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    Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

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    Type
    Article
    Authors
    Nivoliers, Vincent
    Yan, Dongming cc
    Lévy, Bruno L.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2012-11-06
    Online Publication Date
    2012-11-06
    Print Publication Date
    2014-07
    Permanent link to this record
    http://hdl.handle.net/10754/564627
    
    Metadata
    Show full item record
    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 the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements 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. © 2012 Springer-Verlag London.
    Sponsors
    The authors wish to thank Sylvain Lefebvre for a discussion (about an unrelated topic) that inspired this work, Rhaleb Zayer, Xavier Goaoc, Tamy Boubekeur, Yang Liu and Wenping Wang for many discussions, Loic Marechal, Marc Loriot and the AimAtShape repository for data. This project is partly supported by the European Research Council grant GOODSHAPE ERC-StG-205693 and ANR/NSFC (60625202,60911130368) Program (SHAN Project).
    Publisher
    Springer Nature
    Journal
    Engineering with Computers
    DOI
    10.1007/s00366-012-0291-9
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00366-012-0291-9
    Scopus Count
    Collections
    Articles; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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