Visualizing and representing the evolution of topological features
نویسندگان
چکیده
Simplicial complexes are discrete representations of topological spaces that are practical for computational studies. The first three Betti-numbers (indicating the number of components, tunnels and voids), as well as the topological persistence of each such feature, is welldefined and can be efficiently computed for simplicial complexes embedded in 2D and 3D [1, 2]. We introduce a novel representation of the evolution of topological features in simplicial complexes using socalled tunnel-trees in 2D and void-trees in 3D. This new representation makes it possible to analyze topological evolution by applying tools for analysis of binary trees. Furthermore it supplies a new method for visualizing topological evolution.
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