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
N1 - Publisher Copyright:
© 2014 The Science and Information (SAI) Organization.
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 -