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Copier-coller 3D : paramétrisation cohérente de maillages triangulaires

Abstract : We propose an efficient algorithm for the global parameterization of triangulated surfaces. First, cone singularities are automatically detected in visually significant locations ; this process is computationally efficient and aims at detecting such cones at vertices of the mesh where high values of area distortion can be predicted prior to the actual parameterization. In order to ensure continuity across conic cuts resulted after cutting the mesh open through the detected cones, affine transition functions are employed ; these will be integrated into a linear system which aims at minimizing angular distortion. In this thesis we also present a new Cross-Parameterization algorithm which, given two input triangular meshes and sparse user landmark correspondences, computes topologically and geometrically consistent parameterizations. The simultaneous consistent parameterization of the meshes is achieved in a matter of only a few seconds, solving at most four linear systems in a least squares sense. We validate the results of the proposed algorithms by providing extensive experimental results, demonstrating the time efficiency, as well as the quality - illustrated by examining accepted distortion measures. The computational efficiency of the presented algorithms allows their usage in interactive applications, where the user can modify or add cone singularities (or landmark correspondences for the cross-parameterization pipeline) and still obtain results in practical running times.
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Submitted on : Tuesday, November 9, 2021 - 5:43:28 PM
Last modification on : Tuesday, January 18, 2022 - 6:14:54 PM
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  • HAL Id : tel-03422770, version 1



Ana-Maria Vintescu. Copier-coller 3D : paramétrisation cohérente de maillages triangulaires. Géométrie algorithmique [cs.CG]. Télécom ParisTech, 2017. Français. ⟨NNT : 2017ENST0031⟩. ⟨tel-03422770⟩



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