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

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45472

Shi,  Kuangyu
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45606

Theisel,  Holger
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zitation

Shi, K., Theisel, H., & Seidel, H.-P. (2007). Extracting Separation Surfaces of Path Line Oriented Topology in Periodic 2D Time-Dependent Vector Fields. Journal of WSCG, 15(1-3), 75-82.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-1F2D-6
Zusammenfassung
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.