Triangulating a nonconvex polytope

This paper is concerned with the problem of partitioning a three-dimensional nonconvex polytope into a small number of elementary convex parts. The need for such decompositions arises in tool design, computer-aided manufacturing, finite-element methods, and robotics. Our main result is an algorithm for decomposing a nonconvex polytope of zero genus withn vertices andr reflex edges intoO(n +r ²) tetrahedra. This bound is asymptotically tight in the worst case. The algorithm requiresO(n +r ²) space and runs inO((n +r ²) logr) time.This research was supported in part by the National Science Foundation under Grant CCR-8700917.