Locating Closed Hyperstreamlines in Second Order Tensor Fields

The analysis and visualization of tensor fields is an advancing area in scientific visualization. Topology-based methods that investigate the eigenvector fields of second order tensor fields have gained increasing interest in recent years. Most algorithms focus on features known from vector fields, such as saddle points and attracting or repelling nodes. However, more complex features, such as closed hyperstreamlines are usually neglected. In this chapter, a method for detecting closed hyperstreamlines in tensor fields as a topological feature is presented. The method is based on a special treatment of cases where a hyperstreamline reenters a cell and prevents infinite cycling during hyperstreamline calculation. The algorithm checks for possible exits of a loop of crossed edges and detects structurally stable closed hyperstreamlines. These global features cannot be detected by conventional topology and feature detection algorithms used for the visualization of second order tensor fields