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要旨:
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 Poincaré map as a discrete dynamical system. Due to pseudo discontinuities
in this map and the discrete integration scheme,
separatrices between the basins can’t be obtained as integral curves. Instead
we choose a point-wise approach to segment the
Poincaré map and apply image analysis 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 demonstrate its utility.
