The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectory-based vector field visualization techniques. I describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used...
Asymmetric tensor fields present new challenges for visualization techniques such as hyperstreamline placement and glyph packing. This is because the physical behaviors of the tensors are fundamentally different inside real domains where eigenvalues are real and complex domains where eigenvalues are complex. We present a hybrid visualization approach in which...
Visualizing asymmetric tensors is an important task in understanding fluid dynamics. In this paper, we describe topological analysis and visualization techniques for asymmetric tensor fields on surfaces based on analyzing the impact of the symmetric and antisymmetric components of the tensor field on its eigenvalues and eigenvectors. At the core...
The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight into the vector field that is difficult to infer from traditional trajectory-based vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these...
Most existing flow visualization techniques focus on the analysis and visualization of the vector field that describes the flow. In this paper, we employ a rather different approach by performing tensor field analysis and visualization on the gradient of the vector field, which can provide additional and complementary information to...
The use of data extracted from particle image velocimetry (PIV) along with vector and tensor visualization techniques provides a valuable tool for understanding a complex flow field. By studying a simple geometric structure such as a cylinder under a simple transient waveform, fundamental mechanisms of wake development under solitary wave...
Asymmetric tensor fields are useful for understanding fluid flow and solid deformation. They present new challenges, however, for traditional tensor field visualization techniques such as hyperstreamline placement and glyph packing. This is because the physical behavior of tensors inside real domains where eigenvalues are real is fundamentally different from the...
Analysis, visualization, and design of vector fields on surfaces have a wide variety of major applications in both scientific visualization and computer graphics. On the one hand, analysis and visualization of vector fields provide critical insights to the flow data produced from simulation or experiments of various engineering processes. On...
Flow separation is an important phenomenon in fluid dynamics because of the effect it has on lift and drag on immersed bodies. Areas of swirl within a separated flow region may have a distinct effect on the surface forces, modifying the lift and drag characteristics. A correlation between the passage...
Many applications in computer graphics and geometry processing rely on the ability to
locally orient 2D and 3D entities on a surface, or inside a volume, such as the sinusoidal
kernels in Gabor noise, the color and geometry textures in pattern synthesis, and the
finite elements in remeshing. In these...