Open source vector field topology

Abstract

A myriad of physical phenomena, such as fluid flows, magnetic fields, and population dynamics are described by vector fields. More often than not, vector fields are complex and their analysis is challenging.Vector field topology is a powerful analysis technique that consists in identifying the most essential structure of a vector field. Its topological features include critical points and separatrices, which segment the domain into regions of coherent flow behavior, provide a sparse and semantically meaningful representation of the underlying data.However, a broad adoption of this formidable technique has been hampered by the lack of open source software implementing it. The Visualization Toolkit (VTK) now contains the filter vtkVectorFieldTopology that extracts the topological skeleton of 2D and 3D vector fields. This paper describes our implementation and demonstrates its broad applicability with two real-world examples from hydrology and space physics.

Keywords

• Vector field
• Topology
• Critical point
• Separatrix