The Expected Extremes In A Delaunay Triangulation (1991) [24 citations — 3 self]
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author = {Marshall Bern and David Eppstein and Frances Yao},
title = {The Expected Extremes In A Delaunay Triangulation},
year = {1991}
}
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Abstract:
We give an expected-case analysis of Delaunay triangulations. To avoid edge e#ects 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 .Ford 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 #(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. Keywords: Computational geometry, Delaunay triangulation, probabilistic analysis 1. Introduction Suppose that # is a set of points (called sites) in Euclidean d-space, such that no d + 2 sites lie on a sphere (a general position assumption). In the Delaunay triangulation of #, a set of d + 1 sites defines a d-simplex of the triangulation exac...
