A sweepcircle algorithm for Voronoi diagrams

Extended abstract
  • Frank Dehne
  • Rolf Klein
Graphs, Geometry And Data Structures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 314)


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.


computational geometry cone shortest path sweepline algorithm sweepcircle algorithm Voronoi diagrams 


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    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. 235–244Google Scholar
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    F. Dehne, R. Klein, "A sweepcircle algorithm for Voronoi diagrams on cones", Tech.Rep., School of Computer Science, Carleton University, Ottawa, Canada K1S5B6, 1987Google Scholar
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    S. Fortune, "A sweeline algorithm for Voronoi diagrams", Algorithmica, vol. 2, No.2, 1987, pp.153–174CrossRefGoogle Scholar
  4. [4]
    R.Klein and D.Wood, "Voronoi diagram for general metrices in the plane", in preparationGoogle Scholar
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    Thurston, "The geometry of circles: Voronoi diagrams, Moebius transformations, convex hulls, Fortune's algorithm, the cut locus and parametrization of shapes", unpublished notes, Princeton, 1986Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Frank Dehne
    • 1
  • Rolf Klein
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Institut für Angewandte Informatik und Formale BeschreibungsverfahrenUniv. KarlsruheKarlsruheW.-Germany

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