Path Line Oriented Topology for Periodic 2D Time-Dependent Vector Fields

Abstract

This paper presents an approach to extracting a path line oriented topological segmentation for periodic 2D timedependent vector fields. Topological methods aiming in capturing the asymptotic behavior of path lines rarely exist because path lines are usually only defined over a fixed time-interval, making statements about their asymptotic behavior impossible. For the data class of periodic vector fields, this restriction does not apply any more. Our approach detects critical path lines as well as basins from which the path lines converge to the critical ones. We demonstrate our approach on a number of test data sets.