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Boat-sail Voronoi diagram and its computation based on a cone-approximation scheme

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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 proposed method.

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Authors and Affiliations

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

    Tetsushi Nishida & Kokichi Sugihara

Authors
  1. Tetsushi Nishida
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  2. Kokichi Sugihara
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Correspondence to Tetsushi Nishida.

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Nishida, T., Sugihara, K. Boat-sail Voronoi diagram and its computation based on a cone-approximation scheme. Japan J. Indust. Appl. Math. 22, 367–383 (2005). https://doi.org/10.1007/BF03167490

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  • DOI: https://doi.org/10.1007/BF03167490

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