Metric-driven RoSy field design and remeshing

IEEE Transactions on Visualization and Computer Graphics

Volumn 16, Issue 1, 2010, Pages 95-108

  Lai, Yu Kun ^a   Jin, Miao ^b   Xie, Xuexiang ^c   He, Ying ^c   Palacios, Jonathan ^d   Zhang, Eugene ^d   Hu, Shi Min ^a   Gu, Xianfeng ^e  

^a TSINGHUA UNIVERSITY   (China)

^b University of Louisiana at Lafayette   (United States)

^c NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^d Oregon State University   (United States)

^e Stony Brook University   (United States)

Author keywords

Design; Metric; Parameterization; Remeshing; Rotational symmetry; Surface

Indexed keywords

ARBITRARY SURFACES; CAN DESIGN; CELTIC KNOTS; COMPATIBILITY CONDITIONS; DESIGN SYSTEMS; FIELD DESIGN; FULL CONTROL; GLOBAL CONSTRAINTS; GLOBAL SYMMETRIES; HOLONOMY; LOCAL SYMMETRY; PARALLEL TRANSPORT; REMESHING; RIEMANNIAN METRICS; ROTATIONAL SYMMETRIES; ROTATIONAL SYMMETRY;

DESIGN;

ARTICLE; COMPUTER GRAPHICS; COMPUTER INTERFACE; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; METHODOLOGY; THEORETICAL MODEL; THREE DIMENSIONAL IMAGING;

COMPUTER GRAPHICS; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; IMAGING, THREE-DIMENSIONAL; MODELS, THEORETICAL; USER-COMPUTER INTERFACE;

EID: 70450252050     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2009.59     Document Type: Article

References (40)

