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A paradigm for robust geometric algorithms

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Abstract

This paper explores a paradigm for producing geometrical algorithms in which logical decisions that depend on finite-precision numerical calculation cannot lead to failure. It applies this paradigm to the task of intersecting two convex polyhedral objects. A key tool in this work is a method of perturbing embedding polyhedra in ways consistent with their topology.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, 14853, Ithaca, NY, USA

    John E. Hopcroft

  2. Department of Mathematics, Cornell University, 14853, Ithaca, NY, USA

    Peter J. Kahn

Authors
  1. John E. Hopcroft
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  2. Peter J. Kahn
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Additional information

Communicated by C. K. Wong.

Work on this paper was supported in part by NSF Grant DMC-86-17355, NSF Grant DMS-87-02070, ONR Grant N00014-86-0281, ONR Grant N00014-88-0591, and the U.S. Army Research Office through MSI, Cornell University.

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Hopcroft, J.E., Kahn, P.J. A paradigm for robust geometric algorithms. Algorithmica 7, 339–380 (1992). https://doi.org/10.1007/BF01758769

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  • DOI: https://doi.org/10.1007/BF01758769

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