Efficient collision detection for moving polyhedra

In this paper we consider the following problem: given two general polyhedra of complexity $n$, one of which is moving translationally or rotating about a fixed axis, determine the first collision (if any) between them. We present an algorithm with running time $O(n^{8/5 + \epsilon})$ for the case of translational movements and running time $O(n^{5/3 + \epsilon})$ for rotational movements, where $\epsilon$ is an arbitrary positive constant. This is the first known algorithm with sub-quadratic running time