Topology-inspired Galilean invariant vector field analysis

Abstract

Vector field topology is one of the most powerful flow visualization tools, because it can break down huge amounts of data into a compact, sparse, and easy to read description with little information loss. It suffers from one main drawback though: The definition of critical points, which is the foundation of vector field topology, is highly dependent on the frame of reference. In this paper we propose to consider every point as a critical point and locally adjust the frame of reference to the most persistent ones, that means the extrema of the determinant of the Jacobian. The result is not the extraction of one well-suited frame of reference, but the simultaneous visualization of the dominating frames of reference in the different areas of the flow field. Each of them could individually be perceived by an observer traveling along these critical points. We show all important ones at once.