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 |
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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 (Formerly, School of Automation) |

Date Deposited: | 15 Jul 2009 07:01 |

Last Modified: | 19 Sep 2010 05:34 |

URI: | http://eprints.iisc.ernet.in/id/eprint/20737 |

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