SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
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
Image-guided streamline placement
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
3DSketch: modeling by digitizing with a smart 3D pen
MULTIMEDIA '97 Proceedings of the fifth ACM international conference on Multimedia
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Scientific Visualization - Methods and Applications
Informatics - 10 Years Back. 10 Years Ahead.
Interaction of light and tensor fields
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
The visualization and measurement of left ventricular deformation
APBC '03 Proceedings of the First Asia-Pacific bioinformatics conference on Bioinformatics 2003 - Volume 19
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Scientific Visualization: methods and applications
SCCG '03 Proceedings of the 19th spring conference on Computer graphics
The visualization of myocardial strain for the improved analysis of cardiac mechanics
Proceedings of the 2nd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
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
Topological Lines in 3D Tensor Fields and Discriminant Hessian Factorization
IEEE Transactions on Visualization and Computer Graphics
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Rotational symmetry field design on surfaces
ACM SIGGRAPH 2007 papers
Topological Visualization of Brain Diffusion MRI Data
IEEE Transactions on Visualization and Computer Graphics
Interactive procedural street modeling
ACM SIGGRAPH 2008 papers
Computing lines of curvature for implicit surfaces
Computer Aided Geometric Design
New Scalar Measures for Diffusion-Weighted MRI Visualization
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Automatic skeleton extraction and splitting of target objects
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Simple quad domains for field aligned mesh parametrization
Proceedings of the 2011 SIGGRAPH Asia Conference
Complete tensor field topology on 2D triangulated manifolds embedded in 3D
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Topological features in 2D symmetric higher-order tensor fields
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Human action recognition based on skeleton splitting
Expert Systems with Applications: An International Journal
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We study the topology of symmetric, second-order tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. We extract topological skeletons of the eigenvector fields, and we track their evolution over time. We study tensor topological transitions and correlate tensor and vector data.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. We identify two kinds of elementary degenerate points, which we call wedges and trisectors. They can combine to form more familiar singularities---such as saddles, nodes, centers, or foci. However, these are generally unstable structures in tensor fields.Finally, we show a topological rule that puts a constraint on the topology of tensor fields defined across surfaces, extending to tensor fields the Pointcaré-Hopf theorem for vector fields.