Data structures and algorithms for topological analysis

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.
Type de document :
Communication dans un congrès
Science and Information Conference (SAI), 2014, Aug 2014, London, United Kingdom. IEEE, Science and Information Conference (SAI), 2014, IEEE conference, pp.302--312, 2014, Science and Information Conference (SAI), 2014. 〈http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6918204〉
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https://hal.archives-ouvertes.fr/hal-01205762
Contributeur : Dominique Michelucci <>
Soumis le : dimanche 27 septembre 2015 - 17:36:06
Dernière modification le : mercredi 12 septembre 2018 - 01:26:50

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  • HAL Id : hal-01205762, version 1

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Jean-Marc Cane, George Tzoumas, Dominique Michelucci, Marta Hidalgo, Foufou Sebti. Data structures and algorithms for topological analysis. Science and Information Conference (SAI), 2014, Aug 2014, London, United Kingdom. IEEE, Science and Information Conference (SAI), 2014, IEEE conference, pp.302--312, 2014, Science and Information Conference (SAI), 2014. 〈http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6918204〉. 〈hal-01205762〉

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