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Article Dans Une Revue Computer Graphics Forum Année : 2013

Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Résumé

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.

Dates et versions

hal-00930030 , version 1 (14-01-2014)

Identifiants

Citer

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