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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics