volume 33, issue 1, P83-115 2004
DOI: 10.1007/s00454-004-1089-3
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## Abstract: The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R 3 with spread has complexity O( 3 ). This bound is tight in the worst case for all = O( √ n). In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to regular triangulations of k-ply systems of balls, unions of several dense point sets, and uniform samples of smooth surfa…

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