InforLorV4, Main, Exploration, bibRecord, 001088

Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Identifieur interne : 001088 ( Main/Exploration ); précédent : 001087; suivant : 001089

Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Auteurs : Gilles-Philippe Paillé [Canada] ; Pierre Poulain [Canada] ; Bruno Lévy [France]

Source :

Computer Graphics Forum [ 0167-7055 ] ; 2013-08.

RBID : Hal:hal-00930030

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.

Url:

https://hal.inria.fr/hal-00930030

DOI: 10.1111/cgf.12177

Affiliations:

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Le document en format XML

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Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

Source :

Abstract

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