OFC-Delaunay triangulation: A new efficient algorithm for merging two adjacent Delaunay triangulations

Abstract

In this paper, we present an efficient algorithm, namely Orienting and Final Circles (OFC)-Delaunay Triangulation, for constructing the Delaunay triangulation of a finite planar point set using the idea of the Method of Orienting Curves (introduced by Phu in Zur Lösung einer regulären Aufgabenklasse der optimalen Steuerung im Groen mittels Orientierungskurven, Optimization 18(1) (1987) 65–81 and Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner, Optimization 18(3) (1987) 349–359). The concepts of orienting and final circles are introduced. The Delaunay edges are determined by orienting circles and a final circle. Our algorithm has [Formula: see text]([Formula: see text]) worst-case running time. The algorithm is implemented in Python and some numerical examples are presented.