Approximation of multiplicatively weighted crystal growth Voronoi diagram and its application

Abstract

Abstract A multiplicatively weighted crystal growth Voronoi diagram is a type of planar segmentation diagram that can result when crystals grow at different speeds from several points. In this paper, we first define a multiplicatively weighted crystal growth Voronoi diagram, discuss its properties, and find the analytic solution for the simple case. The approximate solution method for the complex case is constructed by using a difference method for partial differential equations called the fast marching method. Then the multiplicatively weighted crystal growth Voronoi diagram is used to construct a technique for optimum path planning of competing mobile robots. © 2002 Scripta Technica, Electron Comm Jpn Pt 3, 85(6): 21–31, 2002