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Journal Articles Discrete and Computational Geometry Year : 2023

Delaunay and Regular Triangulations as Lexicographic Optimal Chains

David Cohen-Steiner
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André Lieutier
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Julien Vuillamy
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Abstract

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.
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hal-04119345 , version 1 (06-06-2023)

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David Cohen-Steiner, André Lieutier, Julien Vuillamy. Delaunay and Regular Triangulations as Lexicographic Optimal Chains. Discrete and Computational Geometry, 2023, 70, pp.1-50. ⟨10.1007/s00454-023-00485-1⟩. ⟨hal-04119345⟩
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