Extracting Separation Surfaces of Path Line Oriented Topology in Periodic 2D Time-Dependent Vector Fields

This paper presents an approach to extracting the separation surfaces from periodic 2D time-dependent vector fields based on a recently introduced path line oriented topology. This topology is based on critical path lines which repeat the same spatial cycle per time period. Around those path lines there are areas of similar asymptotic flow behavior basins which are captured by a 2D Poincare map as a discrete dynamical system. Due to pseudo discontinuities in this map and the discrete integration scheme, separatrices between the basins can not be obtained as integral curves. Instead we choose a point-wise approach to segment the Poincare map and apply computer vision algorithms to extract the 2D separation curves. Starting from those curves we integrate separation surfaces which partition the periodic 2D time-dependent vector field into areas of similar path line behavior. We apply our approach to a number of data sets to to demonstrate its utility.

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