Abstract
Morse-Smale complexes are gaining in popularity as a tool in scientific data analysis and visualization. The cells of the complex represent contiguous regions of uniform flow properties, and in many application domains, features can be described by carefully extracting these cells. However, existing techniques only describe how to extract ascending and descending manifolds of critical points, and their intersections; given two critical points p and q of index i and i + 1 respectively, these methods are not able to determine how many cells the intersection of ascending manifold of p and the descending manifold of q form, or distinguish between them. In this paper, we use the framework provided by discrete Morse theory to describe a combinatorial algorithm for computing all cells of the Morse-Smale complex, where the interior of each cell is simply connected, as the theory prescribes. Furthermore, we provide data structures that enable a practical implementation.
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