Parallel Computation of 3D Morse-Smale Complexes
Computer Graphics Forum
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
Technical Section: Topological saliency
Computers and Graphics
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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The Morse-Smale complex is a useful topological data structure for the analysis and visualization of scalar data. This paper describes an algorithm that processes all mesh elements of the domain in parallel to compute the Morse-Smale complex of large 2D datasets at interactive speeds. We employ a reformulation of the Morse-Smale complex using Forman's Discrete Morse Theory and achieve scalability by computing the discrete gradient using local accesses only. We also introduce a novel approach to merge gradient paths that ensures accurate geometry of the computed complex. We demonstrate that our algorithm performs well on both multicore environments and on massively parallel architectures such as the GPU.