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Échantillonnage pour l'approximation de fonctions sur des maillages

Abstract : Digitalisation is an operation which consists in storing an object in a computer for further manipulation using data processing tools. In this document, we are interested in the digitalisation of three-dimensional objects. It is first a matter of recording the shape of the object. Many methods have been developed to address this problem, and we will focus on objects described as meshes. On such objects the storage of attributes like colour, temperature or electrical charge is often useful, depending on the application. We will describe two complementary approaches to deal with this issue. The first one relies on texture mapping. This technique consists in unfolding ? parametrising ? the mesh on a flat image in which the attribute is stored. A value recovered from the image can therefore be associated with each point of the object. We will describe a method which hides the seam artifact, commonly encountered using this technique. Unfolding the mesh demands that its quality be good, which is not always the case. We thus secondly describe a surface sampling method based on a restricted Voronoï diagram. We especially detail how to efficiently compute such an object and how to optimise it with respect to some quality measure. These results are then applied to the surface fitting problem
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Submitted on : Thursday, March 29, 2018 - 12:14:17 PM
Last modification on : Saturday, October 16, 2021 - 11:26:08 AM
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Vincent Nivoliers. Échantillonnage pour l'approximation de fonctions sur des maillages. Autre [cs.OH]. Université de Lorraine, 2012. Français. ⟨NNT : 2012LORR0161⟩. ⟨tel-01749364⟩



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