Science China Information Sciences

, Volume 56, Issue 9, pp 1–12 | Cite as

Approximate Poisson disk sampling on mesh

  • Bo Geng
  • HuiJuan Zhang
  • Heng Wang
  • GuoPing Wang
Research Paper


Poisson disk sampling has been widely used in many applications such as remeshing, procedural texturing, object distribution, illumination, etc. While 2D Poisson disk sampling is intensively studied in recent years, direct Poisson disk sampling on 2-manifold surface is rarely covered. In this paper, we present a novel framework which generates approximate Poisson disk distribution directly on mesh, a discrete representation of 2-manifold surfaces. Our framework is easy to implement and provides extra flexibility to specified sampling issues like feature-preserving sampling and adaptive sampling. We integrate the tensor voting method into feature detection and adaptive sample radius calculation. Remeshing as a special downstream application is also addressed. According to our experiment results, our framework is efficient, robust, and widely applicable.


Poisson disk sampling feature preserving sampling adaptive sampling remeshing tensor voting 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dippé M A Z, Wold E H. Antialiasing through stochastic sampling. In: Proceedings of the SIGGRAPH Conference. New York: ACM, 1985. 69–78Google Scholar
  2. 2.
    Cook R L. Stochastic sampling in computer graphics. ACM Trans Graphic, 1986, 5: 51–72CrossRefGoogle Scholar
  3. 3.
    Mitchell D P. Generating antialiased images at low sampling densities. In: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ′87. New York: ACM, 1987. 65–72CrossRefGoogle Scholar
  4. 4.
    Hachisuka T, Jarosz W, Weistroffer R P, et al. Multidimensional adaptive sampling and reconstruction for ray tracing. ACM Trans Graphic, 2008, 27: Article No. 33Google Scholar
  5. 5.
    Lehtinen J, Zwicker M, Turquin E, et al. A meshless hierarchical representation for light transport. ACM Trans Graphic, 2008, 27: Article No. 37Google Scholar
  6. 6.
    Mitchell D P. Spectrally optimal sampling for distribution ray tracing. SIGGRAPH Comput Graph, 1991, 25: 157–164CrossRefGoogle Scholar
  7. 7.
    Deussen O, Hanrahan P, Lintermann B, et al. Realistic modeling and rendering of plant ecosystems. In: Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ′98. New York: ACM, 1998. 275–286CrossRefGoogle Scholar
  8. 8.
    Deussen O, Hiller S, van Overveld C, et al. Floating points: a method for computing stipple drawings. Comput Graph Forum, 2000, 19: 40–51CrossRefGoogle Scholar
  9. 9.
    Lagae A, Dutré P. A comparison of methods for generating Poisson disk distributions. Comput Graph Forum, 2008, 27: 114–129CrossRefGoogle Scholar
  10. 10.
    Gamito M N, Maddock S C. Accurate multidimensional Poisson-disk sampling. ACM Trans Graphic, 2009, 29: Article No.8Google Scholar
  11. 11.
    Jones T R. Efficient generation of Poisson-disk sampling patterns. J Graph Tool, 2006, 11: 27–36CrossRefGoogle Scholar
  12. 12.
    Dunbar D, Humphreys G. A spatial data structure for fast Poisson-disk sample generation. ACM Trans Graphic, 2006, 25: 503–508CrossRefGoogle Scholar
  13. 13.
    White K B, Cline D, Egbert P K. Poisson disk point sets by hierarchical dart throwing. In: Proceedings of the IEEE Symposium on Interactive Ray Tracing. Washington DC: IEEE Computer Society, 2007. 129–132CrossRefGoogle Scholar
  14. 14.
    Wei L. Parallel Poisson disk sampling. ACM Trans Graphic, 2008, 27: Article No. 20Google Scholar
  15. 15.
    Lloyd S P. Least squares quantization in PCM. IEEE Trans Inform Theory, 1982, 28: 129–137MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Balzer M, Schlömer T, Deussen O. Capacity-constrained point distributions: a variant of Lloyd’s method. In: ACM SIGGRAPH. New York: ACM, 2009. Article No. 86Google Scholar
  17. 17.
    Liu Y, Wang W, Lvy B, et al. On centroidal voronoi tessellation-energy smoothness and fast computation. ACM Trans Graphic, 2009, 28: Article No. 101Google Scholar
  18. 18.
    Ostromoukhov V, Donohue C, Jodoin P. Fast hierarchical importance sampling with blue noise properties. In: ACM SIGGRAPH. New York: ACM, 2004. 488–495Google Scholar
  19. 19.
    Ostromoukhov V. Sampling with polyominoes. ACM Trans Graphic, 2007, 26: Article No. 78Google Scholar
  20. 20.
    Hiller S, Deussen O, Keller A. Tiled blue noise samples. In: Proceedings of the Vision Modeling and Visualization Conference. Aka GmbH, 2001. 265–272Google Scholar
  21. 21.
    Lagae A, Dutré P. A procedural object distribution function. ACM Trans Graphic, 2005, 24: 1442–1461CrossRefGoogle Scholar
  22. 22.
    Lagae A, Dutré P. An alternative for wang tiles: colored edges versus colored corners. ACM Trans Graphic, 2006, 25: 1442–1459CrossRefGoogle Scholar
  23. 23.
    Fu Y, Zhou B. Direct sampling on surfaces for high quality remeshing. Comput Aided Geom D, 2009, 26: 711–723MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Cline D, Jeschke S, White K, et al. Dart throwing on surfaces. Comput Graph Forum, 2009, 28: 1217–1226CrossRefGoogle Scholar
  25. 25.
    Li H, Lo K, Leung M, et al. Dual Poisson-disk tiling: an efficient method for distributing features on arbitrary surfaces. IEEE Trans Vis Comput Gr, 2008, 14: 982–998CrossRefGoogle Scholar
  26. 26.
    Pottmann H, Steiner T, Hofer M, et al. The isophotic metric and its applications to feature sensitive morphology on surfaces. LNCS, 2004, 3024: 560–572Google Scholar
  27. 27.
    Kim H S, Choi H K, Lee K H. Feature detection of triangular meshes based on tensor voting theory. Comput Aided Design, 2009, 41: 47–58CrossRefGoogle Scholar
  28. 28.
    Ulichney R A. Digital Halftoning. Boston: MIT Press, 1987. 189–205Google Scholar
  29. 29.
    McCool M, Fiume E. Hierarchical Poisson disk sampling distributions. In: Proceedings of the Conference on Graphics interface′92. San Francisco: Morgan Kaufmann Publishers Inc., 1992. 94–105Google Scholar
  30. 30.
    Yue W N, Guo Q W, Zhang J, et al. 3D triangular mesh optimization for geometry processing in CAD. In: ACM International Conference on Solid and Physical Modeling 2007 (SPM ′07). New York: ACM, 2007. 23–34Google Scholar
  31. 31.
    Chen X, Golovinskiy A, Funkhouser T. A benchmark for 3D mesh segmentation. In: ACM SIGGRAPH. New York: ACM, 2009. Article No. 73Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Bo Geng
    • 1
  • HuiJuan Zhang
    • 1
  • Heng Wang
    • 1
  • GuoPing Wang
    • 1
    • 2
  1. 1.Graphics and Interactive Technology Lab of Dept. of Computer SciencePeking UniversityBeijingChina
  2. 2.The Key Lab of Machine perception and intelligentMOEBeijingChina

Personalised recommendations