The Expected Extremes in a Delaunay Triangulation
نویسندگان
چکیده
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). Altogether our results provide some measure of the suitability of the Delaunay triangulation for certain applications, such as interpolation and mesh generation.
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عنوان ژورنال:
- Int. J. Comput. Geometry Appl.
دوره 1 شماره
صفحات -
تاریخ انتشار 1991