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Jingqi Yan, Xin Yang, Pengfei Shi, David Zhang, "Mesh Parameterization by Minimizing the Synthesized Distortion Metric with the CoefficientOptimizing Algorithm," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 1, pp. 8392, January/February, 2006.  
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@article{ 10.1109/TVCG.2006.10, author = {Jingqi Yan and Xin Yang and Pengfei Shi and David Zhang}, title = {Mesh Parameterization by Minimizing the Synthesized Distortion Metric with the CoefficientOptimizing Algorithm}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {12}, number = {1}, issn = {10772626}, year = {2006}, pages = {8392}, doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.10}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Mesh Parameterization by Minimizing the Synthesized Distortion Metric with the CoefficientOptimizing Algorithm IS  1 SN  10772626 SP83 EP92 EPD  8392 A1  Jingqi Yan, A1  Xin Yang, A1  Pengfei Shi, A1  David Zhang, PY  2006 KW  Mesh parameterization KW  texture mapping KW  barycentric mapping KW  conformal mapping KW  harmonic mapping. VL  12 JA  IEEE Transactions on Visualization and Computer Graphics ER   
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 coefficientoptimizing algorithm. At each iteration, rather than updating the positions immediately after the local optimization, the coefficientoptimizing 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 coefficientoptimizing algorithm has been demonstrated in many experiments.
[1] P. Alliez, M. Meyer, and M. Desbrun, “Interactive Geomety Remeshing,” Proc. ACM SIGGRAPH 2002, pp. 347354, 2002.
[2] C. Bennis, J.M. Vézien, G. Iglésias, and A. Gagalowicz, “Piecewise Surface Flattening for NonDistorted Texture Mapping,” Computer Graphics, vol. 25, no. 4, pp. 237246, July 1991.
[3] M. Botsch, C. Rössl, and L. Kobbelt, “Feature Sensitive Sampling for Interactive Remeshing,” Proc. Vision, Modeling, and Visualization 2000, pp. 129136, 2000.
[4] P. Degener, J. Meseth, and R. Klein, “An Adaptable Surface Parameterization Method,” Proc. 12th Int'l Meshing Roundtable, pp. 227237, 2003.
[5] M. Desbrun, M. Meyer, and P. Alliez, “Intrinsic Parametrizations of Surface Meshes,” Computer Graphics Forum, vol. 21, no. 3, pp. 209218, 2002.
[6] M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, “Multiresolution Analysis of Arbitrary Meshes,” Proc. ACM SIGGRAPH '95, pp. 173182, Aug. 1995.
[7] M.S. Floater, “Parametrization and Smooth Approximation of Surface Triangulations,” Computer Aided Geometric Design, vol. 14, no. 3, pp. 231250, 1997.
[8] M.S. Floater, “Mean Value Coordinates,” Computer Aided Geometric Design, vol. 20, no. 1, pp. 1927, 2003.
[9] M.S. Floater and C. Gotsman, “How to Morph Tilings Injectively,” J. Computational and Applied Math., vol. 101, pp. 117129, 1999.
[10] C. Gotsman, X. Gu, and A. Sheffer, “Fundamentals of Spherical Parameterization for 3D Meshes,” ACM Trans. Graphics, vol. 22, no. 3, pp. 358363, July 2003.
[11] X. Gu, S. Gortler, and H. Hoppe, “Geometry Images,” Proc. ACM SIGGRAPH 2002, pp. 355361, 2002.
[12] I. Guskov, K. Vidimce, W. Sweldens, and P. Schröder, “Normal Meshes,” Proc. ACM SIGGRAPH 2000, pp. 95102, 2000.
[13] S. Haker, S. Angenent, A. Tannenbaum, R. Kikinis, G. Sapiro, and M. Halle, “Conformal Surface Parameterization for Texture Mapping,” IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 2, pp. 181189, Apr.June 2000.
