Computing Delaunay Triangulations in Manhattan and Maximum Metric

We modify the incremental algorithm for computing Voronoi diagrams in the Euclidean metric proposed by Ohya, Iri and Murota 6] in order to obtain an algorithm for computing Voronoi diagrams (resp. Delaunay triangulations) in Man-hattan and Maximum metric, that is rather simply to implement. We generalize the notions of \Voronoi diagram" and \Delaunay triangulation" in such a way that these structures still can be computed by an algorithm very similar to the one of Ohya, Iri and Murota, and that they contain { as special cases { analogons to the Euclidean Voronoi diagram (Delaunay triangulation) in the Manhattan and Maximum metric. In this paper, we give a detailed description of the algorithm, that makes it (rather) easy to write a computer program that computes Delaunay triangulations for Manhattan or Maximum metric.