The Community for Technology Leaders
RSS Icon
Issue No.06 - June (2012 vol.18)
pp: 865-878
Matthias Nieser , Freie Universität Berlin, Berlin
Jonathan Palacios , Oregon State University, Corvallis
Konrad Polthier , Freie Universität Berlin, Berlin
Eugene Zhang , Oregon State University, Corvallis
Surface parameterization, rotational symmetry, hexagonal global parameterization, triangular remeshing, pattern synthesis on surfaces, texture synthesis, geometry synthesis, regular patterns.
Matthias Nieser, Jonathan Palacios, Konrad Polthier, Eugene Zhang, "Hexagonal Global Parameterization of Arbitrary Surfaces", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 6, pp. 865-878, June 2012, doi:10.1109/TVCG.2011.118
[1] A. Schiftner, M. Höbinger, J. Wallner, and H. Pottmann, “Packing Circles and Spheres on Surfaces,” Proc. SIGGRAPH Asia, pp. 1-8, 2009.
[2] C.S. Kaplan and D.H. Salesin, “Islamic Star Patterns in Absolute Geometry,” ACM Trans. Graphics, vol. 23, no. 2, pp. 97-119, 2004.
[3] Z.J. Wood, P. Schröder, D. Breen, and M. Desbrun, “Semi-Regular Mesh Extraction from Volumes,” Proc. Conf. Visualization (VIS), pp. 275-282, 2000.
[4] 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.
[5] F. Kälberer, M. Nieser, and K. Polthier, “QuadCover - Surface Parameterization Using Branched Coverings,” Computer Graphics Forum, vol. 26, no. 3, pp. 375-384, 2007.
[6] D. Bommes, H. Zimmer, and L. Kobbelt, “Mixed-Integer Quadrangulation,” ACM Trans. Graphics, vol. 28, no. 3, pp. 1-10, 2009.
[7] J. Palacios and E. Zhang, “Rotational Symmetry Field Design on Surfaces,” Proc. SIGGRAPH, p. 55, 2007.
[8] M.S. Floater and K. Hormann, “Surface Parameterization: A Tutorial and Survey,” Advances in Multiresolution for Geometric Modelling, pp. 157-186, Springer Verlag, 2005.
[9] K. Hormann, K. Polthier, and A. Sheffer, “Mesh Parameterization: Theory and Practice,” Proc. SIGGRAPH Asia, no. 11, 2008.
[10] 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. 181-189, Apr.-June 2000.
[11] X. Gu and S.-T. Yau, “Global Conformal Surface Parameterization,” Proc. ACM SIGGRAPH Symp. Geometry Processing (SGP), pp. 127-137, 2003.
[12] M. Jin, Y. Wang, S.-T. Yau, and X. Gu, “Optimal Global Conformal Surface Parameterization,” Proc. IEEE Visualization, pp. 267-274, 2004.
[13] L. Kharevych, B. Springborn, and P. Schröder, “Discrete Conformal Mappings Via Circle Patterns,” ACM Trans. Graphics, vol. 25, no. 2, pp. 412-438, 2006.
[14] 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.
[15] B. Springborn, P. Schröder, and U. Pinkall, “Conformal Equivalence of Triangle Meshes,” ACM Trans. Graphics, vol. 27, pp. 77:1-77:11, Aug. 2008.
[16] S. Dong, S. Kircher, and M. Garland, “Harmonic Functions for Quadrilateral Remeshing of Arbitrary Manifolds,” Computer Aided Geometric Design, vol. 22, pp. 392-423, 2005.
[17] S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J.C. Hart, “Spectral Surface Quadrangulation,” Proc. SIGGRAPH '06, pp. 1057-1066, 2006.
[18] Y. Tong, P. Alliez, D. Cohen-Steiner, and M. Desbrun, “Designing Quadrangulations with Discrete Harmonic Forms,” Proc. Fourth Eurographics Symp. Geometry Processing (SGP), 2006.
