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Symbolic treatment of geometric degeneracies

  • Computational Geometry
  • Conference paper
  • First Online:
System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 113))

Abstract

Many descriptions of algorithms in computational geometry exclude degeneracies by fiat. Practitioners are left to their own devices for dealing with degeneracies when implementing such algorithms. Since degeneracies tend to be numerous and hard to enumerate exhaustively, this is often a reason for not implementing theoretical algorithms. This paper proposes a powerful symbolic scheme for treating degeneracies. Our method is simple to use, and is applicable for a wide variety of problems in computational geometry (in particular, whenever random perturbations are applicable). Our method is deterministic but is as efficient as probabilistic schemes. Illustrations, limitations and wider issues are discussed.

Supported in part by NSF grants #DCR-84-01898 and #DCR-84-01633.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012, New York, NY

    Chee-Keng Yap

Authors
  1. Chee-Keng Yap
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Masao Iri Keiji Yajima

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© 1988 International Federation for Information Processing

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Yap, CK. (1988). Symbolic treatment of geometric degeneracies. In: Iri, M., Yajima, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042803

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  • DOI: https://doi.org/10.1007/BFb0042803

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19238-1

  • Online ISBN: 978-3-540-39164-7

  • eBook Packages: Springer Book Archive

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