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Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Gilles-Philippe Paillé 1 Pierre Poulain 1 Bruno Lévy 2
2 ALICE - Geometry and Lighting
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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 vol- ume 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 im- plicitly 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 ap- ply 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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Submitted on : Tuesday, January 14, 2014 - 11:19:06 AM
Last modification on : Friday, January 8, 2021 - 3:12:02 PM

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Gilles-Philippe Paillé, Pierre Poulain, Bruno Lévy. Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization. Computer Graphics Forum, Wiley, 2013, 32 (5), pp.103-112. ⟨10.1111/cgf.12177⟩. ⟨hal-00930030⟩



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