[19] E. Zhang, J. Hays, and G. Turk, “Interactive Tensor Field Design and Visualization on Surfaces,” IEEE Trans. Visualization Computer Graphics, vol. 13, no. 1, pp. 94-107, Jan./Feb. 2007.
[20] J.L. Helman and L. Hesselink, “Visualizing Vector Field Topology in Fluid Flows,” IEEE Computer Graphics and Applications, vol. 11, no. 3, pp. 36-46, May 1991.
[21] T. Delmarcelle and L. Hesselink, “The Topology of Symmetric, Second-Order Tensor Fields,” IEEE Conf. Visualization, pp. 140-147, 1994.
[22] E. Praun, A. Finkelstein, and H. Hoppe, “Lapped Textures,” Proc. SIGGRAPH, pp. 465-470, 2000.
[23] G. Turk, “Texture Synthesis on Surfaces,” Proc. SIGGRAPH, 2001.
[24] L.Y. Wei and M. Levoy, “Texture Synthesis over Arbitrary Manifold Surfaces,” Proc. SIGGRAPH, pp. 355-360, 2001.
[25] J. Stam, “Flows on Surfaces of Arbitrary Topology,” Proc. SIGGRAPH, 2003.
[26] J.J. van Wijk, “Image Based Flow Visualization for Curved Surfaces,” Proc. IEEE Visualization, pp. 123-130, 2003.
[27] M. Fisher, P. Schröder, M. Desbrun, and H. Hoppe, “Design of Tangent Vector Fields,” Proc. SIGGRAPH, p. 56, 2007.
[28] H. Theisel, “Designing 2D Vector Fields of Arbitrary Topology,” Proc. Eurographics Conf., vol. 21, pp. 595-604, 2002.
[29] W.-C. Li, B. Vallet, N. Ray, and B. Lévy, “Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces,” IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 1315-1322, Sept./Oct. 2006.
[30] E. Zhang, K. Mischaikow, and G. Turk, “Vector Field Design on Surfaces,” ACM Trans. Graphics, vol. 25, no. 4, pp. 1294-1326, 2006.
[31] G. Chen, G. Esch, P. Wonka, P. Müller, and E. Zhang, “Interactive Procedural Street Modeling,” ACM Trans. Graphics, vol. 27, no. 3, pp. 1-10, 2008.
[32] A. Hertzmann and D. Zorin, “Illustrating Smooth Surfaces,” Proc. SIGGRAPH, pp. 517-526, 2000.
[33] N. Ray, B. Vallet, W.C. Li, and B. Lévy, “N-Symmetry Direction Field Design,” ACM Trans. Graphics, vol. 27, no. 2, pp. 1-13, 2008.
[34] J. Palacios and E. Zhang, “Interactive Visualization of Rotational Symmetry Fields on Surfaces,” IEEE Trans. Visualization and Computer Graphics, vol. 17, no. 7, pp. 947-955, July 2011.
[35] Y.-K. Lai, M. Jin, X. Xie, Y. He, J. Palacios, E. Zhang, S.-M. Hu, and X. Gu, “Metric-Driven Rosy Field Design and Remeshing,” IEEE Trans. Visualization and Computer Graphics, vol. 16, no. 1, pp. 95-108, Jan./Feb. 2010.
[36] M. Zhang, J. Huang, X. Liu, and H. Bao, “A Wave-Based Anisotropic Quadrangulation Method,” ACM Trans. Graphics, vol. 29, pp. 1-8, 2010.
[37] K. Crane, M. Desbrun, and P. Schröder, “Trivial Connections on Discrete Surfaces,” Computer Graphic Forum, vol. 29, no. 5, pp. 1525-1533, 2010.
[38] N. Ray, B. Vallet, L. Alonso, and B. Lévy, “Geometry Aware Direction Field Design,” ACM Trans. Graphics, vol. 29, no. 1, 2009.
[39] K. Xu, D. Cohen-Or, T. Ju, L. Liu, H. Zhang, S. Zhou, and Y. Xiong, “Feature-Aligned Shape Texturing,” ACM Trans. Graphics, vol. 28, no. 5, pp. 1-7, 2009.
