A note on Delaunay diagonal flips

Abstract Suppose we wish to transform an arbitrary triangulation of a point set into its Delaunay triangulation. A Delaunay diagonal flip replaces the common edge of two abutting triangles with the opposite diagonal if the resulting triangles would locally satisfy the Delaunay empty-circle condition. We show that Θ ( n 2 ) Delaunay diagonal flips are necessary and sufficient to transform any triangulation into the Delaunay triangulation.