Published December 3, 2019
| Version v1
Publication
Regular triangulations as lexicographic optimal chains
- Others:
- COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)
- Understanding the Shape of Data (DATASHAPE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)
- Dassault Systèmes
- Geometric Modeling of 3D Environments (TITANE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Description
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.
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-02391285
- URN
- urn:oai:HAL:hal-02391285v1
- Origin repository
- UNICA