[40] M. Meyer, M. Desbrun, P. Schröder, and A.H. Barr, “Discrete Differential Geometry Operators for Triangulated 2-Manifolds,” Visualization and Mathematics III, Springer, 2002.
[41] E. Zhang, H. Yeh, Z. Lin, and R.S. Laramee, “Asymmetric Tensor Analysis for Flow Visualization,” IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 1, pp. 106-122, Jan./Feb. 2009.
[42] J.J. Koenderink and A.J. van Doorn, “Surface Shape and Curvature Scales,” Image and Vision Computing, vol. 10, pp. 557-565, Oct. 1992.
[43] A.N. Hirani, “Discrete Exterior Calculus,” PhD dissertation, 2003.
[44] M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, “Multiresolution Analysis of Arbitrary Meshes,” Proc. SIGGRAPH, pp. 173-182, 1995.
[45] K. Polthier and E. Preuss, “Identifying Vector Field Singularities Using a Discrete Hodge Decomposition,” Visualization and Mathematics III, pp. 113-134, Springer Verlag 2003.
[46] J. Erickson and K. Whittlesey, “Greedy Optimal Homotopy and Homology Generators,” Proc. ACM-SIAM Symp. Discrete Algorithms, pp. 1038-1046, 2005.
[47] F. Kälberer, M. Nieser, and K. Polthier, “Stripe Parameterization of Tubular Surfaces,” Topological Methods in Data Analysis and Visualization: Theory, Algorithms and Applications, Springer Verlag, 2009.
[48] L.-Y. Wei, S. Lefebvre, V. Kwatra, and G. Turk, “State of the Art in Example-Based Texture Synthesis,” Proc. Eurographics, 2009.
[49] Y. Liu, W.-C. Lin, and J. Hays, “Near-Regular Texture Analysis and Manipulation,” Proc. SIGGRAPH, pp. 368-376, 2004.
[50] P. Alliez, G. Ucelli, C. Gotsman, and M. Attene, “Recent Advances in Remeshing of Surfaces,” Shape Analysis and Structuring, Springer, 2005.
[51] X. Gu, S.J. Gortler, and H. Hoppe, “Geometry Images,” ACM Trans. Graphics, vol. 21, no. 3, pp. 355-361, 2002.
[52] P. Alliez, M. Meyer, and M. Desbrun, “Interactive Geometry Remeshing,” Proc. SIGGRAPH, pp. 347-354, 2002.
[53] P. Alliez, E.C. de Verdiere, O. Devillers, and M. Isenburg, “Isotropic Surface Remeshing,” Proc. Shape Modeling Int'l (SMI), p. 49, 2003.
[54] A. Khodakovsky, N. Litke, and P. Schröder, “Globally Smooth Parameterizations with Low Distortion,” Proc. SIGGRAPH '03, 2003.
[55] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh Optimization,” Proc. SIGGRAPH, pp. 19-26, 1993.
[56] P. Lindstrom and G. Turk, “Image-Driven Simplification,” ACM Trans. Graphics, vol. 19, no. 3, pp. 204-241, 2000.
[57] V. Surazhsky and C. Gotsman, “Explicit Surface Remeshing,” Proc. ACM SIGGRAPH Symp. Geometry Processing (SGP), 2003.
[58] G. Turk, “Re-Tiling Polygonal Surfaces,” Proc. SIGGRAPH, 1992.
[59] D.-M. Yan, B. Lévy, Y. Liu, F. Sun, and W. Wang, “Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram,” Proc. Symp. Geometry Processing (SGP), pp. 1445-1454, 2009.
[60] E. Akleman, J. Chen, Q. Xing, and J.L. Gross, “Cyclic Plain-Weaving on Polygonal Mesh Surfaces with Graph Rotation Systems,” ACM Trans. Graphics, vol. 28, no. 3, pp. 1-8, 2009.
21 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool