Time-varying Reeb graphs for continuous space--time data

Authors:
Herbert Edelsbrunner;John Harer;Ajith Mascarenhas;Valerio Pascucci;Jack Snoeyink
Affiliations:
Department of Computer Science and Mathematics, Duke University, Durham, and Raindrop Geomagic, Research Triangle Park, NC, USA;Department of Mathematics and Computer Science, Duke University, Durham, NC, USA;Center for Applied Scientific Computing, Lawrence Livermore National Labs, Livermore, CA, USA;Center for Applied Scientific Computing, Lawrence Livermore National Labs, Livermore, CA, USA;Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2008

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Abstract

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.