This Article 
 Bibliographic References 
 Add to: 
Efficient and Flexible Sampling with Blue Noise Properties of Triangular Meshes
June 2012 (vol. 18 no. 6)
pp. 914-924
M. Corsini, Visual Comput. Lab., Ist. di Scienza e Tecnol. dell'Inf., Pisa, Italy
P. Cignoni, Visual Comput. Lab., Ist. di Scienza e Tecnol. dell'Inf., Pisa, Italy
R. Scopigno, Visual Comput. Lab., Ist. di Scienza e Tecnol. dell'Inf., Pisa, Italy
This paper deals with the problem of taking random samples over the surface of a 3D mesh describing and evaluating efficient algorithms for generating different distributions. We discuss first the problem of generating a Monte Carlo distribution in an efficient and practical way avoiding common pitfalls. Then, we propose Constrained Poisson-disk sampling, a new Poisson-disk sampling scheme for polygonal meshes which can be easily tweaked in order to generate customized set of points such as importance sampling or distributions with generic geometric constraints. In particular, two algorithms based on this approach are presented. An in-depth analysis of the frequency characterization and performance of the proposed algorithms are also presented and discussed.

[1] H. Li, K.-Y. Lo, M.-K. Leung, and C.-W. Fu, “Dual Poisson-Disk Tiling: An Efficient Method for Distributing Features on Arbitrary Surfaces,” IEEE Trans. Visualization and Computer Graphics, vol. 14, no. 5, pp. 982-998, Sept./Oct 2008.
[2] A. Lagae and P. Dutré, “A Comparison of Methods for Generating Poisson Disk Distributions,” Computer Graphics Forum, vol. 21, no. 1, pp. 114-129, 2008.
[3] D. Cline, S. Jeschke, K. White, A. Razdan, and P. Wonka, “Dart Throwing on Surfaces,” Computer Graphics Forum, vol. 28, no. 4, pp. 1217-1226, 2009.
[4] R.L. Cook, “Stochastic Sampling in Computer Graphics,” ACM Trans. Graphics, vol. 5, no. 1, pp. 51-72, 1986.
[5] M.A.Z. Dippé and E.H. Wold, “Antialiasing through Stochastic Sampling,” Proc. ACM SIGGRAPH '85, pp. 69-78, 1985.
[6] Y. Fu and B. Zhou, “Direct Sampling on Surfaces for High Quality Remeshing,” Proc. Symp. Solid and Physical Modeling (SPM '08), pp. 115-124, 2008.
[7] J. Bowers, R. Wang, L.-Y. Wei, and D. Maletz, “Parallel Poisson Disk Sampling with Spectrum Analysis on Surfaces,” Proc. ACM SIGGRAPH Asia, pp. 166:1-166:10, 2010.
[8] K. White, D. Cline, and P. Egbert, “Poisson Disk Point Sets by Hierarchical Dart Throwing,” Proc. IEEE Symp. Interactive Ray Tracing (RT '07), pp. 129-132, Sept. 2007.
[9] P. Cignoni, M. Corsini, and G. Ranzuglia, “Meshlab: An Open-Source 3D Mesh Processing System,” ERCIM News, vol. 73, pp. 45-46, http:/, 2008.
[10] M.F. Cohen, J. Shade, S. Hiller, and O. Deussen, “Wang Tiles for Image and Texture Generation,” Proc. ACM SIGGRAPH, pp. 287-294, 2003.
[11] 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.
[12] A. Lagae and P. Dutré, “A Procedural Object Distribution Function,” ACM Trans. Graphics, vol. 24, no. 4, pp. 1442-1461, 2005.
[13] A. Lagae and P. Dutré, “Poisson Sphere Distributions,” Proc. Vision, Modeling, and Visualization, pp. 373-379, Nov. 2006.
[14] V. Ostromoukhov, C. Donohue, and P.-M. Jodoin, “Fast Hierarchical Importance Sampling with Blue Noise Properties,” ACM Trans. Graphics, vol. 23, no. 3, pp. 488-495, 2004.
[15] 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.
[16] T.R. Jones, “Efficient Generation of Poisson-Disk Sampling Patterns,” J. Graphics Tools, vol. 11, no. 2, pp. 27-36, 2006.
[17] L.-Y. Wei, “Parallel Poisson Disk Sampling,” ACM Trans. Graphics, vol. 27, no. 3, pp. 1-9, 2008.
[18] G. Turk, “Re-Tiling Polygonal Surfaces,” ACM SIGGRAPH Computer Graphics, vol. 26, no. 2, pp. 55-64, 1992.
[19] X. Jiao and M.T. Heath, “Feature Detection for Surface Meshes,” Proc. Eighth Int'l Conf. Numerical Grid Generation in Computational Field Simulations, pp. 705-714, 2002.
[20] D. Knuth, The Art of Computer Programming: Seminumerical Algorithms, vol. 2, third ed. Addison-Wesley, 1997.
[21] W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in C. Cambridge Univ. Press, 1992.
[22] M. Teschner, B. Heidelberger, M. Mueller, D. Pomeranets, and M. Gross, “Optimized Spatial Hashing for Collision Detection of Deformable Objects,” Proc. Vision, Modeling, Visualization (VMV), pp. 47-54, 2003.
[23] T. Schlömer and O. Deussen, “Towards a Standardized Spectral Analysis of Point Sets with Applications in Graphics,” technical report, Univ. of Konstanz, May 2010.

Index Terms:
Monte Carlo methods,Three dimensional displays,Noise measurement,Complexity theory,Algorithm design and analysis,Context modeling,Monte Carlo methods.,Geometry processing,computational geometry,three-dimensional graphics and realism,sampling,Poisson-disk sampling
M. Corsini, P. Cignoni, R. Scopigno, "Efficient and Flexible Sampling with Blue Noise Properties of Triangular Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 6, pp. 914-924, June 2012, doi:10.1109/TVCG.2012.34
Usage of this product signifies your acceptance of the Terms of Use.