Detail Preserving Deformation of B-spline Surfaces with Volume Constraint

Geometric constraints have proved to be helpful for shape modeling. Moreover, they are efficient aids in controlling deformations and enhancing animation realism. The present paper adresses the deformation of B-spline surfaces while constraining the volume enclosed by the surface. Both uniform and non-uniform frameworks are considered. The use of level-of-detail (LoD) editing allows the preservation of tne details during coarse deformations of the shape. The key contribution of this paper is the computation of the volume with respect to the appropriate basis for LoD editing: the volume is expressed through all levels of resolution as a trilinear form and recursive formulas are developped to make the computation e±cient. The volume constrained is maintained through a minimization process for which we develop closed solutions. Real-time deformations are reached thanks to sparse data structures and e±cient algorithms.

Keywords

tensor product multiresolution deformation volume constraint B-spline surfaces Geometric Modeling

Domains

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

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SHBE07-cagd.pdf (1.96 Mo)

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https://hal.science/hal-00319636

Submitted on : Monday, September 8, 2008-10:58:11 PM

Last modification on : Thursday, April 4, 2024-9:26:32 PM

Long-term archiving on: Thursday, June 3, 2010-7:03:43 PM

Dates and versions

hal-00319636 , version 1 (08-09-2008)

Identifiers

HAL Id : hal-00319636 , version 1
DOI : 10.1016/j.cagd.2007.10.004

Cite

Basile Sauvage, Stefanie Hahmann, Georges-Pierre Bonneau, Gershon Elber. Detail Preserving Deformation of B-spline Surfaces with Volume Constraint. Computer Aided Geometric Design, 2008, 25 (8), pp.678-696. ⟨10.1016/j.cagd.2007.10.004⟩. ⟨hal-00319636⟩

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