An O(n log n) algorithm for the voronoi diagram of a set of simple curve segments

Let X be a given set of n circular and straight line segments in the plane where two segments may interest only at their endpoints. We introduce a new technique that computes the Voronoi diagram of X in O(n log n) time. This result improves on several previous algorithms for special cases of the problem. The new algorithm is relatively simple, an important factor for the numerous practical applications of the Voronoi diagram.