Constructing Reeb Graphs using Cylinder Maps

Doraiswamy, Harish and Sood, Aneesh and Natarajan, Vijay (2010) Constructing Reeb Graphs using Cylinder Maps. In: 26th Annual Symposium on Computational Geometry, JUN 13-16, 2010, Snowbird, pp. 111-112.

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Abstract

The Reeb graph of a scalar function represents the evolution of the topology of its level sets. In this video, we describe a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Arcs in the Reeb graph are computed in the second step using a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The algorithm is also able to handle non-manifold domains.

Item Type:	Conference Paper
Publisher:	Association for Computing Machinery
Additional Information:	Copy right of this article belongs to Association for Computing Machinery.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	28 Sep 2010 06:56
Last Modified:	28 Sep 2010 06:56
URI:	http://eprints.iisc.ac.in/id/eprint/32482

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