Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations

This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through” the triangulation, after selecting a “good starting point” by random sampling. The analysis generalizes and extends a recent result for dD 2 dimensions by proving this procedure takes expected time close to O.n 1=.dC1/ / for point location in Delaunay triangulations of n random points indD 3 dimensions. Empirical results in both two and three dimensions show that this procedure is efficient in practice. © 1999 Elsevier Science B.V. All rights reserved.

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