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Robust Detection of Singularities in Vector Fields Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Notes on the Simplification of the Morse-Smale Complex

Authors : David Günther, Jan Reininghaus, Hans-Peter Seidel, Tino Weinkauf

Published in: Topological Methods in Data Analysis and Visualization III

Publisher: Springer International Publishing

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Abstract

The Morse-Smale complex can be either explicitly or implicitly represented. Depending on the type of representation, the simplification of the Morse-Smale complex works differently. In the explicit representation, the Morse-Smale complex is directly simplified by explicitly reconnecting the critical points during the simplification. In the implicit representation, on the other hand, the Morse-Smale complex is given by a combinatorial gradient field. In this setting, the simplification changes the combinatorial flow, which yields an indirect simplification of the Morse-Smale complex. The topological complexity of the Morse-Smale complex is reduced in both representations. However, the simplifications generally yield different results. In this chapter, we emphasize properties of the two representations that cause these differences. We also provide a complexity analysis of the two schemes with respect to running time and memory consumption.

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previous chapter Parallel Computation of Nearly Recurrent Components of Piecewise Constant Vector Fields
next chapter Measuring the Distance Between Merge Trees
Footnotes
1
Note that the idea of reversing the flow along a separation line was also used to modify a scalar field based on a simplified contour tree [23].
 
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Metadata
Title
Notes on the Simplification of the Morse-Smale Complex
Authors
David Günther
Jan Reininghaus
Hans-Peter Seidel
Tino Weinkauf
Copyright Year
2014
Book
Topological Methods in Data Analysis and Visualization III

Print ISBN: 978-3-319-04098-1

Electronic ISBN: 978-3-319-04099-8

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-04099-8_9

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