Efficient algorithms for computing Reeb graphs

Doraiswamy, Harish and Natarajan, Vijay (2009) Efficient algorithms for computing Reeb graphs. In: Computational Geometry, 42 (6-7). pp. 606-616.

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Abstract

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(nlogn+nlogg(loglogg)3) time, where n is the number of triangles in the tetrahedral mesh representing the 3-manifold and g is the maximum genus over all level sets of the function. We extend this algorithm to construct Reeb graphs of d-manifolds in O(nlogn(loglogn)3) time, where n is the number of triangles in the simplicial complex that represents the d-manifold. Our result is a significant improvement over the previously known O(n2) algorithm. Finally, we present experimental results of our implementation and demonstrate that our algorithm for 3-manifolds performs efficiently in practice.

Item Type:	Journal Article
Publication:	Computational Geometry
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Computational topology;Algorithms;Dynamic graph;Level set;Manifold;Piecewise-linear function;Reeb graph.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	15 Jul 2009 07:01
Last Modified:	19 Sep 2010 05:34
URI:	http://eprints.iisc.ac.in/id/eprint/20737

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