Volume preservation of multiresolution meshes

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

Geometric Modeling multiresolution meshes Loop subdivision wavelets volume constraint deformation lifting scheme

Domains

Graphics [cs.GR] Computational Geometry [cs.CG]

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SHB07-EG.pdf (933.72 Ko)

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Horse2.jpg (16.5 Ko)

Horse3.jpg (15.54 Ko)

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https://hal.science/hal-00319628

Submitted on : Monday, September 8, 2008-10:25:01 PM

Last modification on : Thursday, April 4, 2024-9:10:24 PM

Long-term archiving on: Monday, October 8, 2012-12:58:22 PM

Dates and versions

hal-00319628 , version 1 (08-09-2008)

Identifiers

HAL Id : hal-00319628 , version 1
DOI : 10.1111/j.1467-8659.2007.01049.x

Cite

Basile Sauvage, Stefanie Hahmann, Georges-Pierre Bonneau. Volume preservation of multiresolution meshes. Computer Graphics Forum, 2007, 26 (3), pp.275-283. ⟨10.1111/j.1467-8659.2007.01049.x⟩. ⟨hal-00319628⟩

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