Crystal Voronoi diagram and its applications

Kei Kobayashi, Kokichi Sugihara

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


This paper studies the multiplicatively weighted crystal-growth Voronoi diagram, which describes the partition of the plane into crystals with different growth speeds. This type of the Voronoi diagram is defined, and its basic properties are investigated. The analytic equation describing the boundary curve is given for a simple case. For the general case, an approximation algorithm is proposed. This algorithm is based on a finite-difference method, called a fast marching method, for solving a special type of a partial differential equation. The proposed algorithm is applied to the planning of a collision-free path for a robot avoiding enemy attacks.

Original languageEnglish
Pages (from-to)681-692
Number of pages12
JournalFuture Generation Computer Systems
Issue number5
Publication statusPublished - 2002 Apr
Externally publishedYes


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

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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