TY - GEN

T1 - Data structures and algorithms for topological analysis

AU - Cane, Jean Marc

AU - Tzoumas, George M.

AU - Michelucci, Dominique

AU - Hidalgo, Marta

AU - Foufou, Sebti

PY - 2014/10/7

Y1 - 2014/10/7

N2 - 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.

AB - 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.

KW - Betti numbers

KW - CIA and HIA algorithms

KW - Euler characteristic

KW - Homology

KW - Homotopy

KW - Morse-Smale complex

KW - Topology

UR - http://www.scopus.com/inward/record.url?scp=84909606210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84909606210&partnerID=8YFLogxK

U2 - 10.1109/SAI.2014.6918204

DO - 10.1109/SAI.2014.6918204

M3 - Conference contribution

AN - SCOPUS:84909606210

T3 - Proceedings of 2014 Science and Information Conference, SAI 2014

SP - 302

EP - 312

BT - Proceedings of 2014 Science and Information Conference, SAI 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 Science and Information Conference, SAI 2014

Y2 - 27 August 2014 through 29 August 2014

ER -