### 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 language | English (US) |
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Title of host publication | Proceedings of 2014 Science and Information Conference, SAI 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 302-312 |

Number of pages | 11 |

ISBN (Electronic) | 9780989319317 |

DOIs | |

State | Published - Oct 7 2014 |

Event | 2014 Science and Information Conference, SAI 2014 - London, United Kingdom Duration: Aug 27 2014 → Aug 29 2014 |

### Publication series

Name | Proceedings of 2014 Science and Information Conference, SAI 2014 |
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### Other

Other | 2014 Science and Information Conference, SAI 2014 |
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Country | United Kingdom |

City | London |

Period | 8/27/14 → 8/29/14 |

### 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

*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