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We use a duality argument to define the cells of the descending Morse complex in terms of the supplied (primal) tetrahedral mesh and those of the ascending complex in terms of its dual mesh. The Morse\u2010Smale complex is then described combinatorially as collections of cells from the intersection of the primal and dual meshes. We introduce a simple compact encoding for discrete vector fields attached to the mesh tetrahedra that is suitable for combination with any topological data structure encoding just the vertices and tetrahedra of the mesh. We demonstrate the effectiveness and scalability of our approach over large unstructured tetrahedral meshes by developing algorithms for computing the discrete gradient field and for extracting the cells of the Morse and Morse\u2010Smale complexes. We compare implementations of our approach on an adjacency\u2010based topological data structure and on the PR\u2010star octree, a compact spatio\u2010topological data structure.<\/jats:p>","DOI":"10.1111\/cgf.12123","type":"journal-article","created":{"date-parts":[[2013,7,1]],"date-time":"2013-07-01T16:59:51Z","timestamp":1372697991000},"page":"361-370","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["A primal\/dual representation for discrete Morse complexes on tetrahedral meshes"],"prefix":"10.1111","volume":"32","author":[{"given":"Kenneth","family":"Weiss","sequence":"first","affiliation":[]},{"given":"Federico","family":"Iuricich","sequence":"additional","affiliation":[]},{"given":"Riccardo","family":"Fellegara","sequence":"additional","affiliation":[]},{"given":"Leila","family":"De Floriani","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2013,7]]},"reference":[{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2317380"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/1391729.1391731"},{"key":"e_1_2_11_4_2","first-page":"351","volume-title":"Proceedings Symposium on Computational Geometry","author":"Cazals F.","year":"2003"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.gmod.2011.05.001"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2011.03.009"},{"key":"e_1_2_11_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2011.244"},{"key":"e_1_2_11_8_2","unstructured":"De FlorianiL. 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