A topology-preserving optimization algorithm for polycube mapping

Computers and Graphics (Pergamon)

Volumn 35, Issue 3, 2011, Pages 639-649

  Wan, Shenghua ^a   Yin, Zhao ^b   Zhang, Kang ^a   Zhang, Hongchao ^a   Li, Xin ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

^b XIAMEN UNIVERSITY   (China)

Author keywords

Domain optimization; Polycube mapping; Surface parameterization

Indexed keywords

GEOMETRY; ITERATIVE METHODS; PARAMETERIZATION;

DOMAIN OPTIMIZATION; ITERATIVE ALGORITHM; OPTIMIZATION ALGORITHMS; OPTIMIZATION FRAMEWORK; PARAMETRIC REPRESENTATIONS; POLYCUBE; SURFACE PARAMETERIZATION; TOPOLOGY PRESERVING;

MAPPING;

EID: 79957858592     PISSN: 00978493     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cag.2011.03.018     Document Type: Conference Paper

References (41)

1. C. Audet, and J.E. Dennis Jr A pattern search filter method for nonlinear programming without derivatives SIAM Journal on Optimization 14 2004 980 1010
2. J. Barzilai, and J.M. Borwein Two-point step size gradient methods IMA Journal of Numerical Analysis 8 1 1988 141 148
3. E.G. Birgin, M.M. Jos, and M. Raydan Nonmonotone spectral projected gradient methods on convex sets SIAM Journal on Optimization 2000 1196 1211
4. Y.-H. Dai, W.W. Hager, K. Schittkowski, and H. Zhang The cyclic BarzilaiBorwein method for unconstrained optimization IMA Journal of Numerical Analysis 26 2006 604 627 (Pubitemid 44048227)
5. Y.-H. Dai, and H. Zhang Adaptive two-point stepsize gradient algorithm Numerical Algorithms 27 2001 377 385 (Pubitemid 33643870)
6. T.A. Davis, and W.W. Hager Dynamic supernodes in sparse Cholesky update/downdate and triangular solves ACM Transactions on Mathematical Software 35 2009 27:1 27:23
7. P. Degener, J. Meseth, and R. Klein An adaptable surface parameterization method IMR 2003 201 213
8. M. Desbrun, M. Meyer, and P. Alliez Intrinsic parameterizations of surface meshes Computer Graphics Forum 21 3 2002 209 218
9. S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J.C. Hart Spectral surface quadrangulation ACM Transactions on Graphics 25 2006 1057 1066 (Pubitemid 44481068)
10. M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle Multiresolution analysis of arbitrary meshes SIGGRAPH 1995 173 182
11. Z. Fan, X. Jin, J. Feng, and H. Sun Mesh morphing using polycube-based cross-parameterization: animating geometrical models Computer Animation and Virtual Worlds 16 34 2005 499 508 (Pubitemid 41495242)
12. M.S. Floater Mean value coordinates Computer Aided Geometric Design 20 1 2003 19 27
13. M.S. Floater, and K. Hormann Surface parameterization: a tutorial and survey Advances in Multiresolution for Geometric Modelling 2005 157 186
14. X. Gu, and S.-T. Yau Global conformal surface parameterization Proceedings of the symposium on geometry processing 2003 127 137
15. X. Guo, X. Li, Y. Bao, X. Gu, and H. Qin Meshless thin-shell simulation based on global conformal parameterization IEEE Transactions on Visualization and Computer Graphics 12 3 2006 375 385
16. W.W. Hager, and H. Zhang A new active set algorithm for box constrained optimization SIAM Journal on Optimization 17 2006 526 557 (Pubitemid 46798079)
17. Han S, Xia J, He Y. Hexahedral shell mesh construction via volumetric polycube map. In: SPM. SPM '10. New York, NY, USA: ACM; 2010. p. 12736.
18. Y. He, H. Wang, C.-W. Fu, and H. Qin A divide-and-conquer approach for automatic polycube map construction Computers & Graphics 33 3 2009 369 380
