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.

@article{SHB07,
author = {Basile Sauvage and Stefanie Hahmann and Georges-Pierre Bonneau},
title = {Volume Preservation of Multiresolution Meshes},
journal = {Comput. Graph. Forum},
volume = 26,
number = {3},
pages = {275--283},
note = {Special Issue: Eurographics'2007},
month = sep,
year = 2007
}