[14] K. Hormann and G. Greiner, “MIPS: An Efficient Global Parameterization Method,” Curve and Surface Design: SaintMalo 1999, P.J. Laurent, P. Sablonnière, and L.L. Schumaker, eds., pp. 153162, Nashville Tenn.: Vanderbilt Univ. Press, 2000.
[15] K. Hormann, U. Labsik, and G. Greiner, “Remeshing Triangulated Surfaces with Optimal Parameterizations,” ComputerAided Design, vol. 33, no. 11, pp. 779788, 2001.
[16] J.R. Kent, W.E. Carlson, and R.E. Parent, “Shape Transformation for Polyhedral Objects,” Proc. ACM SIGGRAPH '92, pp. 4754, July 1992.
[17] A. Lee, W. Sweldens, P. Schröder, L. Cowsar, and D. Dobkin, “MAPS: Multiresolution Adaptive Parameterization of Surfaces,” Proc. ACM SIGGRAPH '98, pp. 95104, 1998.
[18] B. Lévy, “Constrained Texture Mapping for Polygonal Meshes,” Proc. ACM SIGGRAPH 2001, pp. 417424, Aug. 2001.
[19] B. Lévy and J.L. Mallet, “NonDistorted Texture Mapping for Sheared Triangulated Meshes,” Proc. ACM SIGGRAPH '98, pp. 343352, 1998.
[20] B. Lévy, S. Petitjean, N. Ray, and J. Maillot, “Least Squares Conformal Maps for Automatic Texture Atlas Generation,” Proc. ACM SIGGRAPH 2002, pp. 362371, 2002.
[21] J. Maillot, H. Yahia, and A. Verroust, “Interactive Texture Mapping,” Proc. ACM SIGGRAPH '93, pp. 2734, 1993.
[22] U. Pinkall and K. Polthier, “Computing Discrete Minimal Surfaces and Their Conjugates,” Experimental Math., vol. 2, no. 1, pp. 1536, 1993.
[23] E. Praun and H. Hoppe, “Spherical Parameterization and Remeshing,” ACM Trans. Graphics, vol. 22, no. 3, pp. 340349, July 2003.
[24] P. Sander, S. Gortler, J. Snyder, and H. Hoppe, “Signal Specialized Parametrization,” Proc. Eurographics Workshop Rendering 2002, pp. 87100, 2002.
[25] P. Sander, J. Snyder, S. Gortler, and H. Hoppe, “Texture Mapping Progressive Meshes,” Proc. ACM SIGGRAPH 2001, pp. 409416, 2001.
[26] A. Sheffer and E. Sturler, “Parameterization of Faceted Surfaces for Meshing Using AngleBased Flattening,” Eng. with Computers, vol. 17, no. 3, pp. 326337, 2001.
[27] A. Sheffer and E. Sturler, “Smoothing an Overlay Grid to Minimize Linear Distortion in Texture Mapping,” ACM Trans. Graphics, vol. 21, no. 4, pp. 874890, Oct. 2002.
[28] O. Sorkine, D. CohenOr, R. Goldenthal, and D. Lischinski, “BoundedDistortion Piecewise Mesh Parameterization,” Proc. IEEE Visualization 2002, pp. 355362, 2002.
[29] W.T. Tutte, “How to Draw a Graph,” Proc. London Math Soc., vol. 13, pp. 743768, 1963.
[30] H.A. VanderVorst, “BiCGSTAB: A Fast and Smoothly Converging Variant of BiCG for the Solution of Nonsymmetric Linear Systems,” SIAMsci, vol. 13, pp. 631644, 1992.
[31] C.L. Wang, S.F. Smith, and M.F. Yuen, “Surface Flattening Based on Energy Model,” ComputerAided Design, vol. 34, no. 11, pp. 823833, 2002.
[32] S. Yoshizawa, A. Belyaev, and H.P. Seidel, “A Fast and Simple StretchMinimizing Mesh Parameterization,” Proc. Shape Modeling and Applications, pp. 200208, June 2004.