Computing Reeb Graphs as a Union of Contour Trees
نویسندگان
چکیده
منابع مشابه
Efficient algorithms for computing Reeb graphs
The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. We describe an algorithm that constructs the Reeb graph of a Morse function defined on a 3-manifold. Our algorithm maintains connected components of the two dimensional levels sets as a dynamic graph and constructs the Reeb graph in O(n log n+n log...
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Let X be a simplicial complex with a piecewise linear function f : X → R. The Reeb graph Reeb(f,X) is the quotient of X, where we collapse each connected component of f−1(t) to a single point. Let the nodes of Reeb(f,X) be all homologically critical points where any homology of the corresponding component of the level set f−1(t) changes. Then we can label every arc of Reeb(f,X) with the Betti n...
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Reeb graphs represent the topological structure of a manifold based on a scalar-valued, sufficiently smooth function defined on it. The use of more than one function leads to Reeb spaces, which are thus able to capture more features of an object. The structure of the Reeb space of a 3-manifold with boundary with respect to two scalarvalued functions is captured by the layered Reeb graph. We pre...
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ژورنال
عنوان ژورنال: IEEE Transactions on Visualization and Computer Graphics
سال: 2013
ISSN: 1077-2626
DOI: 10.1109/tvcg.2012.115