CSDL Home IEEE Transactions on Visualization & Computer Graphics 2008 vol.14 Issue No.05 - September/October

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Issue No.05 - September/October (2008 vol.14)

pp: 982-998

Kui-Yip Lo , Hong Kong University of Science and Technology, Hong Kong

Man-Kang Leung , Hong Kong University of Science and Technology, Hong Kong

Hongwei Li , Hong Kong University of Science and Technology, Hong Kong

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.53

ABSTRACT

This paper introduces a novel surface-modeling method to stochastically distribute features on arbitrary topological surfaces. The generated distribution of features follows the Poisson disk distribution, so we can have a minimum separation guarantee between features and avoid feature overlap. With the proposed method, we not only can interactively adjust and edit features with the help of the proposed Poisson disk map, but can also efficiently re-distribute features on object surfaces. The underlying mechanism is our dual tiling scheme, known as the Dual Poisson-Disk Tiling. First, we compute the dual of a given surface parameterization, and tile the dual surface by our specially-designed dual tiles; during the pre-processing, the Poisson disk distribution has been pre-generated on these tiles. By dual tiling, we can nicely avoid the problem of corner heterogeneity when tiling arbitrary parameterized surfaces, and can also reduce the tile set complexity. Furthermore, the dual tiling scheme is non-periodic, and we can also maintain a manageable tile set. To demonstrate the applicability of this technique, we explore a number of surface-modeling applications: pattern and shape distribution, bump-mapping, illustrative rendering, mold simulation, the modeling of separable features in texture and BTF, and the distribution of geometric textures in shell space.

INDEX TERMS

Three-Dimensional Graphics and Realism, Computational Geometry and Object Modeling, Applications

CITATION

Kui-Yip Lo, Man-Kang Leung, Hongwei Li, "Dual Poisson-Disk Tiling: An Efficient Method for Distributing Features on Arbitrary Surfaces",

*IEEE Transactions on Visualization & Computer Graphics*, vol.14, no. 5, pp. 982-998, September/October 2008, doi:10.1109/TVCG.2008.53REFERENCES

- [2] J.F. Blinn, “Simulation of Wrinkled Surfaces,”
Proc. Computer Graphics (SIGGRAPH '78), vol. 12, pp. 286-292, Aug. 1978.- [4] E.E. Catmull, “A Subdivision Algorithm for Computer Display of Curved Surfaces,” PhD thesis, Dept. of Computer Science, Univ. of Utah, Dec. 1974.
- [11] O. Deussen, S. Hiller, C. van Overveld, and T. Strothotte, “Floating Points: A Method for Computing Stipple Drawings,”
Computer Graphics Forum, vol. 19, no. 3, pp. 40-51, 2000.- [12] M.A.Z. Dippé and E.H. Wold, “Antialiasing through Stochastic Sampling,”
Proc. Computer Graphics (SIGGRAPH '85), pp. 69-78, 1985.- [17] K.W. Fleischer, D.H. Laidlaw, B.L. Currin, and A.H. Barr, “Cellular Texture Generation,”
Proc. ACM SIGGRAPH '95, pp.239-248, 1995.- [18] M.S. Floater and K. Hormann, “Surface Parameterization: A Tutorial and Survey,”
Advances in Multiresolution for Geometric Modelling, N.A. Dodgson, M.S. Floater, and M.A. Sabin, eds., pp.157-186, Springer Verlag, 2005.- [19] C.-W. Fu and M.-K. Leung, “Texture Tiling on Arbitrary Topological Surfaces Using Wang Tiles,”
Proc. Eurographics Symp. Rendering (EGSR '05), pp. 99-104, June 2005.- [21] S. Hiller, O. Deussen, and A. Keller, “Tiled Blue Noise Samples,”
Proc. Vision, Modeling, and Visualization Conf. (VMV '01), pp. 265-271, 2001.- [22] H.W. Jensen, S.R. Marschner, M. Levoy, and P. Hanrahan, “A Practical Model for Subsurface Light Transport,”
Proc. ACM SIGGRAPH '01, pp. 511-518, 2001.- [23] T.R. Jones, “Efficient Generation of Poisson-Disk Sampling Patterns,”
J. Graphics Tools, vol. 11, no. 2, pp. 27-36, 2006.- [28] A. Lagae, O. Dumont, and P. Dutré, “Geometry Synthesis,”
Proc. ACM SIGGRAPH Sketch, Aug. 2004.- [29] A. Lagae and P. Dutré, “A Procedural Object Distribution Function,”
ACM Trans. Graphics, vol. 24, no. 4, pp. 1442-1461, Oct. 2005.- [30] A. Lagae and P. Dutré, “Template Poisson Disk Tiles,” Technical Report CW 413, Katholieke Universiteit Leuven, May 2005.
- [31] A. Lagae and P. Dutré, “An Alternative for Wang Tiles: Colored Edges versus Colored Corners,”
ACM Trans. Graphics, vol. 25, no. 4, pp. 1442-1459, 2006.- [32] A. Lagae and P. Dutré, “A Comparison of Methods for Generating Poisson Disk Distribution,” Technical Report CW 459, Katholieke Universiteit Leuven, Aug. 2006.
- [33] A. Lagae and P. Dutré, “Poisson Sphere Distributions,”
Proc. Vision, Modeling, and Visualization Conf. (VMV '06), pp. 373-379, 2006.- [38] A. Lu, D.S. Ebert, W. Qiao, M. Kraus, and B. Mora,
Volume Illustration Using Wang Cubes, vol. 26, no. 2,Article 11, 2007.- [39] M. McCool and E. Fiume, “Hierarchical Poisson Disk Sampling Distributions,”
Proc. Graphics Interface Conf. (GI '02), pp. 94-105, 1992.- [42] V. Ostromoukhov, “Sampling with Polyominoes,”
ACM Trans. Graphics, vol. 26, no. 3,Article no. 78, 2007.- [44] M. Peercy, J. Airey, and B. Cabral, “Efficient Bump Mapping Hardware,”
Proc. ACM SIGGRAPH '97, pp. 303-306, 1997.- [48] J. Shade, M. Cohen, and D.P. Mitchell, “Tiling Layered Depth Images,” technical report, Univ. of Washington, 2002.
- [49] P. Sibley, P. Montgomery, and G.E. Marai, “Wang Cubes for Video Synthesis and Geometry Placement,”
Proc. ACM SIGGRAPH Poster Compendium, Aug. 2004.- [50] J. Stam, “Aperiodic Texture Mapping,” Technical Report R046, European Research Consortium for Informatics and Math., 1997.
- [53] X. Tong, J. Zhang, L. Liu, X. Wang, B. Guo, and H.-Y. Shum, “Synthesis of Bidirectional Texture Functions on Arbitrary Surfaces,”
ACM Trans. Graphics, vol. 21, no. 3, pp. 665-672, 2002.- [54] R. Ulichney,
Digital Halftoning. MIT Press, 1987.- [55] H. Wang, “Proving Theorems by Pattern Recognition II,”
Bell Systems Technical J., vol. 40, pp. 1-42, 1961.- [56] H. Wang, “Games, Logic, and Computers,”
Scientific Am., pp. 98-106, Nov. 1965.- [58] E.W. Weisstein, “Cauchy-Frobenius Lemma (a.k.a. Orbit-Counting Theorem),”
From MathWorld—A Wolfram Web Resource, http://mathworld.wolfram.comCauchy-FrobeniusLemma.html , 2008. |