FEM-like Fast Marching Method for the Computation of the Boat-Sail Distance and the Associated Voronoi Diagram
Tetsushi Nishida, Kōkichi Sugihara · 2004
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 di#erential 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 e#ciency and the stableness of the proposal method.