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Approximating Uniform Triangular Meshes for Spheres

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Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

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Abstract

We consider the problem of triangulating a convex polygon on spheres using n Steiner points that minimizes the overall edge length ratio. We establish a relation of this problem to a certain extreme packing problem. Based on this relationship, we develop a heuristic producing 6-approximation for spheres (provided n is chosen sufficiently large). That is, the produced triangular mesh is uniform in this respect.

The method is easy to implement and runs in O(n 3) time and O(n) space.

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Author information

Authors and Affiliations

  1. Department of Architecture and Architectural Systems, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    Naoki Katoh & Hiromichi Kojima

  2. Railway Information Systems, Hikari-machi, Kokubunji, Tokyo, 185-8510

    Ryo Taniguchi

Authors
  1. Naoki Katoh
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  2. Hiromichi Kojima
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  3. Ryo Taniguchi
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Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

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

    Masatsugu Urabe

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© 2001 Springer-Verlag Berlin Heidelberg

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Katoh, N., Kojima, H., Taniguchi, R. (2001). Approximating Uniform Triangular Meshes for Spheres. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_18

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  • DOI: https://doi.org/10.1007/3-540-47738-1_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

  • eBook Packages: Springer Book Archive

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