Derived Fields - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 144

Fig. 14.9 EigenvalueManifold: there are five special points on the manifold, which are positive and
negative scaling, counterclockwise and clockwise rotation, and anisotropic stretching. The Voronoi
decomposition with respect to these five special points partitions the manifold into five cells where
the flow is dominated by different characteristics [ 28 ]. © IEEE Reprinted, with permission, from
IEEE Transactions on Visualization and Computer Graphics 15(1)

Fig. 14.10 Color-coding based on the eigenvalue manifold ( left ) and the combined eigenvalue and
eigenvector manifold ( right )[ 28 ]. © IEEE Reprinted, with permission, from IEEE Transactions on
Visualization and Computer Graphics 15(1)

nated by clockwise rotation. Such results have led Lin et al. [ 13 ] to define asymmetric
tensor field topology in terms of graphs whose nodes correspond to the regions in
the partition and whose edges encode adjacency relationships between the regions.
The eigenvector information in the tensor field is determined purely by

γ r , γ s ,

and from Eq. ( 14.3 ). Note that asymmetric tensors may have real eigenvalues (real

domains) or complex eigenvalues (complex domains). In the latter case no real-valued
eigenvectors exist. Zheng and Pang [ 29 ] introduce the notion of dual-eigenvectors
which they show are the continuous extension of major and minor eigenvectors from

θ