Volume Preservation of Multiresolution Meshes

• Published in: Computer graphics forum Vol. 26; no. 3; pp. 275 - 283
• Main Authors: Sauvage, Basile, Hahmann, Stefanie, Bonneau, Georges-Pierre
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.09.2007; Wiley
• Subjects: and object representations; Animation; Computational Geometry; Computer graphics; Computer Science; constrained deformation; Graphics; I.3.5 [Computer Graphics]: Curve; I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations; I.3.6 [Computer Graphics]: Graphics data structures and data types; I.3.7 [Computer Graphics]: Animation; lifting scheme; multiresolution meshes; solid; Studies; surface; volume computation; wavelets; multiresolution meshes; volume constraint; wavelets; deformation; lifting scheme; Loop subdivision; Geometric Modeling
• ISSN: 0167-7055; 1467-8659; 1467-8659
• DOI: 10.1111/j.1467-8659.2007.01049.x

Geometric constraints have proved to be efficient for enhancing 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. A closed form of the solution is derived.