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Boat-Sail Voronoi diagram on a curved surface

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Abstract

We propose a new generalized Voronoi diagram, called a “boat-sail Voronoi diagram on a curved surface”. This is an extension of the boat-sail Voronoi diagram. The boat-sail Voronoi diagram is the partition of a two-dimensional flow field according to the shortest arrival time of a boat. On the other hand, our new Voronoi diagram subdivides the curbed surface with flow into the regions. In this paper, we derive a partial differential equation to solve the boat-sail Voronoi diagram on a curved surface and show some numerical examples.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyoku, 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 on a curved surface. Japan J. Indust. Appl. Math. 22, 267–278 (2005). https://doi.org/10.1007/BF03167442

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  • DOI: https://doi.org/10.1007/BF03167442

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