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  Asymptotic Analysis of Discrete Normals and Curvatures of Polylines

Langer, T., Belyaev, A., & Seidel, H.-P. (2005). Asymptotic Analysis of Discrete Normals and Curvatures of Polylines. In SCCG '05: Proceedings of the 21st spring conference on Computer graphics (pp. 229-232). New York, NY, USA: ACM.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-25CC-9 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-25CD-7
Genre: Conference Paper

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Langer.Torsten.Full.SpaceCurves.pdf (Any fulltext), 173KB
 
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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 smooth curve from its discrete approximation are important for many computer graphics and computer vision applications. To assess and improve the quality of such an approximation, we assume that the curve is known in general form. Then we can represent the curve by a Taylor series expansion and compare its geometric properties with the corresponding discrete approximations. In turn we can either prove convergence of these approximations towards the true properties as the edge lengths tend to zero, or we can get hints on how to eliminate the error. In this paper, we propose and study discrete schemes for estimating tangent and normal vectors as well as for estimating curvature and torsion of a smooth 3D curve approximated by a polyline. Thereby we make some interesting findings about connections between (smooth) classical curves and certain estimation schemes for polylines.

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Language(s): eng - English
 Dates: 2006-06-192005
 Publication Status: Issued
 Pages: -
 Publishing info: New York, NY, USA : ACM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 279006
Other: Local-ID: C125675300671F7B-519A2B2A83342C3AC12571920048876E-LangerSCCG05
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Title: Untitled Event
Place of Event: Budmerice, Slovakia
Start-/End Date: 2005-05-12

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Title: SCCG '05: Proceedings of the 21st spring conference on Computer graphics
Source Genre: Proceedings
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Publ. Info: New York, NY, USA : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 229 - 232 Identifier: ISBN: 80-223-2057-9