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 collision 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.