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3D asymmetric tensor fields have found many applications in science andengineering domains, such as fluid dynamics and solid mechanics. 3D asymmetrictensors can have complex eigenvalues, which makes their analysis andvisualization more challenging than 3D symmetric tensors. Existing research intensor field visualization focuses on 2D asymmetric tensor fields and 3Dsymmetric tensor fields. In this paper, we address the analysis andvisualization of 3D asymmetric tensor fields. We introduce six topologicalsurfaces and one topological curve, which lead to an eigenvalue space based onthe tensor mode that we define. In addition, we identify severalnon-topological feature surfaces that are nonetheless physically important.Included in our analysis are the realizations that triple degenerate tensorsare structurally stable and form curves, unlike the case for 3D symmetrictensors fields. Furthermore, there are two different ways of measuring therelative strengths of rotation and angular deformation in the tensor fields,unlike the case for 2D asymmetric tensor fields. We extract these featuresurfaces using the A-patches algorithm. However, since three of our featuresurfaces are quadratic, we develop a method to extract quadratic surfaces atany given accuracy. To facilitate the analysis of eigenvector fields, wevisualize a hyperstreamline as a tree stem with the other two eigenvectorsrepresented as thorns in the real domain or the dual-eigenvectors as leaves inthe complex domain. To demonstrate the effectiveness of our analysis andvisualization, we apply our approach to datasets from solid mechanics and fluiddynamics.

Feature Curves and Surfaces of 3D Asymmetric Tensor Fields