Abstract
This chapter introduces a visualization method specifically tailored to the class of tensor fields with properties similar to stress and strain tensors. Such tensor fields play an important role in many application areas such as structure mechanics or solid state physics. The presented technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method consists of two steps: first, the tensor field is interpreted as a distortion of a flat metric with the same topological structure; second, the resulting metric is visualized using a texture-based approach. The method supports an intuitive distinction between positive and negative eigenvalues.
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References
Ed Boring and Alex Pang. Interactive Deformations from Tensor Fields. Proceedings of the Visualization’ 98 Conference, 1998, pp. 297–304.
Brian Cabral and Leith Leedom. Imaging Vector Fields Using Line Integral Convolution. In SIGGRAPH’ 93 Conference Proceedings, 1993, pp. 263–272.
Thierry Delmarcelle and Lambertus Hesselink. Visualization of second order tensor fields and matrix data. Proceedings of the Visualization’ 92 Conference, 1992, pp. 316–323.
Robert B. Haber. Visualization Techniques for Engineering Mechanics. In Computing Systems in Engineering, 1990, pp. 37–50.
Lambertus Hesselink, Thierry Delmarcelle and James L. Helman. Topology of Second-Order Tensor Fields. In Computers in Physics, 1995, pp. 304–311.
Ingrid Hotz. Isometric Embedding by Surface Reconstruction from Distances. Proceedings of the IEEE Visualization’ 02 Conference, 2002, pp. 251–258.
Ingrid Hotz, Louis Feng, Hans Hagen, Bernd Hamann, Boris Jeremic, and Kenneth Joy. Physically Based Methods for Tensor Field Visualization. Proceedings of the IEEE Visualization’ 04 Conference, 2004, pp. 123–130.
Boris Jeremic, Gerik Scheuermann and Jan Frey et al. Tensor Visualization in Computational Geomechanics. In International Journal for Numerical and Analytical Methods in Geomechanics, 2002, pp. 925–944.
Ron D. Kriz, Edward H. Glaessgen and J.D. MacRae. Visualization Blackboard: Visualizing gradients in composite design and fabrication. IEEE Computer Graphics and Applications, vol 15, 1995, pp. 10–13
W. C. de Leeuw and J. J. van Wijk. A Probe for Local Flow Field Visualization. Proceedings of the Visualization’ 93 Conference, 1993, pp. 39–45.
J. Ou and E. Hsu. Generalized Line Integral Convolution Rendering of Diffusion Tensor Fields. Proceedings of the 9th Scientific Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine (ISMRM), p. 790, 2001.
Detlev Stalling and Hans-Christian Hege. Fast and Resolution Independent Line Integral Convolution. In SIGGRAPH’ 95 Conference Proceedings, 1995, pp. 149–256.
Xiaoqiang Zheng and Alex Pang. Volume Deformation For Tensor Visualization. Proceedings of the Visualization’ 02 Conference, 2002, pp. 379–386.
Xiaoqiang Zheng and Alex Pang. Interaction of Light and Tensor Field. Proceedings of VISSYM’ 03, 2003, pp. 157–166.
Xiaoqiang Zheng and Alex Pang. HyperLIC, Proceedings of the IEEE Visualization’ 03 Conference, 2003, pp. 249–256.
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© 2006 Springer-Verlag Berlin Heidelberg
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Hotz, I., Feng, L., Hagen, H., Hamann, B., Joy, K. (2006). Tensor Field Visualization Using a Metric Interpretation. In: Weickert, J., Hagen, H. (eds) Visualization and Processing of Tensor Fields. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31272-2_16
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DOI: https://doi.org/10.1007/3-540-31272-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25032-6
Online ISBN: 978-3-540-31272-7
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