Abstract
In this paper, we propose a method for constructing Voronoi diagrams with two-dimensional obstacles by a simple and practical computer algorithm, using the shortest-path distance of a Delaunay network of many random vertices, which we termed as rDn. By measuring the shortest-path distance of the rDn for the detour distance, this method provides an approximate solution for the Voronoi diagrams with obstacles. We verify the isotropy and stability of the ratio of the shortest-path distance of the rDn and the Euclid distance by a computer experiment. We then show the reliability of the approximate solution by comparing with the exact solution in a simple case, and the effectiveness of this method by solving a sample problem with free shaped obstacles.
