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Regular triangulations as lexicographic optimal chains

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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Dates and versions

hal-02391285 , version 1 (03-12-2019)

Identifiers

  • HAL Id : hal-02391285 , version 1

Cite

David Cohen-Steiner, André Lieutier, Julien Vuillamy. Regular triangulations as lexicographic optimal chains. 2019. ⟨hal-02391285⟩
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