Topology & Tensor Glyphs

Copyright (c) 1991 Institute of Electrical and Electronics Engineers. Reprinted from IEEE Computer Graphics and Applications; Vol. 11, No. 3, pp. 36-46.

Above image shows again the topology of the Jacobian of the velocity field visualized in the previous image. Points in the flow with a zero velocity are called critical points. In the above picture they are shown as sets of arrows and disks. The arrows point in the direction of the real eigenvectors with length proportional to the scaled eigenvalue and color denoting the sign of the eigenvalue. The disks are in the plane spanned by the complex eigenvectors, with color and diameter of a disk proportional to sign and absolute value, respectively, of the real and imaginary part of an eigenvalue. Note that the Jacobian is an unsymmetric second-order tensor and that therefore these glyphs are suitabel for a general second-order tensor.