Four-dimensional representation and collision detection for polytopic objects

An algorithm for detecting the collision of moving objects is presented. The algorithm applies to polyhedral objects that can be represented as convex hulls of finite number of vertices in two or three-dimensional space. This is then extended to a three or four-dimensional space (respectively) to represent the objects and their motion. Nonlinear programming techniques are then employed to detect possible interference. The algorithm detects in one step whether or not the objects will interfere during their motion which may involve pure translations or rotations or both.