A dynamic sampling approach towards computing Voronoi diagram of a set of circles

Abstract

Discretizing the input curves into points or lines is a way of constructing an approximate Voronoi diagram. Sampling the input curves into points requires a fine sample density to obtain a reasonable topological and geometrical accuracy of the Voronoi diagram. In this work, it is shown that an accurate computation of the Voronoi diagram for a set of circles employing a very coarse sample set is possible. The approach proposes the selection of varying number of sample points on each circle dynamically, using the Delaunay graph of center points of circles. We then show that this approach can be used to identify neighborhood information of the circles. The touching disc method is then used to construct the Voronoi diagram with an algorithmic complexity of O(nlogn). The work also demonstrates the robustness and theoretical correctness of the proposed algorithm by considering inputs in non-general position and for a large number of circles of the order of 105.