6533b7dafe1ef96bd126ec99
RESEARCH PRODUCT
Data structures and algorithms for topological analysis
Marta R. HidalgoDominique MichelucciJean Marc CaneSebti FoufouGeorge M. Tzoumassubject
[ INFO ] Computer Science [cs]CIA and HIA algorithmsComputer scienceHomotopyCellular homologyHomology (mathematics)[INFO] Computer Science [cs]TopologyMathematics::Algebraic TopologyRegular homotopyn-connectedHomotopy sphereTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONMoore space (algebraic topology)[INFO]Computer Science [cs]Betti numbersEuler characteristicSingular homologydescription
International audience; 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-08-27 |