Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

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dc.contributor.authorPaillé, Gilles-Philippeen_US
dc.contributor.authorPoulin, Pierreen_US
dc.contributor.authorLévy, Brunoen_US
dc.contributor.editorYaron Lipman and Hao Zhangen_US
dc.date.accessioned2015-02-28T15:50:36Z
dc.date.available2015-02-28T15:50:36Z
dc.date.issued2013en_US
dc.description.abstractWe 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.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.doi10.1111/cgf.12177en_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12177en_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectPhysically based modelingen_US
dc.titleFitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimizationen_US
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32-Issue 5
SGP13: Eurographics Symposium on Geometry Processing (CGF 32-5)