lower limits. We present an exact overlap checking method based on the characterization of all contact configurations. The set of all scaling pairs that two objects contact each other externally is characterized by a decending piecewise linear curve where the switching point of this piecewise linear curve represents the scaling pair as long as the contact configuration changes feature. Then, using this piecewise linear curve, the rectangle of allowable scaling pairs is partitioned into an exact overlap and an exact non-overlap sub-regions. A corresponding decision curve for exact overlap checking is constructed from this scaling decision curve via parametric intersection points of each polyhedron with the shortest path between inner ellipsoids of deformation bounds. Index Terms collision detection, convex polyhedra, deformation, scaling