Voronoi diagram of circles in a large circle

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. © Springer-Verlag 2003.