# Normal Cone Approximation and Offset Shape Isotopy

1 GEOMETRICA - Geometric computing
INRIA Futurs, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This work adresses the problem of the approximation of the normals of the offsets of general compact sets in euclidean spaces. It is proven that for general sampling conditions, it is possible to approximate the gradient vector field of the distance to general compact sets. These conditions involve the $\mu$-reach of the compact set, a recently introduced notion of feature size. As a consequence, we provide a sampling condition that is sufficient to ensure the correctness up to isotopy of a reconstruction given by an offset of the sampling. We also provide a notion of normal cone to general compact sets which is stable under perturbation.
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Type de document :
Rapport
[Research Report] RR-6100, INRIA. 2007, pp.21
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https://hal.inria.fr/inria-00124825
Contributeur : Frédéric Chazal <>
Soumis le : samedi 20 janvier 2007 - 10:18:04
Dernière modification le : vendredi 23 février 2018 - 14:20:08
Document(s) archivé(s) le : lundi 27 juin 2011 - 15:35:58

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ApproxGradRRNum.pdf
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• HAL Id : inria-00124825, version 2

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Frédéric Chazal, David Cohen-Steiner, André Lieutier. Normal Cone Approximation and Offset Shape Isotopy. [Research Report] RR-6100, INRIA. 2007, pp.21. 〈inria-00124825v2〉

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