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Title: Mesh parameterization by minimizing the synthesized distortion metric with the coefficient-optimizing algorithm
Authors: Yan, J
Yang, X
Shi, P
Zhang, DD 
Issue Date: Jan-2006
Source: IEEE transactions on visualization and computer graphics, Jan./Feb. 2006, v. 12, no. 1, p. 83-92
Abstract: The parameterization of a 3D mesh into a planar domain requires a distortion metric and a minimizing process. Most previous work has sought to minimize the average area distortion, the average angle distortion, or a combination of these. Typical distortion metrics can reflect the overall performance of parameterizations but discount high local deformations. This affects the performance of postprocessing operations such as uniform remeshing and texture mapping. This paper introduces a new metric that synthesizes the average distortions and the variances of both the area deformations and the angle deformations over an entire mesh. Experiments show that, when compared with previous work, the use of synthesized distortion metric performs satisfactorily in terms of both the average area deformation and the average angle deformation; furthermore, the area and angle deformations are distributed more uniformly. This paper also develops a new iterative process for minimizing the synthesized distortion, the coefficient-optimizing algorithm. At each iteration, rather than updating the positions immediately after the local optimization, the coefficient-optimizing algorithm first update the coefficients for the linear convex combination and then globally updates the positions by solving the Laplace system. The high performance of the coefficient-optimizing algorithm has been demonstrated in many experiments.
Keywords: Mesh parameterization
Texture mapping
Barycentric mapping
Conformal mapping
Harmonic mapping
Publisher: Institute of Electrical and Electronics Engineers
Journal: IEEE transactions on visualization and computer graphics 
ISSN: 1077-2626
EISSN: 1941-0506
DOI: 10.1109/TVCG.2006.10
Rights: © 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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