Finite Time Steady 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 towards infinity. For some applications, a segmentation of the flow into areas of similar behavior for a finite integration time is desired. We introduce an approach for a finite-time segmentation of a steady vector field and equip the separatrices 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 provide a visual encoding for the 2D and 3D case. The result is an augmented topological skeleton. We demonstrate the approach on several artificial and simulated vector fields.