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Nonregular triangulations, view graphs of triangulations, and linear programming duality

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Book cover Discrete and Computational Geometry (JCDCG 2000)

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

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Abstract

For a triangulation and a point, we define a directed graph representing the order of the maximal dimensional simplices in the triangulation viewed from the point. We prove that triangulations having a cycle the reverse of which is not a cycle in this graph viewed from some point are forming a (proper) subclass of nonregular triangulations. We use linear programming duality to investigate further properties of nonregular triangulations in connection with this graph.

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Author information

Authors and Affiliations

  1. Dept. of Information Science, Univ. of Tokyo, 113-0033, Japan

    Fumihiko Takeuchi

Authors
  1. Fumihiko Takeuchi
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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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Takeuchi, F. (2001). Nonregular triangulations, view graphs of triangulations, and linear programming duality. 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_31

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  • DOI: https://doi.org/10.1007/3-540-47738-1_31

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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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