Certified computation of planar Morse-Smale complexes

Amit Chattopadhyay, Gert Vegter, Chee K. 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

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

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

Keywords

  • Certified computing
  • Interval arithmetic
  • Morse-Smale complex

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

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