A Primal/ Dual Representation for Discrete Morse Complexes on Tetrahedral Meshes

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dc.contributor.authorWeiss, Kennethen_US
dc.contributor.authorIuricich, Federicoen_US
dc.contributor.authorFellegara, Riccardoen_US
dc.contributor.authorFloriani, Leila Deen_US
dc.contributor.editorB. Preim, P. Rheingans, and H. Theiselen_US
dc.date.accessioned2015-02-28T15:31:10Z
dc.date.available2015-02-28T15:31:10Z
dc.date.issued2013en_US
dc.description.abstractWe consider the problem of computing discrete Morse and Morse-Smale complexes on an unstructured tetrahedral mesh discretizing the domain of a 3D scalar field. 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-Smale 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-Smale complexes. We compare implementations of our approach on an adjacency-based topological data structure and on the PR-star octree, a compact spatio-topological data structure.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12123en_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.titleA Primal/ Dual Representation for Discrete Morse Complexes on Tetrahedral Meshesen_US
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