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Theses

Sur l'approximation discrète des courbures des courbes planes et des surfaces de l'espace euclidien de dimension 3.

Abstract : This thesis deals with discrete approximations of curvatures at a point on a smooth curve or surface. The angular defect provides a good approximation of the curvature at a point P on a smooth curve. We give an estimation of the error between the discrete curvature at P and the smooth one, using the 1-germ of the curvature at P, a parameter related to the geometry of the curve and the length of the approximation. In the case of a smooth surface S, the angular defect of a regular mesh approaches a homogenous polynomial of degree two in the principal curvatures. We give an estimation of the difference between the discrete curvature and this polynomial. We show that if we precisely control the geometry of the mesh, we have a good estimation of the difference between the discrete curvature and this polynomial. We finally show how to shrink the mesh to have convergence results when the mesh size tends towards 0.
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Theses
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https://tel.archives-ouvertes.fr/tel-00186301
Contributor : Fabrice Orgeret <>
Submitted on : Thursday, November 8, 2007 - 4:15:12 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:14 PM
Long-term archiving on: : Monday, April 12, 2010 - 1:41:25 AM

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  • HAL Id : tel-00186301, version 1

Citation

Fabrice Orgeret. Sur l'approximation discrète des courbures des courbes planes et des surfaces de l'espace euclidien de dimension 3.. Mathématiques [math]. Université Claude Bernard - Lyon I, 2007. Français. ⟨tel-00186301⟩

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