Issue No.06 - June (2012 vol.18)
Andrzej Szymczak , Colorado School of Mines, Golden
Eugene Zhang , Oregon State University, Corvallis
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2011.88
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 subtriangle 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.
Morse decomposition, vector field topology.
Andrzej Szymczak, Eugene Zhang, "Robust Morse Decompositions of Piecewise Constant Vector Fields", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 6, pp. 938-951, June 2012, doi:10.1109/TVCG.2011.88