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  Notes on the Simplification of the Morse-Smale Complex

Guenther, D., Reininghaus, J., Seidel, H.-P., & Weinkauf, T. (2014). Notes on the Simplification of the Morse-Smale Complex. In P.-T. Bremer, I. Hotz, V. Pascucci, & R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III (pp. 135-150). Cham: Springer. doi:10.1007/978-3-319-04099-8_9.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-52F3-3 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0024-52F6-E
Genre: Conference Paper
Latex : Notes on the Simplification of the {Morse}-{Smale} Complex

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 Creators:
Guenther, David1, Author           
Reininghaus, Jan1, Author
Seidel, Hans-Peter2, Author           
Weinkauf, Tino2, Author           
Affiliations:
1External Organizations, ou_persistent22              
2Computer Graphics, MPI for Informatics, Max Planck Society, ou_40047              

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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 paper, we emphasize the differences between these two representations, and provide a high-level discussion about their advantages and limitations.

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Language(s): eng - English
 Dates: 20142014
 Publication Status: Issued
 Pages: -
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 Rev. Type: -
 Identifiers: BibTex Citekey: guenther13a
DOI: 10.1007/978-3-319-04099-8_9
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Title: TopoInVis
Place of Event: Davis, CA, USA
Start-/End Date: 2013-03-04 - 2013-03-06

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Title: Topological Methods in Data Analysis and Visualization III
  Subtitle : Theory, Algorithms, and Applications
  Abbreviation : TopoInVis 2013
Source Genre: Proceedings
 Creator(s):
Bremer, Peer-Timo1, Editor
Hotz, Ingrid1, Editor
Pascucci, Valerio1, Editor
Peikert, Ronald1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Cham : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 135 - 150 Identifier: ISBN: 978-3-319-04098-1

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Title: Mathematics and Visualization
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