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.
Keywords: multiresolution meshes; Loop subdivision, lifting scheme, wavelets, volume constraint; deformation.
B. Sauvage, S.Hahmann, GP. Bonneau
Volume preservation of multiresolution meshes ,
Computer Graphics Forum (Proceedings of Eurographics 2007), Volume 26, Number 3 - 2007
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