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International Conference on Computational Science and Its Applications

ICCSA 2003: Computational Science and Its Applications — ICCSA 2003 pp 847–855Cite as

Voronoi Diagram of Circles in a Large Circle

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

Abstract

Presented in this paper is an algorithm to compute a Voronoi diagram of circles contained in a sufficiently large circle, where the interior circles are not necessarily disjoint. Given circles in a large circle, the region in the large circle is divided into regions associated with the circles. The algorithm first constructs the ordinary point Voronoi diagram of centers of inner circles. Then, it modifies the point Voronoi diagram considering the large enclosing circle so that the seed topology for the desired Voronoi diagram is obtained by a number of edge-flip operations. After getting the correct topological information, the equations of edges are computed in a rational quadratic Bézier curve form.

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Hanyang University, 17 Haengdang-Dong, Seongdong-Ku, Seoul, 133-791, Korea

    Deok-Soo Kim & Donguk Kim

  2. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Kokichi Sugihara

Authors
  1. Deok-Soo Kim
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  2. Donguk Kim
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  3. Kokichi Sugihara
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Cite this paper

Kim, DS., Kim, D., Sugihara, K. (2003). Voronoi Diagram of Circles in a Large Circle. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_86

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  • DOI: https://doi.org/10.1007/3-540-44842-X_86

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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