TY - JOUR
T1 - Crystal Voronoi diagram and its applications
AU - Kobayashi, Kei
AU - Sugihara, Kokichi
N1 - Funding Information:
The authors express their thanks to Prof. K. Hayami, Mr. T. Nishida and Mr. S. Horiuchi of the University of Tokyo for valuable comments. This work is supported by the Grant-in-Aid for Scientific Research of the Japanese Ministry of Education, Science, Sports and Culture.
PY - 2002/4
Y1 - 2002/4
N2 - 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.
AB - 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.
KW - Crystal-growth model
KW - Fast marching method
KW - Multiplicatively weighted Voronoi diagram
KW - Robot path planning
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U2 - 10.1016/S0167-739X(02)00033-X
DO - 10.1016/S0167-739X(02)00033-X
M3 - Article
AN - SCOPUS:0036532421
VL - 18
SP - 681
EP - 692
JO - Future Generation Computer Systems
JF - Future Generation Computer Systems
SN - 0167-739X
IS - 5
ER -