Voronoi diagram of circles in a large circle

Authors:
Deok-Soo Kim;Donguk Kim;Kokichi Sugihara
Affiliations:
Department of Industrial Engineering, Hanyang University, Seoul, Korea;Department of Industrial Engineering, Hanyang University, Seoul, Korea;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Year:
2003

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Abstract

Presented in this paper is an algorithm to compute a Voronoi diagram of circles contained in a sufficiently large circle, where the interior circles are not necessarily disjoint. Given circles in a large circle, the region in the large circle is divided into regions associated with the circles. The algorithm first constructs the ordinary point Voronoi diagram of centers of inner circles. Then, it modifies the point Voronoi diagram considering the large enclosing circle so that the seed topology for the desired Voronoi diagram is obtained by a number of edge-flip operations. After getting the correct topological information, the equations of edges are computed in a rational quadratic Bézier curve form.