Approximation of multiplicatively weighted crystal growth voronoi diagram and its application

Kei Kobayashi, Kokichi Sugihara

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)21-31
Number of pages11
JournalElectronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Issue number6
Publication statusPublished - 2002 Jun
Externally publishedYes



  • Competing robots
  • Crystal growth model
  • Fast marching method
  • Multiplicatively weighted Voronoi diagram
  • Robot path planning

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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