# Regular and non-regular point sets: properties and reconstruction

1 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion of $r$-sampling to the practical case of discrete shapes, seems much more realistic than previously proposed conditions based on properties of the underlying continuous shapes. Indeed, contrary to previous sampling criteria, our regularity condition can be checked on the basis of the samples alone and can be turned into a provably correct curve and surface reconstruction algorithm. Our reconstruction methods can also be applied to non-regular and unorganized point sets, revealing a larger part of the inner structure of such point sets than past approaches. Several real-size reconstruction examples validate the new method.
Mots-clés :
Type de document :
Article dans une revue
Computational Geometry, Elsevier, 2001, 19 (2-3), pp.101--126. 〈10.1016/S0925-7721(01)00016-5〉
Domaine :

https://hal.inria.fr/inria-00100428
Contributeur : Publications Loria <>
Soumis le : jeudi 26 mai 2011 - 16:31:56
Dernière modification le : jeudi 11 janvier 2018 - 06:20:04
Document(s) archivé(s) le : samedi 27 août 2011 - 02:21:49

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BoyerPetitjean_cgta01.pdf
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### Citation

Sylvain Petitjean, Edmond Boyer. Regular and non-regular point sets: properties and reconstruction. Computational Geometry, Elsevier, 2001, 19 (2-3), pp.101--126. 〈10.1016/S0925-7721(01)00016-5〉. 〈inria-00100428〉

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