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International Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 1989: Foundations of Software Technology and Theoretical Computer Science pp 267–279Cite as

Robust decompositions of polyhedra

  • Geometric Algorithms
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 405))

Abstract

We present a simple and robust algorithm to compute a convex decomposition of a non-convex polyhedron of arbitrary genus. The algorithm takes a topologically correct representation of a non-convex polyhedron S and produces a worst-case optimal O(N 2) number of topologically correct representations of convex polyhedra S i , with ∪ i S i = S, in O(nN 2 + N 4) time and O(n N + N 3) space, where n is the number of edges of S, N is the total number of notches or reflex edges. Our algorithm can be made to run in O((nN + N 3) logN) time if robustness is not desired. The robustness of the algorithm stems from its ability to handle all degenerate configurations as well as to maintain topological consistency, while doing floating-point numerical computations. The convex decomposition algorithm is independent of the precision used in the numerical calculations. With slight modifications it also yields a triangulation of the polyhedra into a set of tetrahedra.

Supported in part by ARO Contract DAAG29-85-C0018 under Cornell MSI, NSF grant DMS 88-16286 and ONR contract N00014-88-K-0402.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Purdue University, 47907, West Lafayette, IN

    Chanderjit L. Bajaj & Tamal K. Dey

Authors
  1. Chanderjit L. Bajaj
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  2. Tamal K. Dey
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Editor information

C. E. Veni Madhavan

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© 1989 Springer-Verlag Berlin Heidelberg

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Bajaj, C.L., Dey, T.K. (1989). Robust decompositions of polyhedra. In: Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1989. Lecture Notes in Computer Science, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52048-1_49

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  • DOI: https://doi.org/10.1007/3-540-52048-1_49

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52048-1

  • Online ISBN: 978-3-540-46872-1

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