Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields

Abstract

Tensor fields can be found in most areas of physics and engineering sciences. Topology-based methods provide efficient means for visualizing symmetric, second-order, planar tensor fields. Yet, for tensor fields with complicated structure typically encountered in turbulent flows, topology-based techniques lead to cluttered pictures that confuse the interpretation and are of little help for analysts. In this paper, we present a hierarchical method that merges close degenerate points into one. This results in a simplified topology and a clarified depiction, though globally maintaining the qualitative properties of the original data. The whole process can be seen as a scaling of the topological information that neglects details of small scale and only retains their structural aspect in the large. We extend here previous work dealing with planar vector fields. Results are demonstrated on a computational fluid dynamics(CFD) dataset.