An incremental construction algorithm for Delaunay triangulation based on two-level uniform subdivision
Žalik, Borut ; Kolingerová, Ivana
The report introduces a new algorithm for constructing Delaunay triangulation in 2D. It belongs to the class of incremental construction algorithms. The bottleneck of these algorithms is the search ...for a triangle into which a point, which is tried to be integrated into triangulation, falls. We transform this problem to the closest point problem. The search for the closest point is sped-up by two-level uniform subdivision. In this way, the most important drawback of the unform subdivision, i.e., it does not give good results when geometric data are distributed non-uniformly, has been reduced. The algorithm has been compared to two other algorithms programmed by the authors of the paper: Guibas, Knuth, and Sharir's algorithm, and Fang and Piegl's algorithm using uniformly distributed data. The real data sets from geographical database have been employed. The presented algorithm is faster than referenced algorithms. It is also not memory demanding. Beside these, it will be shown that features of the algorithm do not getting worse when real data (non-uniformly distributed) are used. The worst case time complexity is O(▫$n[sub]2$▫), but this case is not expected in real situations. The time complexity obtained by measuring spent CPU time is much better: O(▫$n[sup]1,1$▫), where n is the number of points being triangulated.
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Založništvo in izdelava - Maribor : Faculty of Electrical Engineering and Computer Science, Laboratory for geometrical modelling and multimedia algorithms, 2001
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