Topology Simplification of Symmetric, Second-Order 2D Tensor Fields

Numerical simulations of tubulent flows produce both vector and tensor fields that exhibit complex structural behavior. The topological study of these datasets dramatically reduces the amount of information required for analysis. However, the presence of many features of small scale creates a cluttered depiction that confuses interpretation. In this paper, we extend previous work dealing with vector fields to symmetric, second-order tensor fields. A simplification method is presented that removes degenerate points from the topology pairwise, driven by arbitrary criteria measuring their importance in the overall structure. It is based on an important property of piecewise linear tensor fields that we prove in the paper. Grid and interpolation scheme are preserved since the method uses small local changes of the given discrete tensor values to achieve simplification. The resulting topology is clarified significantly though structurally consistent with the original one. The basic idea behind this technique leads back to the theory of bifurcations and suggests and interpretation as a continuous simplification process.