Certified computation of planar Morse-Smale complexes

Amit Chattopadhyay, Gert Vegter, Chee Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Morse-Smale complex is an important tool for global topological analysis in various problems of computational geometry and topology. Algorithms for Morse-Smale complexes have been presented in case of piecewise linear manifolds [9]. However, previous research in this field does not provide certified methods in the case of smooth functions. In the current paper we use interval arithmetic to compute a topologically correct approximation of Morse-Smale complex of smooth functions of two variables. The algorithm can also compute geometrically close Morse-Smale complex.

Original languageEnglish (US)
Title of host publicationProceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012
Pages259-268
Number of pages10
DOIs
StatePublished - 2012
Event28th Annual Symposuim on Computational Geometry, SCG 2012 - Chapel Hill, NC, United States
Duration: Jun 17 2012Jun 20 2012

Other

Other28th Annual Symposuim on Computational Geometry, SCG 2012
CountryUnited States
CityChapel Hill, NC
Period6/17/126/20/12

Fingerprint

Computational geometry
Smooth function
Computational Topology
Topology
Interval Arithmetic
Computational Geometry
Piecewise Linear
Approximation

Keywords

  • Certified computing
  • Interval arithmetic
  • Morse-Smale complex

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology
  • Theoretical Computer Science

Cite this

Chattopadhyay, A., Vegter, G., & Yap, C. (2012). Certified computation of planar Morse-Smale complexes. In Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012 (pp. 259-268) https://doi.org/10.1145/2261250.2261288

Certified computation of planar Morse-Smale complexes. / Chattopadhyay, Amit; Vegter, Gert; Yap, Chee.

Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012. 2012. p. 259-268.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chattopadhyay, A, Vegter, G & Yap, C 2012, Certified computation of planar Morse-Smale complexes. in Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012. pp. 259-268, 28th Annual Symposuim on Computational Geometry, SCG 2012, Chapel Hill, NC, United States, 6/17/12. https://doi.org/10.1145/2261250.2261288
Chattopadhyay A, Vegter G, Yap C. Certified computation of planar Morse-Smale complexes. In Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012. 2012. p. 259-268 https://doi.org/10.1145/2261250.2261288
Chattopadhyay, Amit ; Vegter, Gert ; Yap, Chee. / Certified computation of planar Morse-Smale complexes. Proceedings of the 28th Annual Symposuim on Computational Geometry, SCG 2012. 2012. pp. 259-268
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