Fast collision detection in four-dimensional space

In this paper, we consider the collision detection problem for general objects. A four-dimensional approach is proposed for this problem which detects exactly and in one-step when and where the earliest collison will occur between the objects. This is done by using four-dimensional sets to represent the objects in both space and time. The problem is then posed as a nonlinear programming problem. The algorithm can handle the case of a rigid body moving on a general path in R² or R³ with simultaneous translation and rotation. Simulation results on some example problems are given, and show that the algorithm is superior to those available in the literature.