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“Fitting Polynomial Volumes to Surface Meshes with Voronoi Squared Distance Minimization”
Gilles-Philippe Paillé, Pierre Poulin and Bruno Lévy
ACM/EG Symposium on Geometry Processing / Computer Graphics Forum, 2013

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 Voronoi 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.

BibTex reference

@INPROCEEDINGS{paille:FPV:09,
   AUTHOR     = "Gilles-Philippe Paillé and Pierre Poulin and Bruno Lévy
                   ",
   TITLE      = "Fitting Polynomial Volumes to Surface Meshes with Voronoi Squared Dis
                   tance Minimization",
   BOOKTITLE  = "ACM/EG Symposium on Geometry Processing / Computer Graphics Forum",
   YEAR       = "2013",
}

Supplemental material, links, hindsight ...

This is joint work with Montreal University. See author's homepages and lab websites below :

Gilles Philippe Paillé

Pierre Poulin


See also project page in Montreal University website.