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