Robust Morse Decompositions of Piecewise Constant Vector Fields Public Deposited

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This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by IEEE-Institute of Electrical and Electronics Engineers and can be found at:  http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945.

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  • In this paper, we introduce a new approach to computing a Morse decomposition of a vector field on a triangulated manifold surface. The basic idea is to convert the input vector field to a piecewise constant (PC) vector field, whose trajectories can be computed using simple geometric rules. To overcome the intrinsic difficulty in PC vector fields (in particular, discontinuity along mesh edges), we borrow results from the theory of differential inclusions. The input vector field and its PC variant have similar Morse decompositions. We introduce a robust and efficient algorithm to compute Morse decompositions of a PC vector field. Our approach provides sub-triangle precision for Morse sets. In addition, we describe a Morse set classification framework which we use to color code the Morse sets in order to enhance the visualization. We demonstrate the benefits of our approach with three well-known simulation data sets, for which our method has produced Morse decompositions that are similar to or finer than those obtained using existing techniques, and is over an order of magnitude faster.
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  • Szymczak, A.; Zhang, E.; , "Robust Morse Decompositions of Piecewise Constant Vector Fields," Visualization and Computer Graphics, IEEE Transactions on , vol.18, no.6, pp.938-951, June 2012 doi: 10.1109/TVCG.2011.88
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  • description.provenance : Made available in DSpace on 2012-12-27T01:23:44Z (GMT). No. of bitstreams: 1 ZhangEugeneEECSRobustMorseDecompositions.pdf: 8661427 bytes, checksum: f93479584ec6642efbb7496e9b190e38 (MD5) Previous issue date: 2012-06
  • description.provenance : Approved for entry into archive by Deanne Bruner(deanne.bruner@oregonstate.edu) on 2012-12-27T01:23:44Z (GMT) No. of bitstreams: 1 ZhangEugeneEECSRobustMorseDecompositions.pdf: 8661427 bytes, checksum: f93479584ec6642efbb7496e9b190e38 (MD5)
  • description.provenance : Submitted by Deanne Bruner (deanne.bruner@oregonstate.edu) on 2012-12-27T01:22:00Z No. of bitstreams: 1 ZhangEugeneEECSRobustMorseDecompositions.pdf: 8661427 bytes, checksum: f93479584ec6642efbb7496e9b190e38 (MD5)

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