We propose a fast approximation of the Voronoi diagram for a set of pairwise disjoint arcs on a plane. The arcs represented by parameterized curves. For curves we obtain a partition for which the Voronoi diagram is built. After the transformations in the Voronoi diagram, the result is approximated by Bezier curves and elliptic arcs. In this paper, we also propose the elaboration and optimization of the approximation. The total complexity of the algorithm is O(N log?N ) (worst-case).