Volume Preservation of Multiresolution Meshes
Résumé
Geometric constraints have proved to be effi cient for enhancing the realism of shape animation. Our presentation 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 coeffi cients. Effi ciency 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. A closed form of the solution is derived.