CSDL Home IEEE Transactions on Visualization & Computer Graphics 2008 vol.14 Issue No.02 - March/April

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Issue No.02 - March/April (2008 vol.14)

pp: 342-354

ABSTRACT

We present a practical approach to generate stochastic anisotropic samples with Poisson-disk characteristic over a two-dimensional domain. In contrast to isotropic samples, we understand anisotropic samples as non-overlapping ellipses whose size and density match a given anisotropic metric. Anisotropic noise samples are useful for many visualization and graphics applications. The spot samples can be used as input for texture generation, e.g., line integral convolution (LIC), but can also be used directly for visualization. The definition of the spot samples using a metric tensor makes them especially suitable for the visualization of tensor fields that can be translated into a metric. Our work combines ideas from sampling theory and mesh generation. To generate these samples with the desired properties we construct a first set of non-overlapping ellipses whose distribution closely matches the underlying metric. This set of samples is used as input for a generalized anisotropic Lloyd relaxation to distribute noise samples more evenly. Instead of computing the Voronoi tessellation explicitly, we introduce a discrete approach which combines the Voronoi cell and centroid computation in one step. Our method supports automatic packing of the elliptical samples, resulting in textures similar to those generated by anisotropic reaction-diffusion methods. We use Fourier analysis tools for quality measurement of uniformly distributed samples.

INDEX TERMS

Flow visualization, Computer Graphics, Picture/Image Generation, Sampling, Relaxation

CITATION

Louis Feng, Ingrid Hotz, Bernd Hamann, Kenneth Joy, "Anisotropic Noise Samples",

*IEEE Transactions on Visualization & Computer Graphics*, vol.14, no. 2, pp. 342-354, March/April 2008, doi:10.1109/TVCG.2007.70434REFERENCES

- [1] V. Ostromoukhov, “A Simple and Efficient Error-Diffusion Algorithm,”
Proc. ACM SIGGRAPH '01, pp. 567-572, 2001.- [3] R. Ulichney,
Digital Halftoning. MIT Press, 1987.- [5] P. Alliez, É. Colin de Verdière, O. Devillers, and M. Isenburg, “Isotropic Surface Remeshing,”
Proc. Int'l Conf. Shape Modeling and Applications (SMI '03), p. 49, 2003.- [7] F. Labelle and J.R. Shewchuk, “Anisotropic Voronoi Diagrams and Guaranteed-Quality Anisotropic Mesh Generation,”
Proc. 19th Ann. Symp. Computational Geometry (SCG '03), pp. 191-200, 2003.- [8] K. Shimada, A. Yamada, and T. Itoh, “Anisotropic Triangulation of Parametric Surfaces via Close Packing of Ellipsoids,”
Int'l J.Computational Geometry Applications, vol. 10, no. 4, pp. 417-440, 2000.- [11] B. Cabral and L. Leedom, “Imaging Vector Fields Using Line Integral Convolution,”
Proc. ACM SIGGRAPH '93, vol. 27, pp. 263-272, Aug. 1993.- [14] R.M. Kirby, H. Marmanis, and D.H. Laidlaw, “Visualizing Multivalued Data from 2D Incompressible Flows Using Concepts from Painting,”
Proc. 10th IEEE Conf. Visualization (VIS '99), pp.333-340, citeseer.ist.psu.edukirby99visualizing.html , 1999.- [18] A.S. Glassner, “Principles of Digital Image Synthesis,”
Morgan Kaufmann Series in Computer Graphics and Geometric Modeling, vol. 2, Morgan Kaufmann, 1995.- [23] A. Hausner, “Simulating Decorative Mosaics,”
Proc. ACM SIGGRAPH '01, pp. 573-578, citeseer.ist.psu.edu/kindlmann00strategies.htmlhttp:/ /citeseer.ist.psu.eduhausner 01simulating.html , 2001.- [24] L.-P. Fritzsche, H. Hellwig, S. Hiller, and O. Deussen, “Interactive Design of Authentic Looking Mosaics Using Voronoi Structures,”
Proc. Second Int'l Symp. Voronoi Diagrams in Science and Eng. (VD'05), http://citeseer.ist.psu.edu744345.html, 2005.- [27] G. Turk and D. Banks, “Image-Guided Streamline Placement,”
Proc. ACM SIGGRAPH '96, vol. 30, pp. 453-460, citeseer.ist.psu.edu/hoff99fast.htmlhttp:/ /visinfo.zib.de/EVlib/Show?EVL-1998-331citeseer.csail.mit. edu turk96imageguided.html , 1996.- [29] E.N. Gilbert, “Gray Codes and Paths on the N-Cube,”
Bell System Technical J., vol. 37, no. 3, pp. 815-826, 1958.- [30] G. Kindlmann, “Superquadric Tensor Glyphs,”
Proc. IEEE TCVG/EG Symp. Visualization, pp. 147-154, May 2004. |