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Exact and Approximate Quadratures for Curvature Tensor Estimation

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44882

Langer,  Torsten
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44112

Belyaev,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zitation

Langer, T., Belyaev, A., & Seidel, H.-P. (2005). Exact and Approximate Quadratures for Curvature Tensor Estimation. In G. Greiner, J. Hornegger, H. Niemann, & M. Stamminger (Eds.), Vision, Modeling, and Visualization 2005 (pp. 421-428). Berlin: Akademische Verlagsgesellschaft Aka.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-2674-5
Zusammenfassung
Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. In this paper, we derive exact quadrature formulae for mean curvature, Gaussian curvature, and the Taubin integral representation of the curvature tensor. The exact quadratures are then used to obtain reliable estimates of the curvature tensor of a smooth surface approximated by a dense triangle mesh. The proposed method is fast and easy to implement. It is highly competitive with conventional curvature tensor estimation approaches. Additionally, we show that the curvature tensor approximated as proposed by us converges towards the true curvature tensor as the edge lengths tend to zero.