19. K. Hormann, B. Lévy, and A. Sheffer Mesh parameterization: theory and practice ACM Siggraph 2007 course vol. 11 2007 1 87
20. V. Kraevoy, and A. Sheffer Cross-parameterization and compatible remeshing of 3D models ACM Transactions on Graphics 23 3 2004 861 869
21. H. Li, K.-Y. Lo, M.-K. Leung, and C.-W. Fu Dual poisson-disk tiling: an efficient method for distributing features on arbitrary surfaces IEEE Transactions on Visualization and Computer Graphics 14 5 2008 982 998
22. X. Li, X. Gu, and H. Qin Surface mapping using consistent pants decomposition IEEE Transactions on Visualization and Computer Graphics 15 4 2009 558 571
23. Li X, Guo X, Wang H, He Y, Gu X, Qin H. Harmonic volumetric mapping for solid modeling applications. In: SPM. New York, NY, USA; ACM: 2007. p. 10920. (Pubitemid 47582476)
24. J. Lin, X. Jin, Z. Fan, and C.C.L. Wang Automatic polycube-maps GMP 2008 3 16
25. J. Moré The LevenbergMarquardt algorithm: implementation and theory G. Watson, Numerical analysis. Lecture notes in mathematics vol. 630 1978 Springer Berlin, Heidelberg 105 116
26. J.J. Moré, and S.W. Wild Benchmarking derivative-free optimization algorithms SIAM Journal on Optimization 20 1 2009 172 191
27. N. Pietroni, M. Tarini, and P. Cignoni Almost isometric mesh parameterization through abstract domains IEEE Transactions on Visualization and Computer Graphics 16 4 2010 621 635
28. U. Pinkall, and K. Polthier Computing discrete minimal surfaces and their conjugates Experimental Mathematics 2 1 1993 15 36
29. M.J.D. Powell Least Frobenius norm updating of quadratic models that satisfy interpolation conditions Mathematical Programming 100 2004 183 215 (Pubitemid 40871709)
30. E. Praun, W. Sweldens, and P. Schröder Consistent mesh parameterizations ACM SIGGRAPH 2001 179 184 (Pubitemid 33047302)
31. N. Ray, W. Li, B. Lévy, A. Sheffer, and P. Alliez Periodic global parameterization ACM Transactions on Graphics 25 4 2006 1460 1485 (Pubitemid 44917213)
32. A. Sheffer, E. Praun, and K. Rose Mesh parameterization methods and their applications Foundations and Trends in Computer Graphics and Vision 2 2 2006 105 171 (Pubitemid 46732197)
33. M. Tarini, K. Hormann, P. Cignoni, and C. Montani Polycube-maps ACM SIGGRAPH 2004 853 860
34. Wang H, He Y, Li X, Gu X, Qin H. Polycube splines. In: SPM. New York, NY, USA: ACM; 2007. p. 24151. (Pubitemid 47582488)
35. Wang H, Jin M, He Y, Gu X, Qin H. User-controllable polycube map for manifold spline construction. In: SPM. New York, NY, USA: ACM; 2008. p. 397404.
36. J. Xia, I. Garcia, Y. He, S.-Q. Xin, and G. Patow Editable polycube map for GPU-based subdivision surfaces Symposium on interactive 3D graphics and games 2011 151 158
37. K. Xu, H. Zhang, D. Cohen-Or, and Y. Xiong Technical section: dynamic harmonic fields for surface processing Computers & Graphics 33 2009 391 398
38. H. Zhang, A.R. Conn, and K. Scheinberg A derivative-free algorithm for the least-squares minimization SIAM Journal on Optimization 20 2010 3555 3576
39. X. Li, X. Guo, H. Wang, Y. He, X. Gu, and H. Qin Meshless harmonic volumetric mapping using fundamental solution methods IEEE Transactions on Automation Science and Engineering (TASE) 6 3 2009 409 422
40. X. Li, X. Xu, S. Wan, Z. Yin, and W. Yu Feature-aligned harmonic volumetric mapping using MFS Computers & Graphics 34 3 2010 242 251
41. X. Li, Y. Bao, X. Guo, M. Jin, X. Gu, and H. Qin Globally optimal surface mapping for shapes of arbitrary topology IEEE Transactions on Visualization and Computer Graphics (TVCG) 14 4 2008 805 819 (Pubitemid 351780208)