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...
Branched covering spaces are a mathematical concept which originates from complex analysis and topology and has found applications in tensor field topology and geometry re-meshing. Given a manifold surface and an N-way rotational symmetry field, a branched covering space is a manifold surface that has an N-to-1 map to the...
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...
3D symmetric tensor fields have a wide range of applications, such as in solid and fluid mechanics, medical imaging, meteorology, molecular dynamics, geophysics and computer graphics. There has been much research carried out in this field, yet our knowledge of the tensor field is still at its initial stage to...
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...
The importance of data visualization is becoming increasingly more substantial to the field of optimization and engineering design where a carefully designed visualization of the data on decision parameters (i.e Decision Space) and performance functions (i.e Objective Space) is critical to the success of the decision making process.
One of...
Potential water scarcity and drought conditions are predicted in and around Eugene, Oregon due to decreased snowpack and subsequent decreased snowmelt in the Western Cascade Mountains. This phenomenon was triggered by a long-term trend of warmer winters scientifically linked to global climate change patterns (Dalton et al. 2013). Numerous stakeholders,...
Tensor mathematics provides a powerful language to visualize and analyze physical phenomena. In the last three decades, tensors have been used in various application areas. The visualization and analysis of tensors fields have seen much advance, both in 2D and 3D. However, the physical interpretations of the topological analysis are...
Given k terminal pairs (s₁,t₁),(s₂,t₂),..., (s[subscript k],t[subscript k]) in an edge-weighted graph G, the k Shortest Vertex-Disjoint Paths problem is to find a collection P₁, P₂,..., P[subscript k] of vertex-disjoint paths with minimum total length, where P[subscript i] is an s[subscript i]-to-t[subscript i] path. As a special case of the...