Simplification of Morse Decompositions Using Morse Set Mergers
Mathematics and Visualization Topological Methods in Data Analysis and Visualization III(2014)
摘要
A common problem of vector field topology algorithms is the large number of the resulting topological features. This chapter describes a method to simplify Morse decompositions by iteratively merging pairs of Morse sets that are adjacent in the Morse Connection Graph (MCG). When Morse sets A and B are merged, they are replaced by a single Morse set, that can be thought of as the union of A, B and all trajectories connecting A and B. Pairs of Morse sets to be merged can be picked based on a variety of criteria. For example, one can allow only pairs whose merger results in a topologically simple Morse set to be selected, and give preference to mergers leading to small Morse sets.
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关键词
Vector Field,Transition Graph,Periodic Trajectory,Hasse Diagram,Fixed Point Index
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