Abstract
This paper presents an automatic method for computing an anisotropic 2D shape distribution on an arbitrary 2-manifold mesh. Our method allows the user to specify the direction as well as the density of the distribution. Using a pre-computed lookup table, our method can efficiently detect collision among the shapes to be distributed on the 3D mesh. In contrast to existing approaches, which usually assume the 2D objects are isotropic and have simple geometry, our method works for complex 2D objects and can guarantee the distribution is conflict-free, which is a critical constraint in many applications. It is able to compute multi-class shape distributions in parallel. Our method does not require global parameterization of the input 3D mesh. Instead, it computes local parameterizations on the fly using geodesic polar coordinates. Thanks to a recent breakthrough in geodesic computation, the local parameterization can be computed at low cost. As a result, our method can be applied to models with complicated geometry and topology. Experimental results on a wide range of 3D models and 2D anisotropic shapes demonstrate the good performance and effectiveness of our method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Wei, L. Y. Parallel Poisson disk sampling. ACM Transactions on Graphics Vol. 27, No. 3, Article No. 20, 2008.
Ebeida, M. S.; Davidson, A. A.; Patney, A.; Knupp, P. M.; Mitchell, S. A.; Owens, J. D. Efficient maximal Poisson disk sampling. ACM Transactions on Graphics Vol. 30, No. 4, Article No. 49, 2011.
Yan, D. M.; Wonka, P. Gap processing for adaptive maximal Poisson disk sampling. ACM Transactions on Graphics Vol. 32, No. 5, Article No. 148, 2013.
Wei, L. Y. Multi class blue noise sampling. ACM Transactions on Graphics Vol. 29, No. 4, Article No. 79, 2010.
Chen, J.; Ge, X.; Wei, L. Y.; Wang, B.; Wang, Y.; Wang, H.; Fei, Y.; Qian, K. L.; Yong, J. H.; Wang, W. Bilateral blue noise sampling. ACM Transactions on Graphics Vol. 32, No. 6, Article No. 216, 2013.
Bowers, J.; Wang, R.; Wei, L. Y.; Maletz, D. Parallel Poisson disk sampling with spectrum analysis on surfaces. ACM Transactions on Graphics Vol. 29, No. 6, Article No. 166, 2010.
Ying, X.; Xin, S. Q.; Sun, Q.; He, Y. An intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. IEEE Transactions on Visualization and Computer Graphics Vol. 19, No. 9, 1425–1437, 2013.
Li, H.; Wei, L. Y.; Sander, P. V.; Fu, C. W. Anisotropic blue noise sampling. ACM Transactions on Graphics Vol. 29, No. 6, Article No. 167, 2010.
Peyrot, J. L.; Payan, F.; Antonini, M. Feature preserving direct blue noise sampling for surface meshes. In: Eurographics 2013. Short Papers. Otaduy, M. A.; Sorkine, O. Eds. The Eurographics Association, 9–12, 2013.
Quinn, J. A.; Langbein, F. C.; Lai, Y. K.; Martin, R. R. Generalized anisotropic stratified surface sampling. IEEE Transactions on Visualization and Computer Graphics Vol. 19, No. 7, 1143–1157, 2013.
Zhong, Z.; Guo, X.; Wang, W.; Levy, B.; Sun, F.; Liu, Y.; Mao, W. Particle based anisotropic surface meshing. ACM Transactions on Graphics Vol. 32, No. 4, Article No. 99, 2013.
Chen, Z.; Yuan, Z.; Choi, Y. K.; Liu, L.; Wang, W. Variational blue noise sampling. IEEE Transactions on Visualization and Computer Graphics Vol. 18, No. 10, 1784–1796, 2012.
Liang, G.; Lu, L.; Chen, Z.; Yang, C. Poisson disk sampling through disk packing. Computational Visual Media Vol. 1, No. 1, 17–26, 2015.
Dunbar, D.; Humphreys, G. A spatial data structure for fast Poisson disk sample generation. ACM Transactions on Graphics Vol. 25, No. 3, 503–508, 2006.
Gamito, M. N.; Maddock, S. C. Accurate multidimensional Poisson disk sampling. ACM Transactions on Graphics Vol. 29, No. 1, Article No. 8, 2009.
Fattal, R. Blue noise point sampling using kernel density model. ACM Transactions on Graphics Vol. 30, No. 4, Article No. 48, 2011.
