Edge-flipping algorithm for computing the circle set Voronoi diagram

원 집합의 보로노이 다이어그램을 구하는 모서리 플립 알고리듬

Presented in this paper is an algorithm to compute the Voronoi diagram of a circle set from the Voronoi diagram of a point set. The circles are located in Euclidean plane, the radii of the circles are non-negative and not necessarily equal, and the circles are allowed to intersect each other. The idea of the algorithm is to use the topology of the point set Voronoi diagram as a seed so that the correct topology of the circle set Voronoi diagram can be obtained through a number of edge flipping operations. Then, the geometries of the Voronoi edges of the circle set Voronoi diagram are computed. The main advantages of the proposed algorithm are in its robustness, speed, and the simplicity in its concept as well as implementation.