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Topics in Surface Discretization

David Cohen-Steiner 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : A rapidly growing number of applications requires to deal with three-dimensional objects on a computer. These objects are usually represented by triangulated surfaces. This thesis addresses three problems one encounters when dealing with such surfaces. We first give an algorithm which builds a volumic Delaunay triangulation containing a given triangulated surface as a sub-complex. Such triangulations are useful for numerical simulations for instance. Then, we introduce a generalisation of curvature which applies to non-necessarily smooth objects, thus in particular to triangulated surfaces, and we study its stability. This generalisation is then used to design an algorithm for remeshing triangulated surfaces while aiming to reach an optimal complexity/distortion ratio. Finally, we give an algorithm for meshing implicit surfaces which guarantees that the output has the same topology as the input surface.
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  • HAL Id : tel-00832502, version 1



David Cohen-Steiner. Topics in Surface Discretization. Computational Geometry [cs.CG]. Ecole Polytechnique X, 2004. English. ⟨tel-00832502⟩



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