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Article Dans Une Revue Annals of Mathematics and Physics Année : 2023

Covariance edges matrix of geometric elements

Résumé

In this paper, we introduce a new matrix associated with polygons and polyhedrons, namely the covariance edges matrix. We show that, for a regular polygon or polyhedron the corresponding matrix is proportional to the identity of size two or three. Based on this fact, we propose, as an application, several algebraic shape quality measures for convex polygons or polyhedrons. Furthermore, this matrix may be related to the metric of a simplex. Future studies will be devoted to the definition of the covariance edges matrix for higher elements and real applications to mesh optimisation.
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Dates et versions

hal-04238396 , version 1 (10-11-2023)

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Florian Blachère, Houman Borouchaki. Covariance edges matrix of geometric elements. Annals of Mathematics and Physics, 2023, 6 (2), pp.100-107. ⟨10.17352/amp.000088⟩. ⟨hal-04238396⟩
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