1. J. Palacios and E. Zhang, "Rotational Symmetry Field Design on Surfaces," ACM Trans. Graphics, vol.26, no.3, p. 55, 2007.
2. N. Ray, B. Vallet, W.-C. Li, and B. Levy, "N-Symmetry Direction Field Design," ACM Trans. Graphics, vol.27, no.2, pp. 10:1-10:13, 2008.
3. L. Kharevych, B. Springborn, and P. Schröder, "Discrete Conformal Mappings via Circle Patterns," ACM Trans. Graphics, vol.25, no.2, pp. 412-438, 2006.
4. M. Jin, J. Kim, F. Luo, and X. Gu, "Discrete Surface Ricci Flow: Theories and Applications," Math. of Surfaces XII, pp. 209-232, Springer, 2007.
5. E. Praun, A. Finkelstein, and H. Hoppe, "Lapped Textures," Proc. ACM SIGGRAPH, pp. 465-470, Aug. 2000.
6. G. Turk, "Texture Synthesis on Surfaces," Proc. ACM SIGGRAPH, pp. 347-354, 2001.
7. L.Y. Wei and M. Levoy, "Texture Synthesis over Arbitrary Manifold Surfaces," Proc. ACM SIGGRAPH, pp. 355-360, 2001.
8. J. Stam, "Flows on Surfaces of Arbitrary Topology," Proc. ACM SIGGRAPH, vol.22, no.3, pp. 724-731, July 2003.
9. J.J. van Wijk, "Image Based Flow Visualization," Proc. ACM SIGGRAPH, vol.21, no.3, pp. 745-754, July 2002.
10. J.J. van Wijk, "Image Based Flow Visualization for Curved Surfaces," Proc. IEEE Visualization Conf., pp. 123-130, Oct. 2003.
11. H. Theisel, "Designing 2d Vector Fields of Arbitrary Topology," Proc. Eurographics Conf., vol.21, pp. 595-604, 2002.
12. E. Zhang, K. Mischaikow, and G. Turk, "Vector Field Design on Surfaces," ACM Trans. Graphics, vol.25, no.4, pp. 1294-1326, 2006.
13. G. Chen, K. Mischaikow, R.S. Laramee, P. Pilarczyk, and E. Zhang, "Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition," IEEE Trans. Visualization and Computer Graphics, vol.13, no.4, pp. 769-785, July/Aug. 2007.
14. E. Zhang, J. Hays, and G. Turk, "Interactive Tensor Field Design and Visualization on Surfaces," IEEE Trans. Visualization and Computer Graphics, vol.13, no.1, pp. 94-107, Jan./Feb. 2007.
15. M. Fisher, P. Schröder, M. Desbrun, and H. Hoppe, "Design of Tangent Vector Fields," ACM Trans. Graphics, vol.26, no.3, p. 56, 2007.
16. A. Hertzmann and D. Zorin, "Illustrating Smooth Surfaces," Proc. ACM SIGGRAPH, pp. 517-526, Aug. 2000.
17. N. Ray, W.C. Li, B. Lévy, A. Sheffer, and P. Alliez, "Periodic Global Parameterization," ACM Trans. Graphics, vol.25, no.4, pp. 1460-1485, 2006.
18. Y. Tong, P. Alliez, D. Cohen-Steiner, and M. Desbrun, "Designing Quadrangulations with Discrete Harmonic Forms," Proc. Symp. Geometry Processing, pp. 201-210, 2006.
19. F. Kälberer, M. Nieser, and K. Polthier, "Quadcover-Surface Parameterization Using Branched Coverings," Computer Graphics Forum, vol.26, no.10, pp. 375-384, Sept. 2007.
20. A. Girshick, V. Interrante, S. Haker, and T. Lemoine, "Line Direction Matters: An Argument for the Use of Principal Directions in 3D Line Drawings," Proc. Int'l Symp. Non-Photorealistic Animation and Rendering (NPAR), pp. 43-52, 2000.
21. M. Meyer, M. Desbrun, P. Schröder, and A.H. Barr, "Discrete Differential-Geometry Operators for Triangulated 2-Manifolds," Proc. Workshop Visualization and Math. (VisMath), 2002.
22. D. Cohen-Steiner and J. Morvan, "Restricted Delaunay Triangulations and Normal Cycle," Proc. ACM SIGGRAPH Symp. Computational Geometry, pp. 312-321, 2003.
23. S. Rusinkiewicz, "Estimating Curvatures and Their Derivatives on Triangle Meshes," Proc. Int'l Symp. 3D Data Processing, Visualization, and Transmission (3DPVT), pp. 486-493, 2004.
24. S. Zelinka and M. Garland, "Jump Map-Based Interactive Texture Synthesis," ACM Trans. Graphics, vol.23, no.4, pp. 930-962, 2004.
25. X. Ni, M. Garland, and J.C. Hart, "Fair Morse Functions for Extracting the Topological Structure of a Surface Mesh," ACM Trans. Graphics, vol.23, no.3, pp. 613-622, 2004.
26. M. Kaplan and E. Cohen, "Computer Generated Celtic Design," Proc. 14th Eurographics Workshop Rendering Techniques, pp. 2-19, 2003.
27. K. Zhou, X. Huang, X. Wang, Y. Tong, M. Desbrun, B. Guo, and H.-Y. Shum, "Mesh Quilting for Geometric Texture Synthesis," ACM Trans. Graphics, vol.25, no.3, pp. 690-697, 2006.
28. P. Alliez, D. Cohen-Steiner, O. Devillers, B. Lévy, and M. Desbrun, "Anisotropic Polygonal Remeshing," ACM Trans. Graphics, vol.22, no.3, pp. 485-493, July 2003.
29. M. Marinov and L. Kobbelt, "Direct Anisotropic Quad-Dominant Remeshing," Proc. 12th Pacific Conf. Computer Graphics and Applications, pp. 207-216, 2004.
30. S. Dong, S. Kircher, and M. Garland, "Harmonic Functions for Quadrilateral Remeshing of Arbitrary Manifolds," Computer Aided Geometric Design (CAGD), no.5, pp. 392-423, 2005.
31. S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J.C. Hart, "Spectral Surface Quadrangulation," ACM Trans. Graphics, vol.25, no.3, pp. 1057-1066, 2006.
32. R.S. Hamilton, "Three-Manifolds with Positive Ricci Curvature," J. Differential Geometry, vol.17, pp. 255-306, 1982.
33. M. Ben-Chen, C. Gotsman, and G. Bunin, "Conformal Flattening by Curvature Prescription and Metric Scaling," Computer Graphics Forum, vol.27, no.2, pp. 449-458, 2008.
34. F. Luo, "Combinatorial Yamabe Flow on Surfaces," Comm. Contemporary Math., vol.6, pp. 765-780, 2004.
35. B. Springborn, P. Schröder, and U. Pinkall, "Conformal Equivalence of Triangle Meshes," ACM Trans. Graphics, vol.27, no.3, p. 77, 2008.
36. K. Polthier and M. Schmies, "Straightest Geodesics on Polyhedral Surfaces," Proc. Math. Visualization Conf., pp. 391-398, 1998.
37. M. Tarini, K. Hormann, P. Cignoni, and C. Montani, "Polycube-Maps, " ACM Trans. Graphics, vol.23, no.3, pp. 853-860, 2004.
38. H. Wang, Y. He, X. Li, X. Gu, and H. Qin, "Polycube Splines," Proc. ACM SIGGRAPH Symp. Solid and Physical Modeling, pp. 241-251, 2007.
39. U. Pinkall and K. Polthier, "Computing Discrete Minimal Surfaces and Their Conjugates," Experimental Math., vol.2, pp. 15-36, 1993.
40. X.D. Gu and S.-T. Yau, "Global Conformal Surface Parameterization," Proc. Symp. Geometry Processing, pp. 127-137, 2003.