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International Symposium on Algorithms and Computation

ISAAC 2003: Algorithms and Computation pp 26–35Cite as

Voronoi Diagram in the Flow Field

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

Abstract

A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, and a numerical method for solving this problem is constructed. The method is a modification of a so-called fast marching method originally proposed for the eikonal equation. Computational experiments show the efficiency and the stableness of the proposal method.

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References

  1. Aronov, B.: On the geodesic Voronoi diagram of point sites in a simple polygon. Algorithmica 4, 109–140 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ash, P.F., Bolker, E.D.: Generalized Dirichlet tessellations. Geometriae Dedicata 20, 209–243 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  3. Courant, R., Hilbert, D.: Methods of Mathematical Physics Volume II. Wiley, Chichester (1989)

    Book  MATH  Google Scholar 

  4. Fortune, S.: Voronoi diagrams and Delaunay triangulations. In: Du, D.-Z., Hwang, F.K. (eds.) Computing in Euclidean Geometry, pp. 193–233. World Scientific Publishing, Singapore (1992)

    Google Scholar 

  5. Kobayashi, K., Sugihara, K.: Crystal Voronoi diagram and its applications. Future Generation Computer System 18, 681–692 (2002)

    Article  Google Scholar 

  6. Lee, D.-T.: Two-dimensional Voronoi diagrams in the L p -metric. Journal of the ACM 27, 604–618 (1980)

    Article  MATH  Google Scholar 

  7. Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations – Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley and Sons, Chichester (2000)

    MATH  Google Scholar 

  8. Sethian, J.A.: Fast marching method. SIAM Review 41, 199–235 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Sethian, J.A.: Level Set Methods and Fast Marching Methods, 2nd edn. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  10. Sugihara, K.: Voronoi diagrams in a river. International Journal of Computational Geometry and Applications 2, 29–48 (1992)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematical Informatics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Tetsushi Nishida & Kokichi Sugihara

Authors
  1. Tetsushi Nishida
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  2. Kokichi Sugihara
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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© 2003 Springer-Verlag Berlin Heidelberg

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Nishida, T., Sugihara, K. (2003). Voronoi Diagram in the Flow Field. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_5

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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