Data structures and algorithms for topological analysis

Jean Marc Cane, George M. Tzoumas, Dominique Michelucci, Marta Hidalgo, Sebti Foufou

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

Abstract

One of the steps of geometric modeling is to know the topology and/or the geometry of the objects considered. This paper presents different data structures and algorithms used in this study. We are particularly interested by algebraic structures, eg homotopy and homology groups, the Betti numbers, the Euler characteristic, or the Morse-Smale complex. We have to be able to compute these data structures, and for (homotopy and homology) groups, we also want to compute their generators. We are also interested in algorithms CIA and HIA presented in the thesis of Nicolas DELANOUE, which respectively compute the connected components and the homotopy type of a set defined by a CSG (constructive solid geometry) tree. We would like to generalize these algorithms to sets defined by projection.

Original languageEnglish (US)
Title of host publicationProceedings of 2014 Science and Information Conference, SAI 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages302-312
Number of pages11
ISBN (Electronic)9780989319317
DOIs
StatePublished - Oct 7 2014
Event2014 Science and Information Conference, SAI 2014 - London, United Kingdom
Duration: Aug 27 2014Aug 29 2014

Publication series

NameProceedings of 2014 Science and Information Conference, SAI 2014

Other

Other2014 Science and Information Conference, SAI 2014
CountryUnited Kingdom
CityLondon
Period8/27/148/29/14

Keywords

  • Betti numbers
  • CIA and HIA algorithms
  • Euler characteristic
  • Homology
  • Homotopy
  • Morse-Smale complex
  • Topology

ASJC Scopus subject areas

  • Information Systems

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  • Cite this

    Cane, J. M., Tzoumas, G. M., Michelucci, D., Hidalgo, M., & Foufou, S. (2014). Data structures and algorithms for topological analysis. In Proceedings of 2014 Science and Information Conference, SAI 2014 (pp. 302-312). [6918204] (Proceedings of 2014 Science and Information Conference, SAI 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAI.2014.6918204