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  Linear Angle Based Parameterization

Zayer, R., Lévy, B., & Seidel, H.-P. (2007). Linear Angle Based Parameterization. In D. Fellner, & S. Spencer (Eds.), SGP 2007 (pp. 135-141). Aire-la-Ville, Switzerland: Eurographics Association. doi:10.2312/SGP/SGP07/135-141.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-1FB6-E Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0023-D49C-E
Genre: Conference Paper

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The current file is a preliminary version of the article. Please find the definite version in the proceedings of the ACM/EG Symposium on Geometry Processing 2007 (SGP '07). The definite electronic version is available online at diglib.eg.org.
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 Creators:
Zayer, Rhaleb1, Author           
Lévy, Bruno2, Author
Seidel, Hans-Peter1, Author           
Affiliations:
1Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              
2External Organizations, ou_persistent22              

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 Abstract: In the field of mesh parameterization, the impact of angular and boundary distortion on parameterization quality have brought forward the need for robust and efficient free boundary angle preserving methods. One of the most prominent approaches in this direction is the Angle Based Flattening (ABF) which directly formulates the problem as a constrained nonlinear optimization in terms of angles. Since the original formulation of the ABF, a steady research effort has been dedicated to improving its efficiency. As for any well posed numerical problem, the solution is generally an approximation of the underlying mathematical equations. The economy and accuracy of the solution are to a great extent affected by the kind of approximation used. In this work we reformulate the problem based on the notion of error of estimation. A careful manipulation of the resulting equations yields for the first time a linear version of angle based parameterization. The error induced by this linearization is quadratic in terms of the error in angles and the validity of the approximation is further supported by numerical results. Besides performance speedup, the simplicity of the current setup makes re-implementation and reproduction of our results straightforward.

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Language(s): eng - English
 Dates: 2008-03-1420072007
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 356557
DOI: 10.2312/SGP/SGP07/135-141
Other: Local-ID: C12573CC004A8E26-D8DFAA1EB1922B82C12572F4003CDE39-zls:linabp:07
BibTex Citekey: zls:linabp:07
 Degree: -

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Title: Fifth Eurographics Symposium on Geometry Processing
Place of Event: Barcelona, Spain
Start-/End Date: 2007-07-04 - 2007-07-06

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Title: SGP 2007
  Abbreviation : SGP 2007
  Subtitle : Symposium on Geometry Processing 2007 ; Fifth Eurographics Symposium on Geometry Processing ; Barcelona, Spain, July 04 – 06, 2007
Source Genre: Proceedings
 Creator(s):
Fellner, Dieter, Editor
Spencer, Stephen, Editor
Affiliations:
-
Publ. Info: Aire-la-Ville, Switzerland : Eurographics Association
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 135 - 141 Identifier: ISBN: 978-3-905673-46-3