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  Exact and Approximate Quadratures for Curvature Tensor Estimation

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.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2674-5 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0023-E703-F
Genre: Conference Paper

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Torsten_Langer.pdf (Any fulltext), 434KB
 
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Copyright: the editors of Vision, Modeling, and Visualization 2005
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 Creators:
Langer, Torsten1, Author           
Belyaev, Alexander1, Author           
Seidel, Hans-Peter1, Author           
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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 Abstract: 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.

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Language(s): eng - English
 Dates: 2005
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 279004
BibTex Citekey: LangerVMV05
Other: Local-ID: C125675300671F7B-0DAAC76861ABE5FEC12570C1003CF16D-LangerVMV05
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Title: Vision, Modeling, and Visualization 2005
Place of Event: Erlangen, Germany
Start-/End Date: 2005-11-16 - 2005-11-18

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Title: Vision, Modeling, and Visualization 2005
  Abbreviation : VMV 2005
  Subtitle : Proceedings ; November 16-18, 2005, Erlangen, Germany
Source Genre: Proceedings
 Creator(s):
Greiner, Günther1, Editor
Hornegger, Joachim1, Editor
Niemann, Heinrich1, Editor
Stamminger, Marc1, Editor           
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Berlin : Akademische Verlagsgesellschaft Aka
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 421 - 428 Identifier: ISBN: 3-89838-068-8