Fast Collision Detection Method for the Scaled Convex Polyhedral Objects with Relative Motion

For a pair of uniformly scaled convex polyhedral objects, exact collision detection can be performed rather robustly via reference to a descending piecewise linear curve (decision curve) characterizing the set of all scaling pairs that the objects contact each other externally. As the objects undergo a small relative spatial motion, this paper presents via a worked example a fast and simple incremental method to check their collision status without recomputations from scratch. The new decision curve after an intended relative motion could be constructed efficiently, as compare to the without initialization approach which each computation restarts from scratch. This approach has potential application to the assembly problems for designing relative motion that could make a pair of scalable convex polyhedral objects mate precisely, when their locations do not match initially.