The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.02 - February (2011 vol.17)
pp: 231-243
Yuanyuan Li , Arizona State University, Tempe
Fan Bao , Arizona State University, Tempe
Eugene Zhang , Oregon State University, Corvaliis
Yoshihiro Kobayashi , Arizona State University, Tempe
Peter Wonka , Arizona State University, Tempe
ABSTRACT
We show how to model geometric patterns on surfaces. We build on the concept of shape grammars to allow the grammars to be guided by a vector or tensor field. Our approach affords greater artistic freedom in design and enables the use of grammars to create patterns on manifold surfaces. We show several application examples in visualization, anisotropic tiling of mosaics, and geometry synthesis on surfaces. In contrast to previous work, we can create patterns that adapt to the underlying surface rather than distorting the geometry with a texture parameterization. Additionally, we are the first to model patterns with a global structure thanks to the ability to derive field-guided shape grammars on surfaces.
INDEX TERMS
Shape grammars, tensor fields, vector fields, surfaces, geometry synthesis.
CITATION
Yuanyuan Li, Fan Bao, Eugene Zhang, Yoshihiro Kobayashi, Peter Wonka, "Geometry Synthesis on Surfaces Using Field-Guided Shape Grammars", IEEE Transactions on Visualization & Computer Graphics, vol.17, no. 2, pp. 231-243, February 2011, doi:10.1109/TVCG.2010.36
REFERENCES
[1] K. Zhou, X. Huang, X. Wang, Y. Tong, M. Desbrun, B. Guo, and H. Shum, "Mesh Quilting for Geometric Texture Synthesis," Proc. ACM SIGGRAPH '06, vol. 25, no. 3, pp. 690-697, 2006.
[2] G. Turk and D. Banks, "Image-Guided Streamline Placement," Proc. 23rd Ann. Conf. Computer Graphics and Interactive Techniques, pp. 453-460, 1996.
[3] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants. Springer-Verlag, 1991.
[4] Y.I.H. Parish and P. Müller, "Procedural Modeling of Cities," Proc. ACM SIGGRAPH '01, E. Fiume, ed., pp. 301-308, 2001.
[5] P. Prusinkiewicz, M. James, and R. Měch, "Synthetic Topiary," Proc. ACM SIGGRAPH '94, A. Glassner, ed., pp. 351-358, July 1994.
[6] R. Měch and P. Prusinkiewicz, "Visual Models of Plants Interacting with Their Environment," Proc. ACM SIGGRAPH '96, H. Rushmeier, ed., pp. 397-410, Aug. 1996.
[7] P. Prusinkiewicz, P. Mündermann, R. Karwowski, and B. Lane, "The Use of Positional Information in the Modeling of Plants," Proc. ACM SIGGRAPH '01, E. Fiume, ed., pp. 289-300, 2001.
[8] P. Müller, P. Wonka, S. Haegler, A. Ulmer, and L. Van Gool, "Procedural Modeling of Buildings," Proc. ACM SIGGRAPH '06, 2006.
[9] P. Wonka, M. Wimmer, F. Sillion, and W. Ribarsky, "Instant Architecture," ACM Trans. Graphics, vol. 22, no. 3, pp. 669-677, 2003.
[10] M. Lipp, P. Wonka, and M. Wimmer, "Interactive Visual Editing of Grammars for Procedural Architecture," ACM Trans. Graphics, vol. 27, no. 3, pp. 1-10, http://www.cg.tuwien.ac.at/research/publications/ 2008LIPP-2008 IEV/, Aug. 2008.
[11] S. Havemann, "Generative Mesh Modeling," PhD thesis, TU Braunschweig, 2005.
[12] G. Turk, "Texture Synthesis on Surfaces," Proc. ACM SIGGRAPH '01, pp. 347-354, 2001.
[13] A. Hertzmann, "Painterly Rendering with Curved Brush Strokes of Multiple Sizes," Proc. ACM SIGGRAPH '98, pp. 453-460, 1998.
