Visualization and Analysis of Second-Order Tensors: Moving Beyond the Symmetric Positive-Definite Case
Article first published online: 19 NOV 2012
© 2012 The Authors Computer Graphics Forum © 2012 The Eurographics Association and Blackwell Publishing Ltd.
Computer Graphics Forum
Volume 32, Issue 1, pages 49–74, February 2013
How to Cite
Kratz, A., Auer, C., Stommel, M. and Hotz, I. (2013), Visualization and Analysis of Second-Order Tensors: Moving Beyond the Symmetric Positive-Definite Case. Computer Graphics Forum, 32: 49–74. doi: 10.1111/j.1467-8659.2012.03231.x
- Issue published online: 21 FEB 2013
- Article first published online: 19 NOV 2012
- second-order tensors;
- tensor visualization;
- scientific visualization
- I.3.3 [Computer Graphics]: Picture/Image Generation—Line and curve generation
Tensors provide a powerful language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as the final result of simulations or as intermediate product. Due to their complexity, tensors are hard to interpret. This motivates the development of well-conceived visualization methods. As a sub-branch of scientific visualization, tensor field visualization has been especially pushed forward by diffusion tensor imaging. In this review, we focus on second-order tensors that are not diffusion tensors. Until now, these tensors, which might be neither positive-definite nor symmetric, are under-represented in visualization and existing visualization tools are often not appropriate for these tensors. Hence, we discuss the strengths and limitations of existing methods when dealing with such tensors as well as challenges introduced by them. The goal of this paper is to reveal the importance of the field and to encourage the development of new visualization methods for tensors from various application fields.