The Expected Extremes in a Delaunay Triangulation

We give an expected-case analysis of Delaunay triangulations. To avoid edge effects we consider a unit-intensity Poisson process in Euclidean d-space, and then limit attention to the portion of the triangulation within a cube of side n1/d. For d equal to two, we calculate the expected maximum edge length, the expected minimum and maximum angles, and the average aspect ratio of a triangle. We also show that in any fixed dimension the expected maximum vertex degree is Θ(log n/ log log n). Altogether our results provide some measure of the suitability of the Delaunay triangulation for certain applications, such as interpolation and mesh generation.

• Type: Conference
• Year: 1991
• Where: ICALP
• Authors: Marshall W. Bern, David Eppstein, F. Frances Yao
• Keywords: Delaunay Triangulation, ICALP 1991, Maximum Edge Length, Programming Languages, Unit-intensity Poisson Process