Anisotropic and feature sensitive triangular remeshing using normal lifting

Vincent Nivoliers 1, 2 Bruno Lévy 3 Christophe Geuzaine 2
1 R3AM - Rendu Réaliste pour la Réalité Augmentée Mobile
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
3 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : This work describes an automatic method to anisotropically remesh an input bad quality mesh while preserving sharp features. We extend the method of Lévy and Bonneel [17], based on the lifting of the input mesh in a 6D space (position and normal), and the optimization of a restricted Voronoï diagram in that space. The main advantage of this method is that it does not require any parameterization of the input geometry: the remeshing is performed globally, and triangles can overlap several input charts. We improve this work by modifying the objective function minimized in the optimization process, in order to take into account sharp features. This new formulation is a generalization of the work of Lévy and Liu [18], which does not require any explicit tagging of the sharp features. We provide efficient formulas to compute the gradient of our objective function, thus allowing us to use a quasi-Newton solver [19] to perform the minimization.
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Vincent Nivoliers, Bruno Lévy, Christophe Geuzaine. Anisotropic and feature sensitive triangular remeshing using normal lifting. Journal of Computational and Applied Mathematics, Elsevier, 2015, 289, pp.225-240. ⟨10.1016/j.cam.2015.01.041⟩. ⟨hal-01202738⟩

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