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# 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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Reports

Cited literature [23 references]

https://hal.inria.fr/inria-00124825
Contributor : Frédéric Chazal Connect in order to contact the contributor
Submitted on : Saturday, January 20, 2007 - 10:18:04 AM
Last modification on : Friday, February 4, 2022 - 3:09:35 AM
Long-term archiving on: : Monday, June 27, 2011 - 3:35:58 PM

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• HAL Id : inria-00124825, version 2

### Citation

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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