Quality encoding for tetrahedral mesh optimization

Computers and Graphics (Pergamon)

Volumn 33, Issue 3, 2009, Pages 250-261

  Xu, Kai ^a,b   Cheng, Zhi Quan ^a   Wang, Yanzhen ^a   Xiong, Yueshan ^a   Zhang, Hao ^b  

^a NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Algebraic metrics; Quality differential coordinates; Tetrahedral element quality; Tetrahedral mesh optimization

Indexed keywords

ENCODING (SYMBOLS); SIGNAL ENCODING;

ALGEBRAIC METRICS; DIFFERENTIAL COORDINATES; ENERGY MINIMIZATION; OPTIMIZATION SCHEME; SEMI-IMPLICIT INTEGRATION SCHEMES; TETRAHEDRAL ELEMENTS; TETRAHEDRAL MESHES; VARIATIONAL PROBLEMS;

MESH GENERATION;

EID: 67349127331     PISSN: 00978493     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cag.2009.03.020     Document Type: Article

References (36)

1. Alexa M. Local control for mesh morphing. In: Proceedings of the IEEE conference on shape modeling and applications; 2001. p. 209-15.
2. Alliez P., Cohen-Steiner D., Yvinec M., and Desbrun M. Variational tetrahedral meshing. ACM Trans. Graphics 24 3 (2005) 617-625
3. Andrei N. Gradient flow method for nonlinear least squares minimization. Unpublished manuscript, 2004.
4. Botsch M., and Sorkine O. On linear variational surface deformation methods. IEEE Trans. Vis. Comput. Graphics 14 1 (2008) 213-230
5. Chen L. Mesh smoothing schemes based on optimal Delaunay triangulations. Proceedings of the 13th international meshing roundtable (2004) 109-120
6. Cheng S.-W., Dey T.K., Edelsbrunner H., Facello M.A., and Teng S.-H. Sliver exudation. Proceedings of the 15th annual ACM symposium on computational geometry (1999) 1-13
7. Cignoni P., Rocchini C., and Scopigno R. Metro: measuring error on simplified surfaces. Comput. Graphics Forum 17 2 (1998) 167-174
8. Desbrun M., Meyer M., Schröder P., and Barr A.H. Implicit fairing of irregular meshes using diffusion and curvature flow. Proceedings of the ACM SIGGRAPH 99 (1999) 317-324
9. Elcott S., Tong Y., Kanso E., Schröder P., and Desbrun M. Stable, circulation-preserving, simplicial fluids. ACM Trans. Graphics 26 1 (2007) 4:1-12
10. Eppstein D. Global optimization of mesh quality. Tutorial at 10th international meshing roundtable (2001)
11. Escobar J.M., Rodrìguez E., Montenegro R., Montero G., and Gonzàlez-Yuste J.M. Simultaneous untangling and smoothing of tetrahedral meshes. Comput. Methods Appl. Mech. Eng. 192 25 (2003) 2775-2787
12. Fleishman S., Drori I., and Cohen-Or D. Bilateral mesh denoising. ACM Trans. Graphics 22 3 (2003) 950-953
13. Freitag LA. Users manual for opt-ms: local methods for simplicial mesh smoothing and untangling. Technical Report ANL/MCS-TM-239, Argonne National Laboratory, Argonne, IL; 1999.
14. Freitag L.A., and Knupp P.M. Tetrahedral mesh improvement via optimization of the element condition number. Int. J. Numer. Methods Eng. 53 6 (2002) 1377-1391
15. Freitag L.A., Knupp P.M., Munson T., and Shontz S. A comparison of inexact Newton and coordinate descent mesh optimization techniques. Eng. Comput. 22 2 (2006) 61-74
16. Freitag L.A., and Ollivier-Gooch C. A comparison of tetrahedral mesh improvement techniques. Proceedings of the 5th international meshing roundtable (1996) 87-106
17. Freitag L.A., and Ollivier-Gooch C. Tetrahedral mesh improvement using swapping and smoothing. Int. J. Numer. Methods Eng. 40 21 (1997) 3979-4002
18. Geiger B. Nuages: a package for 3d reconstruction, 1996. URL 〈ftp://ftp-sop.inria.fr/prisme/NUAGES/〉.
19. Jones T.R., Durand F., and Desbrun M. Non-iterative, feature-preserving mesh smoothing. ACM Trans. Graphics 22 3 (2003) 943-949
20. Klingner B.M., and Shewchuk J.R. Aggressive tetrahedral mesh improvement. Proceedings of the 16th international meshing roundtable (2007) 3-23
21. Knupp P.M. Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part ii: a framework for volume mesh optimization and the condition number of the Jacobian matrix. Int. J. Numer. Methods Eng. 48 8 (2000) 1165-1185
22. Knupp P.M. Algebraic mesh quality metrics. SIAM J. Sci. Comput. 23 1 (2001) 193-218
23. Labelle F., and Shewchuk J.R. Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans. Graphics 26 3 (2007) 57:1-10
24. Liu L., Tai C.-L., Ji Z., and Wang G. Non-iterative approach for global mesh optimization. Computer-Aided Des. 39 9 (2007) 772-782
25. Müller M., Dorsey J., McMillan L., Jagnow R., and Cutler B. Stable real-time deformation. Proceedings of the ACM SIGGRAPH/Eurographics symposium on computer animation (2002) 49-54
26. Munson TS. Mesh shape-quality optimization using the inverse mean-ratio metric: tetrahedral proofs. Technical Report ANL/MCS-TM-275, Argonne National Laboratory, Argonne, IL; 2004.
27. Nealen A., Igarashi T., Sorkine O., and Alexa M. Laplacian mesh optimization. Proceedings of the ACM GRAPHITE (2006) 381-389
28. Parthasarathy V.N., Graichen C.M., and Hathaway A.F. A comparison of tetrahedron quality measures. Finite Elem. Anal. Des. 15 3 (1994) 255-261
29. Sherbrooke E.C., Patrikalakis N.M., and Brisson E. An algorithm for the medial axis transform of 3d polyhedral solids. IEEE Trans. Vis. Comput. Graphics 2 1 (1996) 44-61
30. Shewchuk J.R. What is a good linear finite element? Interpolation, conditioning, anisotropy, and quality measures. Proceedings of the 11th international meshing roundtable (2002) 115-126
31. Sorkine O., Lipman Y., Cohen-Or D., Alexa M., Rössl C., and Seidel H.-P. Laplacian surface editing. Proceedings of the Eurographics symposium on geometry processing (2004) 179-188
32. Taubin G. A signal processing approach to fair surface design. Proceedings of the ACM SIGGRAPH 95 (1995) 351-358
33. Toledo S. Taucs: a library of sparse linear solvers, version 2.2, 2003. URL 〈http://www.tau.ac.il/∼stoledo/taucs/〉.
34. Yamashita N, Fukushima M. On the rate of convergence of the Levenberg-Marquardt method. Technical report, Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University; 2000.
35. Zhang H., and Fiume E.L. Mesh smoothing with shape or feature preservation. Advances in modeling, animation, and rendering (2002) 167-182
36. Zhou K., Huang J., Snyder J., Liu X., Bao H., Guo B., et al. Large mesh deformation using the volumetric graph Laplacian. ACM Trans. Graphics 24 3 (2005) 496-503