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. © Springer-Verlag Berlin Heidelberg 2003.
CITATION STYLE
Nishida, T., & Sugihara, K. (2003). Voronoi diagram in the flow field. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2906, 26–35. https://doi.org/10.1007/978-3-540-24587-2_5
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