Imaging vector fields using line integral convolution
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
The visualization of second-order tensor fields
The visualization of second-order tensor fields
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Visualizing Second-Order Tensor Fields with Hyperstreamlines
IEEE Computer Graphics and Applications
A tool for visualizing the topology of three-dimensional vector fields
VIS '91 Proceedings of the 2nd conference on Visualization '91
3DSketch: modeling by digitizing with a smart 3D pen
MULTIMEDIA '97 Proceedings of the fifth ACM international conference on Multimedia
Interactive deformations from tensor fields
Proceedings of the conference on Visualization '98
Isometric embedding by surface reconstruction from distances
Proceedings of the conference on Visualization '02
Visualization of Analytically Defined Dynamical Systems
Dagstuhl '97, Scientific Visualization
Using Virtual Reality to Visualize Scientific, Engineering, and Medical Data
Dagstuhl '97, Scientific Visualization
Physically Based Methods for Tensor Field Visualization
VIS '04 Proceedings of the conference on Visualization '04
Topological Lines in 3D Tensor Fields
VIS '04 Proceedings of the conference on Visualization '04
Visualization of Salt-Induced Stress Perturbations
VIS '04 Proceedings of the conference on Visualization '04
Topological Lines in 3D Tensor Fields and Discriminant Hessian Factorization
IEEE Transactions on Visualization and Computer Graphics
Visualization of Geologic Stress Perturbations Using Mohr Diagrams
IEEE Transactions on Visualization and Computer Graphics
Topological Visualization of Brain Diffusion MRI Data
IEEE Transactions on Visualization and Computer Graphics
New Scalar Measures for Diffusion-Weighted MRI Visualization
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Interpolating 3D diffusion tensors in 2D planar domain by locating degenerate lines
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Complete tensor field topology on 2D triangulated manifolds embedded in 3D
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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We study the topology of symmetric, second-order tensor fields. The results of this study can be readily extended to include general tensor fields through linear combination of symmetric tensor fields and vector fields. The goal is to represent their complex structure by a simple set of carefully chosen points, lines, and surfaces analogous to approaches in vector field topology. We extract topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Our approach is based on the premise: "Analyze, then visualize."The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. Degenerate points play a similar role as critical points in vector fields. In tensor fields we identify two kinds of elementary degenerate points, which we call wedge points and trisector points. They can combine to form more familiar singularities驴such as saddles, nodes, centers, or foci. However, these are generally unstable structures in tensor fields. Based on the notions developed for 2D tensor fields, we extend the theory to include 3D degenerate points. Examples are given on the use of tensor field topology for the interpretation of physical systems.