A fast approximation of the Voronoi diagram for a set of pairwise disjoint arcs

Abstract

We propose a method for fast approximation of the Voronoi diagram for a set of pairwise disjoint arcs on a plane. The arcs are represented by parameterized curves. A set of input curves is discretized into partition set, for which the Voronoi diagram is constructed. After merging corresponding Voronoi cells and removing redundant edges, the Voronoi graph is approximated by Bezier curves. We also propose the elaboration and optimization of the approximation. The total complexity of the algorithm is O N log N in the worst-case.