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Réseaux de Coxeter-Davis et commensurateurs

Frédéric Haglund (1998)

Annales de l'institut Fourier

For each integer k 6 and each finite graph L , we construct a Coxeter group W and a non positively curved polygonal complex A on which W acts properly cocompactly, such that each polygon of A has k edges, and the link of each vertex of A is isomorphic to L . If L is a “generalized m -gon”, then A is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on Aut ( L ) for Aut ( A ) to be non enumerable (which is satisfied if L is a thick classical generalized m -gon). On the other hand,...

Robust Shape Reconstruction and Optimal Transportation

Pierre Alliez, Simon Giraudot, David Cohen-Steiner (2013)

Actes des rencontres du CIRM

We describe a framework for robust shape reconstruction from raw point sets, based on optimal transportation between measures, where the input point sets are seen as distribution of masses. In addition to robustness to defect-laden point sets, hampered with noise and outliers, our approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.

Rotation indices related to Poncelet’s closure theorem

Waldemar Cieślak, Horst Martini, Witold Mozgawa (2015)

Annales UMCS, Mathematica

Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.

Routh’s, Menelaus’ and Generalized Ceva’s Theorems

Boris A. Shminke (2012)

Formalized Mathematics

The goal of this article is to formalize Ceva’s theorem that is in the [8] on the web. Alongside with it formalizations of Routh’s, Menelaus’ and generalized form of Ceva’s theorem itself are provided.

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