Loops in Reeb graphs of 2-manifolds

Discrete and Computational Geometry

Volumn 32, Issue 2, 2004, Pages 231-244

  Cole McLaughlin, Kree ^a   Edelsbrunner, Herbert ^b,c,d   Harer, John ^b,c   Natarajan, Vijay ^c   Pascucci, Valerio ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b DUKE UNIVERSITY   (United States)

^c Duke University   (United States)

^d Raindrop Geomagic   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4344669332     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-004-1122-6     Document Type: Conference Paper

References (18)

1. P. S. Alexandrov. Combinatorial Topology. Republication of three volumes published in 1956, 1957, 1960. Dover, Mineola, New York, 1998.
2. C. L. Bajaj, V. Paseucci, and D. R. Schikore. The contour spectrum. In Proc. IEEE Visualization, 1997, pp. 167-175.
3. H. Carr, J. Snoeyink, and U. Axen. Computing contour trees in all dimensions. Comput. Geom. Theory Appl. 24 (2002), 75-94.
4. T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, Massachusetts, 1994.
5. H. Edelsbrunner, J. Harer, and A. Zomorodian. Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds. Discrete Comput. Geom. 30 (2003), 87-107.
6. A. T. Fomenko and T. L. Kunii, (eds). Topological Methods for Visualization. Springer-Verlag, Tokyo, 1997.
7. M. Goresky and R. MacPhearson. Stratified Morse Theory. Springer-Verlag, Heidelberg, 1988.
8. M. Hilaga, Y. Shinagawa, T. Komura, and T. L. Kunii. Topology matching for fully automatic similarity estimation of 3D shapes. In Computer Graphics Proc., Siggraph 2001, pp. 203-212.
9. M. van Kreveld, R. van Oostrum, C. L. Bajaj, V. Pascucci, and D. R. Schikore. Contour trees and small seed sets for isosurface traversal. In Proc. 13th Ann. Sympos. Computational Geometry., 1997, pp. 212-220.
10. W. S. Massey. Algebraic Topology: An Introduction. Springer-Verlag, New York, 1967.
11. K. Mehlhorn, S. Näher, and H. Alt. A lower bound on the complexity of the union-split-find problem. SIAM J. Comput. 17 (1988), 1093-1102.
12. V. Pascucci and K. Cole-McLaughlin. Parallel computation of the topology of level sets. Algorithmica 38 (2004), 249-268.
13. G. Reeb. Sur les points singuliers d'une forme de Pfaff complément intégrable ou d'une fonction numérique. C. R. Acad. Sci. Paris 222 (1946), 847-849.
14. R. Seidel and C. Aragon. Randomized search trees. Algorithmica 16 (1996), 464-497.
15. H. Seifert and W. Threlfall. Lehrbuch der Topologie. Chelsea, New York, 1934.
16. Y. Shinagawa and T. L. Kunii. Constructing a Reeb graph automatically from cross sections. IEEE Comput. Graphics Appl. 11 (1991), 44-51.
17. Y. Shinagawa, T. L. Kunii, H. Sato, and M. Ibusuki. Modeling contact of two complex objects: with an application to characterizing dental articulations. Comput. Graphics 19 (1995), 21-28.
18. S. Yoshihisa, T. L. Kunii, and Y. L. Kergosian. Surface coding based on Morse theory. IEEE Comput. Graphics Appl. 11 (1991), 66-78.