Cohen, M. F.; Shade, J.; Hiller, S.; Deussen, O. Wang Tiles for image and texture generation. ACM Transactions on Graphics Vol. 22, No. 3, 287–294, 2003.
Kopf, J.; Cohen Or, D.; Deussen, O.; Lischinski, D. Recursive Wang tiles for real time blue noise. ACM Transactions on Graphics Vol. 25, No. 3, 509–518, 2006.
Ostromoukhov, V. Sampling with polyominoes. ACM Transactions on Graphics Vol. 26, No. 3, Article No. 78, 2007.
Zhou, Y.; Huang, H.; Wei, L. Y.; Wang, R. Point sampling with general noise spectrum. ACM Transactions on Graphics Vol. 31, No. 4, Article No. 76, 2012.
Lai, Y. K.; Hu, S. M.; Martin, R. R. Surface mosaics. The Visual Computer Vol. 22, No. 9, 604–611, 2006.
Dos Passos, V. A.; Walter, M. 3D mosaics with variablesized tiles. The Visual Computer Vol. 24, No. 7, 617–623, 2008.
Dos Passos, V. A.; Walter, M. 3D virtual mosaics: Opus palladium and mixed styles. The Visual Computer Vol. 25, No. 10, 939–946, 2009.
Hu, W.; Chen, Z.; Pan, H.; Yu, Y.; Grinspun, E.; Wang, W. Surface mosaic synthesis with irregular tiles. IEEE Transactions on Visualization and Computer Graphics Vol. 22, No. 3, 1302–1313, 2016.
Sun, X.; Zhou, K.; Guo, J.; Xie, G.; Pan, J.; Wang, W.; Guo, B. Line segment sampling with blue noise properties. ACM Transactions on Graphics Vol. 32, No. 4, Article No. 127, 2013.
Battiato, S.; Milone, A.; Puglisi, G. Artificial mosaic generation with gradient vector flow and tile cutting. Journal of Electrical and Computer Engineering Vol. 2013. Article No. 8, 2013.
Hausner, A. Simulating decorative mosaics. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, 573–580, 2001.
Feng, L.; Hotz, I.; Hamann, B.; Joy, K. Anisotropic noise samples. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 2, 342–354, 2008.
Li, H.; Lo, K. Y.; Leung, M. K.; Fu, C. W. Dual Poisson disk tiling: An efficient method for distributing features on arbitrary surfaces. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 5, 982–998, 2008.
Mitchell, J. S. B.; Mount, D. M.; Papadimitriou, C. H. The discrete geodesic problem. SIAM Journal on Computing Vol. 16, No. 4, 647–668, 1987.
Chen, J.; Han, Y. Shortest paths on a polyhedron. In: Proceedings of the 6th Annual Symposium on Computational Geometry, 360–369, 1990.
Liu, Y. J. Exact geodesic metric in 2 manifold triangle meshes using edge based data structures. Computer Aided Design Vol. 45, No. 3, 695–704, 2013.
Surazhsky, V.; Surazhsky, T.; Kirsanov, D.; Gortler, S. J.; Hoppe, H. Fast exact and approximate geodesics on meshes. ACM Transactions on Graphics Vol. 24, No. 3, 553–560, 2005.
Xin, S. Q.; Wang, G. J. Improving Chen and Han’s algorithm on the discrete geodesic problem. ACM Transactions on Graphics Vol. 28, No. 4, Article No. 104, 2009.
Xu, C.; Wang, T. Y.; Liu, Y. J.; Liu, L.; He, Y. Fast wavefront propagation (FWP) for computing exact geodesic distances on meshes. IEEE Transactions on Visualization and Computer Graphics Vol. 21, No. 7, 822–834, 2015.
Ying, X.; Xin, S. Q.; He, Y. Parallel Chen–Han (PCH) algorithm for discrete geodesics. ACM Transactions on Graphics Vol. 33, No. 1, Article No. 9, 2014.
Qin, Y.; Han, X.; Yu, H.; Yu, Y.; Zhang, J. Fast and exact discrete geodesic computation based on triangle oriented wavefront propagation. ACM Transactions on Graphics Vol. 35, No. 4, Article No. 125, 2016.
Sethian, J. A. A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences of the United States of America Vol. 93, No. 4, 1591–1595, 1996.
