Approximation of multiplicatively weighted crystal growth voronoi diagram and its application

Kei Kobayashi; Kokichi Sugihara

doi:10.1002/ecjc.1098

Approximation of multiplicatively weighted crystal growth voronoi diagram and its application

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	21-31
Number of pages	11
Journal	Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)
Volume	85
Issue number	6
DOIs	https://doi.org/10.1002/ecjc.1098
Publication status	Published - 2002 Jun 1
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1002/ecjc.1098

Fingerprint Dive into the research topics of 'Approximation of multiplicatively weighted crystal growth voronoi diagram and its application'. Together they form a unique fingerprint.

Cite this

Approximation of multiplicatively weighted crystal growth voronoi diagram and its application. / Kobayashi, Kei; Sugihara, Kokichi.

In: Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), Vol. 85, No. 6, 01.06.2002, p. 21-31.

Research output: Contribution to journal › Article › peer-review

@article{c5e5ec1bfb1041e6ae4fd863dec04e17,

title = "Approximation of multiplicatively weighted crystal growth voronoi diagram and its application",

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.",

keywords = "Competing robots, Crystal growth model, Fast marching method, Multiplicatively weighted Voronoi diagram, Robot path planning",

author = "Kei Kobayashi and Kokichi Sugihara",

year = "2002",

month = jun,

day = "1",

doi = "10.1002/ecjc.1098",

language = "English",

volume = "85",

pages = "21--31",

journal = "Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)",

issn = "1042-0967",

publisher = "John Wiley and Sons Inc.",

number = "6",

}

TY - JOUR

T1 - Approximation of multiplicatively weighted crystal growth voronoi diagram and its application

AU - Kobayashi, Kei

AU - Sugihara, Kokichi

PY - 2002/6/1

Y1 - 2002/6/1

N2 - 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.

AB - 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.

KW - Competing robots

KW - Crystal growth model

KW - Fast marching method

KW - Multiplicatively weighted Voronoi diagram

KW - Robot path planning

UR - http://www.scopus.com/inward/record.url?scp=0036604844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036604844&partnerID=8YFLogxK

U2 - 10.1002/ecjc.1098

DO - 10.1002/ecjc.1098

M3 - Article

AN - SCOPUS:0036604844

VL - 85

SP - 21

EP - 31

JO - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 1042-0967

IS - 6

ER -

Approximation of multiplicatively weighted crystal growth voronoi diagram and its application

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this