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Efficient computation of Morse-Smale complexes for three-dimensional scalar functions.

Attila Gyulassy, Vijay Natarajan, Valerio Pascucci, and Bernd Hamann.
IEEE Transactions on Visualization and Computer Graphics (IEEE Vis 2007), 13(6), 2007, 1440-1447.


The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.