Asymmetric Tensor Field Visualization for Surfaces

Abstract

Asymmetric tensor field visualization can provide important insight into fluid flows and solid deformations. Existing techniques for asymmetric tensor fields focus on the analysis, and simply use evenly-spaced hyperstreamlines on surfaces following eigenvectors and dual-eigenvectors in the tensor field. In this paper, we describe a hybrid visualization technique in which hyperstreamlines and elliptical glyphs are used in real and complex domains, respectively. This enables a more faithful representation of flow behaviors inside complex domains. In addition, we encode tensor magnitude, an important quantity in tensor field analysis, using the density of hyperstreamlines and sizes of glyphs. This allows colors to be used to encode other important tensor quantities. To facilitate quick visual exploration of the data from different viewpoints and at different resolutions, we employ an efficient image-space approach in which hyperstreamlines and glyphs are generated quickly in the image plane. The combination of these techniques leads to an efficient tensor field visualization system for domain scientists. We demonstrate the effectiveness of our visualization technique through applications to complex simulated engine fluid flow and earthquake deformation data. Feedback from domain expert scientists, who are also co-authors, is provided.

Multi-Scale Topological Analysis of Asymmetric Tensor Fields on Surfaces

“…For a more systematic study of 2D asymmetric tensor fields, Zhang et al [35] introduce the notions of eigenvalue manifold and eigenvector manifold. These notions are applied to visualize asymmetric tensor fields using a combination of glyphs and hyperstreamlines [26]. Recent research on asymmetric tensor fields has focused on the design of proper glyphs [1,12,28].…”

“…The former corresponds to cases where the pure shear component in the tensor is stronger than that of the rotation, while the latter is the reverse. Such a distinction is important for fluid dynamics [26,35,37]. In addition, Zhang et al [35] point out that regardless of whether having real-or complex-valued eigenvalues, it is important to differentiate tensors corresponding to counterclockwise (CCW) rotations from those corresponding to clockwise (CW) rotations.…”

“…Asymmetric tensor fields have found a wide range of applications such as fluid mechanics [26,35,36]. In these applications, a vector field plays a critical role, such as the velocity vector field of a fluid flow and the displacement vector field of an object undergoing deformation.…”

“…In these applications, a vector field plays a critical role, such as the velocity vector field of a fluid flow and the displacement vector field of an object undergoing deformation. While direct vector field visualization techniques such as glyphs [17], streamlines [19], and vector field topology [16] can provide much insight into the vector field, the gradient tensor of the vector field (an asymmetric tensor field) can provide important and complementary information [26,35].…”

“…Existing research on asymmetric tensor fields focuses on the visualization aspect [26,35], such as finding proper glyph representations [2,27] to show local eigenvalue and eigenvector variations in the tensor field. There has been relatively little attention given to the topological structures in the asymmetric tensor field.…”