[14] A. Hertzmann and D. Zorin, "Illustrating Smooth Surfaces," Proc. ACM SIGGRAPH '00, pp. 517-526, 2000.
[15] S. Paris, W. Chang, O.I. Kozhushnyan, W. Jarosz, W. Matusik, M. Zwicker, and F. Durand, "Hair Photobooth: Geometric and Photometric Acquisition of Real Hairstyles," Proc. ACM SIGGRAPH '08, pp. 1-9, 2008.
[16] 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.
[17] J. Palacios and E. Zhang, "Rotational Symmetry Field Design on Surfaces," ACM Trans. Graphics, vol. 26, no. 3, p. 55, 2007.
[18] G. Chen, G. Esch, P. Wonka, P. Müller, and E. Zhang, "Interactive Procedural Street Modeling," ACM Trans. Graphics, vol. 27, no. 3, p. 103, 2008.
[19] M. Marinov and L. Kobbelt, "Direct Anisotropic Quad-Dominant Remeshing," Proc. 12th Pacific Conf. Computer Graphics and Applications (PG '04), pp. 207-216, 2004.
[20] 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.
[21] E. Zhang, K. Mischaikow, and G. Turk, "Vector Field Design on Surfaces," ACM Trans. Graphics, vol. 25, no. 4, pp. 1294-1326, 2006.
[22] 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.
[23] M. Fisher, P. Schröder, M. Desbrun, and H. Hoppe, "Design of Tangent Vector Fields," Proc. ACM SIGGRAPH '07, p. 56, 2007.
[24] N. Ray, B. Vallet, W.C. Li, and B. Lévy, "N-Symmetry Direction Field Design," ACM Trans. Graphics, vol. 27, no. 2, p. 10, 2008.
[25] A. Runions, M. Fuhrer, B. Lane, P. Federl, A.-G. Rolland-Lagan, and P. Prusinkiewicz, "Modeling and Visualization of Leaf Venation Patterns," ACM Trans. Graphics, vol. 24, no. 3, pp. 702-711, 2005.
[26] D. Dunbar and G. Humphreys, "A Spatial Data Structure for Fast Poisson-Disk Sample Generation," ACM Trans. Graphics, vol. 25, no. 3, pp. 503-508, 2006.
[27] G. Turk, "Generating Textures on Arbitrary Surfaces Using Reaction-Diffusion," Proc. ACM SIGGRAPH '91, pp. 289-298, 1991.
[28] J. Kopf, D. Cohen-Or, O. Deussen, and D. Lischinski, "Recursive Wang Tiles for Real-Time Blue Noise," ACM Trans. Graphics, vol. 25, no. 3, pp. 509-518, 2006.
[29] V. Ostromoukhov, "Sampling with Polyominoes," ACM Trans. Graphics, vol. 26, no. 3, p. 78, 2007.
[30] A. Hausner, "Simulating Decorative Mosaics," Proc. ACM SIGGRAPH '01, pp. 573-580, 2001.
[31] J. Kim and F. Pellacini, "Jigsaw Image Mosaics," Proc. ACM SIGGRAPH '02, J. Hughes, ed., pp. 657-664, 2002.
[32] T. Ijiri, R. Mech, T. Igarashi, and G. Miller, "An Example-Based Procedural System for Element Arrangement," Computer Graphics Forum, vol. 27, no. 2, pp. 429-436, 2008.
[33] H. Pottmann, A. Schiftner, P. Bo, H. Schmiedhofer, W. Wang, N. Baldassini, and J. Wallner, "Freeform Surfaces from Single Curved Panels," ACM Trans. Graphics, vol. 27, no. 3, pp. 76:1-76:10, Aug. 2008.
[34] H. Pottmann, Y. Liu, J. Wallner, A. Bobenko, and W. Wang, "Geometry of Multi-Layer Freeform Structures for Architecture," ACM Trans. Graphics, vol. 26, no. 3, pp. 65:1-65:11, July 2007.
