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 with n vertices and r reflex edges into O(n +r²) tetrahedra. This bound is asymptotically tight in the worst case. The algorithm requires O(n +r²) space and runs in O((n +r²) log r) time.