Finite time steady 2D vector field topology

Abstract

Vector Field Topology describes the asymptotic behavior of a flow in a vector field, i.e., the behavior for an integration time converging to infinity. For some applications, a segmentation of the flow in areas of similar behavior for a finite integration time is desired. We introduce an approach for a finite-time segmentation of a steady 2D vector field which avoids the systematic evaluation of the flow map in the whole flow domain. Instead, we consider the separatrices of the topological skeleton and provide them with additional information on how the separation evolves at each point with ongoing integration time. We analyze this behavior and its distribution along a separatrix, and we provide a visual encoding for it. The result is an augmented topological skeleton. We demonstrate the approach on several artificial and simulated vector fields.