THE EXPECTED EXTREMES IN A DELAUNAY TRIANGULATION
Marshall W. Bern, David Eppstein, Frances Yao · International Journal of Computational Geometry & Applications · 1991
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 n 1/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.