[35] Y. Liu, H. Pottmann, J. Wallner, Y.-L. Yang, and W. Wang, "Geometric Modeling with Conical Meshes and Developable Surfaces," ACM Trans. Graphics, vol. 25, no. 3, pp. 681-689, July 2006.
[36] J. Legakis, J. Dorsey, and S.J. Gortler, "Feature-Based Cellular Texturing for Architectural Models," Proc. ACM SIGGRAPH '01, E. Fiume, ed., pp. 309-316, 2001.
[37] A.A. Efros and T.K. Leung, "Texture Synthesis by Non-Parametric Sampling," Proc. IEEE Int'l Conf. Computer Vision, pp. 1033-1038, Sept. 1999.
[38] L. Wei and M. Levoy, "Fast Texture Synthesis Using Tree-Structured Vector Quantization," Proc. 27th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 479-488, 2000.
[39] G. Turk, "Texture Synthesis on Surfaces," Proc. ACM SIGGRAPH '01, pp. 347-354, 2001.
[40] X. Tong, J. Zhang, L. Liu, X. Wang, B. Guo, and H. Shum, "Synthesis of Bidirectional Texture Functions on Arbitrary Surfaces," ACM Trans. Graphics, vol. 21, no. 3, pp. 665-672, 2002.
[41] K. Fleischer, D. Laidlaw, B. Currin, and A. Barr, "Cellular Texture Generation," Proc. 22nd Ann. Conf. Computer Graphics and Interactive Techniques, pp. 239-248, 1995.
[42] A. Efros and W. Freeman, "Image Quilting for Texture Synthesis and Transfer," Proc. ACM SIGGRAPH '01, pp. 341-346, 2001.
[43] L. Liang, C. Liu, Y. Xu, B. Guo, and H. Shum, "Real-Time Texture Synthesis by Patch-Based Sampling," ACM Trans. Graphics, vol. 20, no. 3, pp. 127-150, 2001.
[44] V. Kwatra, A. Schodl, I. Essa, G. Turk, and A. Bobick, "Graphcut Textures: Image and Video Synthesis Using Graph Cuts," ACM Trans. Graphics, vol. 22, no. 3, pp. 277-286, 2003.
[45] P. Bhat, S. Ingram, and G. Turk, "Geometric Texture Synthesis by Example," Proc. Eurographics/ACM SIGGRAPH Symp. Geometry Processing, pp. 41-44, 2004.
[46] P. Müller, "Procedural Modeling of Cities," Proc. ACM SIGGRAPH '06, pp. 139-184, 2006.
[47] N. Chomsky, "Three Models for the Description of Language," IRE Trans. Information Theory, vol. 2, no. 3, pp. 113-124, 1956.
[48] B. O'Neill, Elementary Differential Geometry. Academic Press, 1997.
[49] R. Kimmel and J. Sethian, "Computing Geodesic Paths on Manifolds," Proc. Nat'l Academy of Sciences, USA, vol. 95, no. 15, pp. 8431-8435, citeseer.ist.psu.edu/articlekimmel98computing. html , 1998.
[50] H. Theisel, "Vector Field Curvature and Applications," Doktorarbeit, FB Informatik, Univ. Rostock, 1995.
[51] "Bullet Physics Library," http:/bullet.sourceforge.net, accessed May 11, 2009.
[52] 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, 2003.
[53] P. Haeberli, "Paint by Numbers: Abstract Image Representations," Proc. ACM SIGGRAPH '90, pp. 207-214, 1990.
[54] E. Praun, A. Finkelstein, and H. Hoppe, "Lapped Textures," Proc. ACM SIGGRAPH '00, pp. 465-470, Aug. 2000.
[55] L.Y. Wei and M. Levoy, "Texture Synthesis over Arbitrary Manifold Surfaces," Proc. ACM SIGGRAPH '01, pp. 355-360, 2001.
[56] L. Wang, S. You, and U. Neumann, "Large-Scale Urban Modeling by Combining Ground Level Panoramic and Aerial Imagery," Proc. Third Int'l Symp. 3D Data Processing, Visualization, and Transmission, pp. 806-813, 2006.
18 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool