Generalized delaunay triangulation for planar graphs

Abstract

We introduce the notion of generalized Delaunay triangulation of a planar straight-line graph G=(V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the triangles in the triangulation is maximum among all possible triangulations of the graph. A general algorithm that runs in O(|V|2) time for computing the generalized Delaunay triangulation is presented. When the underlying graph is a simple polygon, a divide-and-conquer algorithm based on the polygon cutting theorem of Chazelle is given that runs in O(|V| log |V|) time. © 1986 Springer-Verlag New York Inc.