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Theses

Triangulation de Delaunay et arbres multidimensionnels

Abstract : This thesis deals mainly with Delaunay triangulations. It is shown that the average complexity of k-dimensional merge processes - according to unRnished sites - is linear, assuming the sites to be quasy-uniformly distributed in an hypercube. This general result is applied to the two-dimensional case, and allows to analyze new Delaunay triangulation algorithms which perform better than those known to this day. The underlying principle is to divide the domain according to k-dimensional trees (quadtree, 2d-tree, bucket-tree. . . ), and then to merge the obtained cells along two directions. We are currently trying to generalize these algorithms to the constrained case (graphs with constraints, and not only vertices). We propose new point location algorithmsC based upon randomisation on a dynamic binary search tree AVL. One of them is faster than Kirkpatrick's optimal algorithm at least up to 12 millions of sites. Their formal average analysis is being done. We use this algorithm to build Delaunay triangulations "on-line" which is one of the most performant known "on-line" method.
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  • HAL Id : tel-00850521, version 1

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Christophe Lemaire. Triangulation de Delaunay et arbres multidimensionnels. Synthèse d'image et réalité virtuelle [cs.GR]. Ecole Nationale Supérieure des Mines de Saint-Etienne; Université Jean Monnet - Saint-Etienne, 1997. Français. ⟨NNT : 1997STET4021⟩. ⟨tel-00850521⟩

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