Fitting Polynomial Volumes to Surface Meshes with Voronoï SDM
Gilles-Philippe Paillé, Pierre Poulin, Bruno Lévy
EG/ACM Symposium on Geometry Processing / Computer Graphics Forum 2013

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Abstract

We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a volume distortion criterion. The result is a point-to-point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoï Squared Distance Minimization (VSDM) combined with a higher-order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi-sharp features to be implicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We apply our method to geometric modeling applications in computer-aided design and computer graphics, including mixed-element meshing, mesh optimization, subdivision volume fitting, and shell meshing.

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Bibtex

@article{PPL13,
    author = {Gilles-Philippe Paill\'e and Pierre Poulin and Bruno L\'evy },
    title = {Fitting Polynomial Volumes to Surface Meshes with {V}orono\"i Squared Distance Minimization},
    journal = {Computer Graphics Forum},
    volume= {32},
    number= {5},
    pages = {103--112},
    year = {2013}
}