Visualizing the topology of symmetric, second-order, time-varying two-dimensional tensor fields

Abstract

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.