Volume preservation of multiresolution meshes

Abstract : Geometric constraints have proved to be efficient for improving the realism of shape animation. The present paper addresses the computation and the preservation of the volume enclosed by multiresolution meshes. A wavelet based representation allows the mesh to be handled at any level of resolution. The key contribution is the calculation of the volume as a trilinear form with respect to the multiresolution coefficients. Efficiency is reached thanks to the pre-processing of a sparse 3D data structure involving the transposition of the filters while represented as a lifting scheme. A versatile and interactive method for preserving the volume during a deformation process is then proposed. It is based on a quadratic minimization subject to a linearization of the volume constraint.
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Submitted on : Monday, September 8, 2008 - 10:25:01 PM
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Basile Sauvage, Stefanie Hahmann, Georges-Pierre Bonneau. Volume preservation of multiresolution meshes. Computer Graphics Forum, Wiley, 2007, 26 (3), pp.275-283. ⟨10.1111/j.1467-8659.2007.01049.x⟩. ⟨hal-00319628⟩

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