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A sweepcircle algorithm for Voronoi diagrams

Extended abstract

  • Graphs, Geometry And Data Structures
  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 314))

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Abstract

The Voronoi diagram of n sites on the surface of a cone has a combinatorial structure rather different from the planar one. We present a sweepcircle algorithm that enables its computation within optimal time O(n log n), using linear storage.

Research supported by NSERC Grant No. A9173

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References

  1. L.P.Chew and R.L.Drysdale III, "Voronoi diagrams based on convex distance functions", Proc. 1st ACM Symposium on Computational Geometry, Baltimore, MD, 1985, pp. 235–244

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  2. F. Dehne, R. Klein, "A sweepcircle algorithm for Voronoi diagrams on cones", Tech.Rep., School of Computer Science, Carleton University, Ottawa, Canada K1S5B6, 1987

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  3. S. Fortune, "A sweeline algorithm for Voronoi diagrams", Algorithmica, vol. 2, No.2, 1987, pp.153–174

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  4. R.Klein and D.Wood, "Voronoi diagram for general metrices in the plane", in preparation

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  5. Thurston, "The geometry of circles: Voronoi diagrams, Moebius transformations, convex hulls, Fortune's algorithm, the cut locus and parametrization of shapes", unpublished notes, Princeton, 1986

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, K1S 5B6, Ottawa, Canada

    Frank Dehne

  2. Institut für Angewandte Informatik und Formale Beschreibungsverfahren, Univ. Karlsruhe, Postfach 6980, D-7500, Karlsruhe, W.-Germany

    Rolf Klein

Authors
  1. Frank Dehne
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  2. Rolf Klein
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Editor information

Herbert Göttler Hana-Jürgen Schneider

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© 1988 Springer-Verlag Berlin Heidelberg

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Dehne, F., Klein, R. (1988). A sweepcircle algorithm for Voronoi diagrams. In: Göttler, H., Schneider, HJ. (eds) Graph-Theoretic Concepts in Computer Science. WG 1987. Lecture Notes in Computer Science, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19422-3_5

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  • DOI: https://doi.org/10.1007/3-540-19422-3_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19422-4

  • Online ISBN: 978-3-540-39264-4

  • eBook Packages: Springer Book Archive

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