2D Asymmetric Tensor Field Topology

  • Zhongzang Lin
  • Harry Yeh
  • Robert S. Laramee
  • Eugene Zhang
Part of the Mathematics and Visualization book series (MATHVISUAL)


In this chapter we define the topology of two-dimensional (2D) asymmetric tensor fields in terms of two graphs corresponding to the eigenvalue and eigenvector analysis for tensor fields, respectively. Asymmetric tensor field topology can not only yield a concise representation of the field, but also provide a framework for spatial-temporal tracking of field features. Furthermore, inherent topological constraints in asymmetric tensor fields can be identified unambiguously through these graphs. We also describe efficient algorithms to compute the topology of a given 2D asymmetric tensor field. We demonstrate the utility of our graph representations for asymmetric tensor field topology with fluid simulation data sets.


Symmetric Tensor Complex Domain Junction Point Velocity Gradient Tensor Real Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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We wish to thank Guoning Chen and Qingqing Deng for their help in generating some of the images shown in this chapter. The constructive comments from the reviewers have made this work stronger. Hamish Carr did an excellent job in presenting this work during the TopoInVis 2011 workshop when none of the authors was able to attend it. The research was partially supported by NSF Grants IIS-0546881 and CCF-0830808.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Zhongzang Lin
    • 1
  • Harry Yeh
    • 1
  • Robert S. Laramee
    • 2
  • Eugene Zhang
    • 1
  1. 1.Oregon State UniversityCorvallisUSA
  2. 2.Swansea UniversityWalesUK

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