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...

• Type: Conference
• Year: 1991
• Where: VISUALIZATION
• Authors: Al Globus, C. Levit, T. Lasinski
• Keywords: Computational fluid Dynamics, Critical Points, Invariant Manifolds, Visualization, VISUALIZATION 1991