Uniform Samples of Generic Surfaces Have Nice Delaunay Triangulations

Letbe a fixed smooth surface in IR3, such that no medial ball touchesmore than four times, counting with multiplicity, or more than three times at any single point. We show that the Delaunay triangulation of any uniform sample ofhas complexity O(nlogn) in the worst case. We also prove that the Delaunay triangulation of n random points onhas complexity O(nlog3 n) with high probability. In both upper bounds,