Triangulating a nonconvex polytope

Bernard Chazelle, Leonidas Palios

Research output: Contribution to journalArticle

83 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)505-526
Number of pages22
JournalDiscrete & Computational Geometry
Volume5
Issue number1
DOIs
StatePublished - Dec 1 1990

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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