论文信息 - Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields

Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields

We introduce the underlying theory behind degenerate points in 2D tensor fields to study the local field properties in the vicinity of linear and nonlinear singularities. The structural stability of these features and their corresponding separatrices are also analyzed. From here, we highlight the main techniques for visualizing and simplifying the topology of both static and time-varying 2D tensor fields.

[1] Hans Hagen,et al. Scaling the {Topology} of 2D symmetric, {Second}-{Order} {Tensor} {Fields} , 2000 .

[2] Lambertus Hesselink,et al. The topology of symmetric, second-order tensor fields , 1994, VIS '94.

[3] Hans Hagen,et al. Tensor Topology Tracking: A Visualization Method for Time‐Dependent 2D Symmetric Tensor Fields , 2001, Comput. Graph. Forum.

[4] J. Rotman. An Introduction to Algebraic Topology , 1957 .

[5] Hans Hagen,et al. Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields , 2003 .

[6] A. Andronov,et al. Qualitative Theory of Second-order Dynamic Systems , 1973 .

[7] Lambertus Hesselink,et al. Representation and display of vector field topology in fluid flow data sets , 1989, Computer.

[8] Robert R. Dickinson. A Unified Approach To The Design Of Visualization Software For The Analysis Of Field Problems , 1989, Photonics West - Lasers and Applications in Science and Engineering.

[9] William H. Press,et al. Numerical recipes in C , 2002 .

[10] Brian Cabral,et al. Imaging vector fields using line integral convolution , 1993, SIGGRAPH.

[11] Brayton Gray,et al. Homotopy theory : an introduction to algebraic topology , 1975 .

[12] Xavier Tricoche,et al. Topology Simplification of Symmetric, Second-Order 2D Tensor Fields , 2004 .

[13] Bernd Hamann,et al. Visualizing local vector field topology , 2000, J. Electronic Imaging.