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Fitting Polynomial Surfaces to Triangular Meshes with Voronoi Squared Distance Minimization

Nivoliers, Vincent, Dong-Ming Yan and Bruno Levy

20th International Meshing Roundtable, Springer-Verlag, pp.601-616, October 23-26 2011

IMR
PROCEEDINGS

20th International Meshing Roundtable
Paris, France
October 23-26, 2011

Project ALICE/Institut National de Recherche en Informatique et en Automatique (INRIA) Nancy Grand Est, LORIA, Institut National Polytechnique de Lorraine (INPL), Geometric Modeling and Scientific Visualization Center, King Abdullah University of Science and Technology (KAUST)
Email: Vincent.Nivoliers@loria.fr, Dongming.Yan@inria.fr, Bruno.Levy@inria.fr

Summary
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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