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VISUALIZATION
1991
IEEE

A Tool for Visualizing the Topology of Three-Dimensional Vector Fields

11 years 4 months ago
A Tool for Visualizing the Topology of Three-Dimensional Vector Fields
We describe a software system, TOPO, that numerically analyzes and graphically displays topological aspects of a three dimensional vector field, v, to produce a single, relatively simple picture that characterizes v. The topology of v that we consider consists of its critical points (where ), their invariant manifolds, and the integral curves connecting these invariant manifolds. Many of the interesting features of v are associated with its critical points. The field in the neighborhood of each critical point is approximated by the Taylor expansion. The coefficients of the first non-zero term of the Taylor expansion around a critical point are the 3x3 matrix . Critical points are classified by examining ’s eigenvalues. The eigenvectors of span the invariant manifolds of the linearized field around a critical point. Curves integrated from initial points on the eigenvectors a small distance from a critical point connect with other critical points (or the boundary) to complete th...
Al Globus, C. Levit, T. Lasinski
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Where VISUALIZATION
Authors Al Globus, C. Levit, T. Lasinski
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