Computational geometry: an introduction
Computational geometry: an introduction
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
On good triangulations in three dimensions
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
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A set P of points in Rd is called simplicial if it has dimension d and contains exactly d + 1 extreme points. We show that when P contains n interior points, there is always one point, called a splitter, that partitions P into d + 1 simplices, none of which contain more than dn /(d + 1) points. A splitter can be found in &Ogr; (d4n) time. Using this result, we give a &Ogr; (d4n log1+1/d n) algorithm for triangulating simplicial point sets that are in general position. In R3 we give an &Ogr; (n logn + k) algorithm for triangulating arbitrary point sets, where k is the number of simplices produced. We exhibit sets of 2n + 1 points in R3 for which the number of simplices produced may vary between (n -1)2 + 1 and 2n -2. We also exhibit point sets for which every triangulation contains a quadratic number of simplices.