Regular triangulations as lexicographic optimal chains
Résumé
We introduce a total order on n-simplices in the n-Euclidean space for which the support of the lexicographic-minimal chain with the convex hull boundary as boundary constraint is precisely the n-dimensional Delaunay triangulation, or in a more general setting, the regular triangulation of a set of weighted points. This new characterization of regular and Delaunay triangulations is motivated by its possible generalization to submanifold triangulations as well as the recent development of polynomial-time triangulation algorithms taking advantage of this order.
Domaines
Géométrie algorithmique [cs.CG]
Fichier principal
LexicographicRegTriangulationResearchReport.pdf (722.17 Ko)
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