The expected extremes in a Delaunay triangulation

@article{Bern1991TheEE,
  title={The expected extremes in a Delaunay triangulation},
  author={Marshall W. Bern and David Eppstein and F. Frances Yao},
  journal={Int. J. Comput. Geometry Appl.},
  year={1991},
  volume={1},
  pages={79-91}
}
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 logn… CONTINUE READING