Static Visualization of Unsteady Flows by Flow Steadification

Abstract

Finding static visual representations of time-varying phenomena is a standard problem in visualization. We are interested in unsteady flow data, i.e., we want to find a static visualization - one single still image - that shows as much of the global behavior of particle trajectories (path lines) as possible. We propose a new approach, which we call steadification: given a time-dependent flow field v, we construct a new steady vector field w such that the stream lines of w correspond to the path lines of v. With this, the temporal behavior of v can be visualized by using standard methods for steady vector field visualization. We present a formal description as a constraint optimization that can be mapped to finding a set cover, a NP-hard problem that is solved approximately and fairly efficiently by a greedy algorithm. As an application, we introduce the first 2D image-based flow visualization technique that shows the behavior of path lines in a static visualization, even if the path lines have a significantly different behavior than stream lines.