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How to compute the Voronoi diagram of line segments: Theoretical and experimental results

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  • First Online:
Algorithms — ESA '94 (ESA 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 855))

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Abstract

Given a set of non-intersecting (except at endpoints) line segments in the plane we want to compute their Voronoi diagram. Although there are several algorithms for this problem in the literature [Yap87, For87, CS89, BDS+92, KMM90] nobody claims to have a correct implementation. This is due to the fact that the algorithms presuppose exact arithmetic and that the Voronoi diagram of segments requires to compute with non-rational algebraic numbers. We report about a detailed study of the numerical precision required for evaluating the geometric test exactly and about first experimental experiences. More specifically, we improve the precision bound implied by classical root separation results by more than two orders of magnitude and we compare the implementation strategies suggested by our theoretical results.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, 66123, Saarbrücken, Germany

    Christoph Burnikel, Kurt Mehlhorn & Stefan Schirra

Authors
  1. Christoph Burnikel
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  2. Kurt Mehlhorn
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  3. Stefan Schirra
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Editor information

Jan van Leeuwen

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© 1994 Springer-Verlag Berlin Heidelberg

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Burnikel, C., Mehlhorn, K., Schirra, S. (1994). How to compute the Voronoi diagram of line segments: Theoretical and experimental results. In: van Leeuwen, J. (eds) Algorithms — ESA '94. ESA 1994. Lecture Notes in Computer Science, vol 855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049411

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  • DOI: https://doi.org/10.1007/BFb0049411

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58434-6

  • Online ISBN: 978-3-540-48794-4

  • eBook Packages: Springer Book Archive

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