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    Fitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimization

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    Type
    Conference Paper
    Authors
    Nivoliers, Vincent
    Yan, Dongming cc
    Lévy, Bruno L.
    KAUST Department
    Visual Computing Center (VCC)
    Date
    2011-12-01
    Permanent link to this record
    http://hdl.handle.net/10754/564480
    
    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 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.
    Journal
    Proceedings of the 20th International Meshing Roundtable, IMR 2011
    Conference/Event name
    20th International Meshing Roundtable, IMR 2011
    ISBN
    9783642247330
    DOI
    10.1007/978-3-642-24734-7-33
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-642-24734-7-33
    Scopus Count
    Collections
    Conference Papers; Visual Computing Center (VCC)

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