Glyphs for General Second-Order 2D and 3D Tensors

Glyphs are a powerful tool for visualizing second-order tensors in a variety of scientic data as they allow to encode physical behavior in geometric properties. Most existing techniques focus on symmetric tensors and exclude non-symmetric tensors where the eigenvectors can be non-orthogonal or complex. We present a new construction of 2d and 3d tensor glyphs based on piecewise rational curves and surfaces with the following properties: invariance to (a) isometries and (b) scaling, (c) direct encoding of all real eigenvalues and eigenvectors, (d) one-to-one relation between the tensors and glyphs, (e) glyph continuity under changing the tensor. We apply the glyphs to visualize the Jacobian matrix fields of a number of 2d and 3d vector fields.