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Proceedings of the 20th International Meshing Roundtable pp 601–617Cite as

Fitting Polynomial Surfaces to Triangular Meshes with Voronoi Squared Distance Minimization

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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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Author information

Authors and Affiliations

  1. Project ALICE / Institut National de Recherche en Informatique et en Automatique (INRIA) Nancy Grand Est, LORIA, France

    Vincent Nivoliers, Dong-Ming Yan & Bruno Lévy

  2. Institut National Polytechnique de Lorraine (INPL), France

    Vincent Nivoliers

  3. Geometric Modeling and Scientific Visualization Center, King Abdullah University of Science and Technology (KAUST), France

    Dong-Ming Yan

Authors
  1. Vincent Nivoliers
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  2. Dong-Ming Yan
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  3. Bruno Lévy
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Editor information

Editors and Affiliations

  1. Sandia National Laboratories, P.O. Box 5800, 87185, Albuquerque, NM, USA

    William Roshan Quadros

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© 2011 Springer-Verlag Berlin Heidelberg

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Nivoliers, V., Yan, DM., Lévy, B. (2011). Fitting Polynomial Surfaces to Triangular Meshes with Voronoi Squared Distance Minimization. In: Quadros, W.R. (eds) Proceedings of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24734-7_33

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  • DOI: https://doi.org/10.1007/978-3-642-24734-7_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24733-0

  • Online ISBN: 978-3-642-24734-7

  • eBook Packages: EngineeringEngineering (R0)

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