Tensor field topology is of importance to research areas of medicine, science, and engineering. Degenerate curves are one of the crucial topological features that provide valuable insights for tensor field visualization. In this thesis, we study the atomic bifurcations of degenerate curves in 3D linear second-order symmetric tensor fields, and...
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...
N-ary relationships, which relate N entities where N is not necessarily two, are omnipresent in real life. In this thesis, we develop a visualization technique for N-ary relationships.
First, we propose a visual metaphor that utilizes vertices and polygons to represent entities and N-ary relationships. Based on this visual metaphor,...
Transportation infrastructure provides a vital service for the functionality of a
city. The efficient design of road networks poses an interesting topic in computer
science for digital content developers. For civil engineers, the visualization of
analysis results on infrastructure both efficiently and intuitively is crucial. The
following contributions are made...
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...
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...
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...
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...
Automatic painterly rendering systems have been proposed but they opted for selecting a single style to generate paintings from images, which lacks the ability of creatively using multiple styles to focus important objects and deemphasize unimportant part of the scenes. We provide a multi-style painting framework to
address this issue...
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...