Topological Extraction of Escape Maps in Divergence-Free Vector Fields

Abstract

An escape map is the partial mapping from seed points to exit points of streamlines in a bounded domain. The escape map is piecewise continuous, and a topological segmentation of the domain boundary yields the regions and curve segments on which it is continuous. Escape maps have recently been introduced in the context of studying the connectivity of coronal holes. Computation of escape maps faces the problem of exponentially diverging streamlines, where standard adaptive streamsurface methods can fail. As a tool to detect such places and to guide escape map computation, a technique based on isoclines has recently been proposed (Machado et al., IEEE Trans. Vis. Comput. Graph. 20(12):2604–2613, 2014). We show in this paper that, in the case of a divergence-free vector field, boundary switch connectors can be used as a purely topological alternative, which to the best of our knowledge is the first practical application of boundary switch connectors. We provide a systematic approach to the topological segmentation of 3D domain boundaries for divergence-free vector fields. Finally, we explore an alternative approach based on streamtubes and targeted at robustness in escape map computation. Simulation results as well as a synthetic vector field are used for validation.