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Fitting Polynomial Surfaces to Triangular Meshes with Voronoi Squared Distance Minimization

Vincent Nivoliers 1, 2, * Dong-Ming Yan 1, 3 Bruno Lévy 1
* Corresponding author
1 ALICE - Geometry and Lighting
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : This paper introduces Voronoi Squared Distance Minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of Centroidal Voronoi Tesselation (CVT), and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh to best approximate the input, without estimating any differential quantities. Therefore it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.
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Vincent Nivoliers, Dong-Ming Yan, Bruno Lévy. Fitting Polynomial Surfaces to Triangular Meshes with Voronoi Squared Distance Minimization. 20th International Meshing Roundtable - IMR 2011, Oct 2011, Paris, France. pp.601-617, ⟨10.1007/978-3-642-24734-7_33⟩. ⟨hal-00763898⟩

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