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Order-k Voronoi Diagrams, k-Sections, and k-Sets

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Discrete and Computational Geometry (JCDCG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1763))

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Abstract

In this paper we characterize all-dimensional faces of order-k Voronoi diagrams. First we introduce the notion of k-section to give a precise definition of these faces. Then, we characterize the unbounded faces by extending the classical notion of k-set. Finally, by studying some relations between k-sections, we give a new proof of the size of order-k Voronoi diagrams in the plane.

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Author information

Authors and Affiliations

  1. Laboratoire MAGE, Université de Haute-Alsace, 4, rue des Frères Lumière, 68093, Mulhouse Cédex, France

    Dominique Schmitt & Jean-Claude Spehner

Authors
  1. Dominique Schmitt
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  2. Jean-Claude Spehner
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, 316-8511, Hitachi Ibaraki, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido, Shimizu, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

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© 2000 Springer-Verlag Berlin Heidelberg

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Schmitt, D., Spehner, JC. (2000). Order-k Voronoi Diagrams, k-Sections, and k-Sets. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_26

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  • DOI: https://doi.org/10.1007/978-3-540-46515-7_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67181-7

  • Online ISBN: 978-3-540-46515-7

  • eBook Packages: Springer Book Archive

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