Advertisement

Computational Visual Media

, Volume 2, Issue 4, pp 305–319 | Cite as

User controllable anisotropic shape distribution on 3D meshes

  • Xiaoning Wang
  • Tien Hung Le
  • Xiang Ying
  • Qian SunEmail author
  • Ying He
Open Access
Research Article

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.

Keywords

shape distribution anisotropic sampling discrete geodesics intrinsic algorithm parallel computing 

Supplementary material

41095_2016_57_MOESM1_ESM.mp4 (110.3 mb)
Supplementary material, approximately 110 MB.

References

  1. [1]
    Wei, L. Y. Parallel Poisson disk sampling. ACM Transactions on Graphics Vol. 27, No. 3, Article No. 20, 2008.Google Scholar
  2. [2]
    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.Google Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    Wei, L. Y. Multi class blue noise sampling. ACM Transactions on Graphics Vol. 29, No. 4, Article No. 79, 2010.Google Scholar
  5. [5]
    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.Google Scholar
  6. [6]
    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.Google Scholar
  7. [7]
    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.CrossRefGoogle Scholar
  8. [8]
    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.Google Scholar
  9. [9]
    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.Google Scholar
  10. [10]
    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.CrossRefGoogle Scholar
  11. [11]
    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.Google Scholar
  12. [12]
    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.CrossRefGoogle Scholar
  13. [13]
    Liang, G.; Lu, L.; Chen, Z.; Yang, C. Poisson disk sampling through disk packing. Computational Visual Media Vol. 1, No. 1, 17–26, 2015.CrossRefGoogle Scholar
  14. [14]
    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.CrossRefGoogle Scholar
  15. [15]
    Gamito, M. N.; Maddock, S. C. Accurate multidimensional Poisson disk sampling. ACM Transactions on Graphics Vol. 29, No. 1, Article No. 8, 2009.Google Scholar
  16. [16]
    Fattal, R. Blue noise point sampling using kernel density model. ACM Transactions on Graphics Vol. 30, No. 4, Article No. 48, 2011.Google Scholar
  17. [17]
    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.CrossRefGoogle Scholar
  18. [18]
    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.CrossRefGoogle Scholar
  19. [19]
    Ostromoukhov, V. Sampling with polyominoes. ACM Transactions on Graphics Vol. 26, No. 3, Article No. 78, 2007.Google Scholar
  20. [20]
    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.Google Scholar
  21. [21]
    Lai, Y. K.; Hu, S. M.; Martin, R. R. Surface mosaics. The Visual Computer Vol. 22, No. 9, 604–611, 2006.CrossRefGoogle Scholar
  22. [22]
    Dos Passos, V. A.; Walter, M. 3D mosaics with variablesized tiles. The Visual Computer Vol. 24, No. 7, 617–623, 2008.CrossRefGoogle Scholar
  23. [23]
    Dos Passos, V. A.; Walter, M. 3D virtual mosaics: Opus palladium and mixed styles. The Visual Computer Vol. 25, No. 10, 939–946, 2009.CrossRefGoogle Scholar
  24. [24]
    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.CrossRefGoogle Scholar
  25. [25]
    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.Google Scholar
  26. [26]
    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.Google Scholar
  27. [27]
    Hausner, A. Simulating decorative mosaics. In: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, 573–580, 2001.Google Scholar
  28. [28]
    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.CrossRefGoogle Scholar
  29. [29]
    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.CrossRefGoogle Scholar
  30. [30]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    Chen, J.; Han, Y. Shortest paths on a polyhedron. In: Proceedings of the 6th Annual Symposium on Computational Geometry, 360–369, 1990.Google Scholar
  32. [32]
    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.CrossRefGoogle Scholar
  33. [33]
    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.CrossRefGoogle Scholar
  34. [34]
    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.Google Scholar
  35. [35]
    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.CrossRefGoogle Scholar
  36. [36]
    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.Google Scholar
  37. [37]
    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.Google Scholar
  38. [38]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    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.Google Scholar
  40. [40]
    Campen, M.; Heistermann, M.; Kobbelt, L. Practical anisotropic geodesy. Computer Graphics Forum Vol. 32, No. 5, 63–71, 2013.CrossRefGoogle Scholar
  41. [41]
    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.Google Scholar
  42. [42]
    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.Google Scholar
  43. [43]
    Dijkstra, E. W. A note on two problems in connexion with graphs. Numerische Mathematik Vol. 1, No. 1, 269–271, 1959.MathSciNetCrossRefzbMATHGoogle Scholar
  44. [44]
    Bertsekas, D. P. A simple and fast label correcting algorithm for shortest paths. Networks Vol. 23, No. 8, 703–709, 1993.CrossRefzbMATHGoogle Scholar
  45. [45]
    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.MathSciNetCrossRefzbMATHGoogle Scholar
  46. [46]
    Schmidt, R.; Grimm, C.; Wyvill, B. Interactive decal compositing with discrete exponential maps. ACM Transactions on Graphics Vol. 25, No. 3, 605–613, 2006.CrossRefGoogle Scholar
  47. [47]
    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.CrossRefGoogle Scholar
  48. [48]
    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.Google Scholar
  49. [49]
    Schmidt, R. Stroke parameterization. Computer Graphics Forum Vol. 32, No. 2pt2, 255–263, 2013.CrossRefGoogle Scholar
  50. [50]
    Crane, K.; Desbrun, M.; Schroder, P. Trivial connections on discrete surfaces. Computer Graphics Forum Vol. 29, No. 5, 1525–1533, 2010.CrossRefGoogle Scholar
  51. [51]
    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.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Xiaoning Wang
    • 1
  • Tien Hung Le
    • 1
  • Xiang Ying
    • 1
  • Qian Sun
    • 1
    Email author
  • Ying He
    • 1
  1. 1.School of Computer Science and EngineeringNanyang Technological UniversitySingaporeSingapore

Personalised recommendations