HAL - INRIA :: [hal-00319636, version 1] Detail Preserving Deformation of B-spline Surfaces with Volume Constraint

hal-00319636, version 1

Detail Preserving Deformation of B-spline Surfaces with Volume Constraint

Basile Sauvage ( Author to contact preferably ) ^1, 2, Stefanie Hahmann () ¹, Georges-Pierre Bonneau () ^1, 3, Gershon Elber ⁴

Computer Aided Geometric Design 25, 8 (2008) 678-696

Abstract: 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.

1: Laboratoire Jean Kuntzmann (LJK)
CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
2: Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection (LSIIT)
CNRS : UMR7005 – Université de Strasbourg
3: EVASION (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
CNRS : UMR5224 – INRIA – Laboratoire Jean Kuntzmann – Institut National Polytechnique de Grenoble (INPG) – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II
4: Center for Graphics and Geometric Computing (CGGC)
Technion - Israel Institute of Technology

hal-00319636, version 1
http://hal.archives-ouvertes.fr/hal-00319636
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From: Stefanie Hahmann <>
Submitted on: Monday, 8 September 2008 22:58:11
Updated on: Thursday, 8 March 2012 10:18:08

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DOI: 10.1016.j.cagd.2007.10.004

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%% hal-00319636, version 1
%% http://hal.archives-ouvertes.fr/hal-00319636
@article{SAUVAGE-2008-319636,
    hal_id = {hal-00319636},
    url = {http://hal.archives-ouvertes.fr/hal-00319636},
    title = {{Detail Preserving Deformation of B-spline Surfaces with Volume Constraint}},
    author = {Sauvage, Basile and Hahmann, Stefanie and Bonneau, Georges-Pierre and Elber, Gershon},
    abstract = {{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$\pm$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$\pm$cient algorithms.}},
    keywords = {Geometric Modeling, multiresolution; B-spline surfaces; tensor product; volume constraint; deformation.},
    language = {English},
    affiliation = {Laboratoire Jean Kuntzmann - LJK , Laboratoire des Sciences de l'Image, de l'Informatique et de la T{\'e}l{\'e}d{\'e}tection - LSIIT , EVASION - INRIA Grenoble Rh{\^o}ne-Alpes / LJK Laboratoire Jean Kuntzmann , Center for Graphics and Geometric Computing - CGGC},
    pages = {678-696},
    journal = {Computer Aided Geometric Design},
    volume = {25},
    number = {8 },
    note = {NoE AIM@SHAPE },
    audience = {international },
    doi = {10.1016.j.cagd.2007.10.004 },
    year = {2008},
    month = Nov,
    pdf = {http://hal.archives-ouvertes.fr/hal-00319636/PDF/SHBE07-cagd.pdf},
}

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