Journal of Applied Mathematics
Volume 2011 (2011), Article ID 142923, 27 pages
Research Article

Visualizing High-Order Symmetric Tensor Field Structure with Differential Operators

West Virginia University, Department of Computer Science and Electrical Engineering, Morgantown, WV 26506, USA

Received 9 September 2010; Accepted 3 April 2011

Academic Editor: Bernard Geurts

Copyright © 2011 Tim McGraw et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The challenge of tensor field visualization is to provide simple and comprehensible representations of data which vary both directionally and spatially. We explore the use of differential operators to extract features from tensor fields. These features can be used to generate skeleton representations of the data that accurately characterize the global field structure. Previously, vector field operators such as gradient, divergence, and curl have previously been used to visualize of flow fields. In this paper, we use generalizations of these operators to locate and classify tensor field degenerate points and to partition the field into regions of homogeneous behavior. We describe the implementation of our feature extraction and demonstrate our new techniques on synthetic data sets of order 2, 3 and 4.