Approximation of the boat-sail Voronoi diagram and its application

Abstract

A new generalized Voronoi diagram, called a boat-sail Voronoi diagram, is defined on the basis of the time necessary for a boat to reach on water surface with flow. 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. We also apply our equation to the simulation of the forest fire. © Springer-Verlag Berlin Heidelberg 2004.