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Linear angle based parameterization

Published: 04 July 2007 Publication History

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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cover image ACM Other conferences
SGP '07: Proceedings of the fifth Eurographics symposium on Geometry processing
July 2007
273 pages
ISBN:9783905673463

Sponsors

  • EUROGRAPHICS: The European Association for Computer Graphics

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Eurographics Association

Goslar, Germany

Publication History

Published: 04 July 2007

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SGP '07
Sponsor:
  • EUROGRAPHICS
SGP '07: Geometry processing
July 4 - 6, 2007
Barcelona, Spain

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SGP '07 Paper Acceptance Rate 21 of 74 submissions, 28%;
Overall Acceptance Rate 64 of 240 submissions, 27%

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  • (2014)A Novel Symmetric Skew-Hamiltonian Isotropic Lanczos Algorithm for Spectral Conformal ParameterizationsJournal of Scientific Computing10.1007/s10915-014-9840-261:3(558-583)Online publication date: 1-Dec-2014
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