Journal
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS
Volume 41, Issue 3, Pages 149-166Publisher
ELSEVIER
DOI: 10.1016/j.comgeo.2007.11.001
Keywords
differential and computational topology; Morse functions; critical points; level sets; Reeb graph; triangulations; combinatorial algorithms
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Funding
- NSF [EIA-99-72879, CCR-00-86013, DMS-01-07621, 0128426]
- University of California Lawrence Livermore National Laboratory [W-7405-Eng-48]
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The Reeb graph is a useful tool in visualizing real-valued data obtained from computational simulations of physical processes. We characterize the evolution of the Reeb graph of a time-varying continuous function defined in three-dimensional space. We show how to maintain the Reeb graph over time and compress the entire sequence of Reeb graphs into a single, partially persistent data structure, and augment this data structure with Betti numbers to describe the topology of level sets and with path seeds to assist in the fast extraction of level sets for visualization. (c) 2008 Elsevier B.V. All rights reserved.
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