Crane, K.; Weischedel, C.; Wardetzky, M. Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics Vol. 32, No. 5, Article No. 152, 2013.
Campen, M.; Heistermann, M.; Kobbelt, L. Practical anisotropic geodesy. Computer Graphics Forum Vol. 32, No. 5, 63–71, 2013.
Xin, S. Q.; Ying, X.; He, Y. Constant time all pairs geodesic distance query on triangle meshes. In: Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, 31–38, 2012.
Ying, X.; Wang, X.; He, Y. Saddle vertex graph (SVG): A novel solution to the discrete geodesic problem. ACM Transactions on Graphics Vol. 32, No. 6, Article No. 170, 2013.
Dijkstra, E. W. A note on two problems in connexion with graphs. Numerische Mathematik Vol. 1, No. 1, 269–271, 1959.
Bertsekas, D. P. A simple and fast label correcting algorithm for shortest paths. Networks Vol. 23, No. 8, 703–709, 1993.
Bertsekas, D. P.; Guerriero, F.; Musmanno, R. Parallel asynchronous label correcting methods for shortest paths. Journal of Optimization Theory and Applications Vol. 88, No. 2, 297–320, 1996.
Schmidt, R.; Grimm, C.; Wyvill, B. Interactive decal compositing with discrete exponential maps. ACM Transactions on Graphics Vol. 25, No. 3, 605–613, 2006.
Wang, X.; Ying, X.; Liu, Y. J.; Xin, S. Q.; Wang, W.; Gu, X.; Mueller Wittig, W.; He, Y. Intrinsic computation of centroidal voronoi tessellation (CVT) on meshes. Computer Aided Design Vol. 58, 51–61, 2015.
Sun, Q.; Zhang, L.; Zhang, M.; Ying, X.; Xin, S. Q.; Xia, J.; He, Y. Texture brush: An interactive surface texturing interface. In: Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, 153–160, 2013.
Schmidt, R. Stroke parameterization. Computer Graphics Forum Vol. 32, No. 2pt2, 255–263, 2013.
Crane, K.; Desbrun, M.; Schroder, P. Trivial connections on discrete surfaces. Computer Graphics Forum Vol. 29, No. 5, 1525–1533, 2010.
Megiddo, N. Linear time algorithms for linear programming in R3 and related problems. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, 329–338, 1982.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is published with open access at Springerlink.com
These authors contributed equally to this work.
Xiaoning Wang received his B.Eng. degree from Tianjin University, China, in 2011, and Ph.D. degree from Nanyang Technological University, Singapore. He is currently a research fellow in the School of Computer Science and Engineering, Nanyang Technological University. His research interests are geometric analysis and computer graphics.
Tien Hung Le received his B.Eng. degree in computer engineering from Bauman Moscow State Technical University, Russia, in 2009. He is currently a Ph.D. candidate in the School of Computer Science and Engineering, Nanyang Technological University, Singapore. His research interests include computing geodesics, point set surfaces, and surface parameterization.
Xiang Ying received his Ph.D. degree in computer science from Nanyang Technological University, Singapore. He is currently an associate professor in Tianjin University, China. His research interests include computer graphics, virtual reality, and GPU computing.
Qian Sun received her Ph.D. degree in computer science from Nanyang Technological University, Singapore. She is currently a research fellow in Fraunhofer IDM@NTU. Her current research interests include human–computer interaction, computer graphics, and data visualization.
Ying He is currently an associate professor in the School of Computer Science and Engineering, Nanyang Technological University, Singapore. He received his B.S. and M.S. degrees in electrical engineering from Tsinghua University, China, and Ph.D. degree in computer science from Stony Brook University, USA. His research interests fall into the general area of visual computing and he is particularly interested in the problems which require geometric analysis and computation. For more information, please visit http://www.ntu.edu.sg/home/yhe.
Open Access The articles published in this journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Other papers from this open access journal are available free of charge from http://www.springer.com/journal/41095. To submit a manuscript, please go to https://www. editorialmanager.com/cvmj.
Electronic supplementary material
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Wang, X., Le, T.H., Ying, X. et al. User controllable anisotropic shape distribution on 3D meshes. Comp. Visual Media 2, 305–319 (2016). https://doi.org/10.1007/s41095-016-0057-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41095-016-0057-1