Superellipsoid-based, Real Symmetric Traceless Tensor Glyphs Motivated by Nematic Liquid Crystal Alignment Visualization
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A glyph-based method for visualizing the nematic liquid crystal alignment tensor is introduced. Unlike previous approaches, the glyph is based upon physically-linked metrics, not offsets of the eigenvalues. These metrics, combined with a set of superellipsoid shapes, communicate both the strength of the crystal's uniaxial alignment and the amount of biaxiality. With small modifications, our approach can visualize any real symmetric traceless tensor.
[1] 1197 J. E. Anderson, P. Watson, and P. J. Bos, Comparisons of the vector method and tensor method for simulating liquid crystal devices. Liquid Crystals, 28: 109–115, 2001.
[2] A. H. Barr, Superquadrics and angle-preserving transformations. IEEE Computer Graphics and Applications, 1 (1): 11–22, April 1981.
[3] P. J. Collings, Liquid Crystals: Nature's Delicate Phase of Matter. Priceton University Press, Princeton, NJ, 2nd. edition, 2002.
[4] P. G. de Gennes, The Physics of Liquid Crystals. Clarendon, Oxford, 1974.
[5] D. S. Ebert, R. M. Rohrer, C. D. Shaw, P. Panda, J. M. Kukla, and D. A. Roberts, Procedural shape generation for multi-dimensional data visualization. Computers & Graphics, 24 (3): 375–384, 2000.
[6] D. S. Ebert and C. D. Shaw, Minimally immersive flow visualization. IEEE Transactions on Visualization and Computer Graphics, 7 (4): 343–350, 2001.
[7] M. G. Forest, Q. Wang, and H. Zhou, Methods for the exact construction of mesoscale spatial structures in liquid crystal polymers. Physica D, 152–153: 288–309, 2001.
[8] M. Hlawitschka and G. Scheuermann, Hot-lines—tracking lines in higher order tensor fields. In C. T. Silva, E. Gröller, and H. Rushmeier, editors, Proceedings of IEEE Visualization 2005, pages 27–34, October 2005.
[9] J. Hobdell and A. H. Windle, A numerical technique for predicting microstructure in liquid crystalline polymers. Liquid Crystals, 23: 157–173, 1997.
[10] G. L. Kindlmann, Superquadric tensor glyphs. In O. Deussen, C. Hansen, D. A. Keim, and D. Saupe, editors, Proceedings of the Eurographics/IEEE VGTC Symposium on Visualization (VisSym '04), pages 147–154, 2004.
[11] R. J. Low, Measuring order and biaxiality. European Journal of Physics, 23: 111–117, 2002.
[12] K. Mehta and T. J. Jankun-Kelly, Detection and visualization of defects in 3d unstructed models of nematic liquid crystals. IEEE Transactions on Visualization and Computer Graphics {Proceedings Visualization/Information Visualization 2006), 12 (5), 2006.
[13] N. Morrtram and C. Newton, Introduction to q-tensor theory. Technical report, Dept. of Mathematics, University of Strathclyde, 2004.
[14] C. D. Shaw, D. S. Ebert, J. M. Kukla, A. Zwa, I. Soboroff, and D. A. Roberts, Data visualization using automatic, perceptually-motivated shapes. In Proceedings of Visual Data Exploration and Analysis. SPIE, Apr.11 1998.
[15] C. D. Shaw, J. Hall, C. Blahut, D. S. Ebert, and D. A. Roberts, Using shape to visualize multivariate data. In Proceedings of the Workshop on New Paradigms in Information Visualization and Manipulation (NPIVM-99), pages 17–20, N.Y., Nov.6 1999. ACM Press.
[16] V. A. Slavin, R. A. Pelcovits, G. Loriot, A. Callan-Jones, and D. H. Laidlaw, Techniques for the visualization of topological defect behavior in nematic liquid crystals. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization/Information Visualization 2006), 12 (5), 2006.
[17] A. Sonnet, A. Kilian, and S. Hess, Alignment tensor versus director: Description of defects in nematic liquid crystals. Physical Review E, 52: 718–722, July 1995.
[18] T. Tsuji and A. D. Rey, Orientation mode selection mechanisms for sheared nematic liquid crystalline materials. Physical Review E, 57 (5): 5609–5625, 1998.
[19] C. Ware, Information Visualization: Perception for Design. Morgan Kaufmann Publishers, second edition, 2004.
[20] C. Westin, S. Peled, H. Gudbjartsson, R. Kikinis, and F. A. Jolesz, Geometrical diffusion measures for MRI from tensor basis analysis. In Proceedings of the Fifth Annual Meeting of the International Society for Magnetic Resonance in Medicine (ISMRM '97), page 1742, Vancouver Canada, April 1997.
[21] H. Wu and R. Mohanraj, Computational simulations for study of a liquid-crystal-based sensor system. In J. Graef, H. Lim, R. Shivaji, B. Soni, and J. Zhu, editors, Proceedings of the Sixth Mississippi State-UAB Conference on Differential Equations and Compuational Simulations, May 2005.
[22] C. Zannoni, Distribution functions and order parameters. In G. Luckhurst and G. Gray, editors, The Molecular Physics of Liquid Crystals, chapter 3, pages 51–83. Academic Press, 1979.
[23] S. Zhang, D. H. Laidlaw, and G. L. Kindlmann, Diffusion tensor MRI visualization. In C. D. Hansen and C. R. Johnson, editors, The Visualization Handbook, chapter 16, pages 327–340. Elsevier Academic Press, 2004.
[24] X. Zheng and A. Pang, 2d asymmetric tensor analysis. In C. T. Silva, E. Gröller, and H. Rushmeier, editors, Proceedings of IEEE Visualization 2005, pages 3–10, Oct. 2005.
[25] Y.-M. Zhu and P. A. Farrell, A vector grouping algorithm for liquid crystal tensor field visualization. Liquid Crystals, 29: 1259–1264, 2002.
Index Terms:
scientific visualization, tensor visualization, symmetric traceless tensor, nematic liquid crystals
Citation:
T.J. Jankun-Kelly, Ketan Mehta, "Superellipsoid-based, Real Symmetric Traceless Tensor Glyphs Motivated by Nematic Liquid Crystal Alignment Visualization," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 5, pp. 1197-1204, Sept. 2006, doi:10.1109/TVCG.2006.181