Presented in this paper is an algorithm to compute a Voronoi diagram of circles in a circle, where circles are located in a large circle. Given circles in a large circle, the region in the plane is divided into regions associated with the given circles. The proposed algorithm uses point Voronoi diagram, and then some topological remedies are applied so that we obtain proper initial topology including enclosing circle. From this initial topology, we can obtain the correct topology by a series of edge-flip operations. After getting the correct topology, the equations of edges are computed and represented in a rational quadratic Bézier curve form.

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.