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Séminaire de Théorie spectrale et géométrie (Grenoble)
Table of contents for this volume | Previous article | Next articleVincent Borrelli
Courbure discrète ponctuelle
Séminaire de Théorie spectrale et géométrie (Grenoble), 25 (2006-2007), p. 25-39, doi: 10.5802/tsg.245
Article PDF | Reviews MR 2478806 | Zbl pre05522003
Class. Math.: 65D18, 53A05
Keywords: Meshes, Curvatures, Approximations
Résumé - Abstract
Let $S$ be a surface of the Euclidean 3-space $\mathbb{E}^3$ and $M$ be a set of triangles forming a piecewise linear approximation of $S$ around a point $P\in S,$ the pointwise discrete curvature $K_d(P)$ of $M$ at the vertex $P$ is defined to be the quotient of the angular defect by the sum of areas of triangles with $P$ as vertex. A natural question is to ask for an estimate of the difference between this discrete curvature $K_d(P)$ and the smooth curvature $K(P)$ of $S$ at $P.$ We present here results from [4], [5], [15] which give majorations of the discrepancy $|K(P)-K_d(P)|.$
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