Time-varying Reeb graphs for continuous space-time data

Computational Geometry: Theory and Applications

Volumn 41, Issue 3, 2008, Pages 149-166

  Edelsbrunner, Herbert ^a   Harer, John ^a   Mascarenhas, Ajith ^b   Pascucci, Valerio ^b   Snoeyink, Jack ^c  

^a DUKE UNIVERSITY   (United States)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^c Brooks Computer Science Building   (United States)

Author keywords

Combinatorial algorithms; Critical points; Differential and computational topology; Level sets; Morse functions; Reeb graph; Triangulations

Indexed keywords

EID: 84867965784     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comgeo.2007.11.001     Document Type: Article

References (26)

1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman The Design and Analysis of Computer Algorithms 1974 Addison-Wesley Reading, MA
2. P.S. Alexandrov Combinatorial Topology 1998 Dover Mineola, NY
3. C.L. Bajaj, V. Pascucci, D.R. Schikore, The contour spectrum, in: Proc. IEEE Conf. Visualization, 1997, pp. 167-175
4. T.F. Banchoff Critical points for embedded polyhedral surfaces Amer. Math. Monthly 77 1970 457 485
5. K.G. Bemis, D. Silver, P.A. Rona, C. Feng, Case study: a methodology for plume visualization with application to real-time acquisition and navigation, in: Proc. IEEE Conf. Visualization, 2000, pp. 481-494
6. H. Carr, J. Snoeyink, and U. Axen Computing contour trees in all dimensions Comput. Geom. 24 2 2003 75 94
7. H. Carr, J. Snoeyink, Path seeds and flexible isosurfaces: Using topology for exploratory visualization, in: Proc. of Eurographics Vis. Sympos. 2003, 2003, pp. 49-58
8. Y.-J. Chiang, T. Lenz, X. Lu, and G. Rote Simple and optimal output-sensitive construction of contour trees using monotone paths Comp. Geom. Theory Appl. 30 2 2005 165 195
9. T. Chiueh, K.-L. Ma, A parallel pipelined renderer for time-varying volume data, in: Proc. Parallel Arch., Alg., Networks, 1997, pp. 9-15
10. K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, Loops in Reeb graphs of 2-manifolds, in: Proc. 14th Ann. Sympos. Comput. Geom., 2003, pp. 344-350
11. C.J.A. Delfinado, and H. Edelsbrunner An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere Comput. Aided Geom. Design 12 1995 771 784
12. J.R. Driscoll, N. Sarnak, D.D. Sleator, and R.E. Tarjan Making data structures persistent J. Comput. Sys. Sci. 38 1989 86 124
13. H. Edelsbrunner, and J. Harer Jacobi sets of multiple Morse functions F. Cucker, Foundations of Computational Mathematics 2004 Cambridge Univ. Press England 37 57
14. H. Edelsbrunner, J. Harer, A. Mascarenhas, V. Pascucci, Time-varying Reeb graphs for continuous space-time data, in: SCG '04: Proc. of the 20th Ann. Sympos. Comput. Geom., 2004, pp. 366-372
15. H. Edelsbrunner, J. Harer, V. Natarajan, V. Pascucci, Morse-Smale complexes for piecewise linear 3-manifolds, in: Proc. 19th Ann. Sympos. Comput. Geom., 2003, pp. 361-370
16. A.T. Fomenko, and T.L. Kunii Topological Methods for Visualization 1997 Springer-Verlag Tokyo, Japan
17. M. van Kreveld, R. von Oostrum, C.L. Bajaj, V. Pascucci, D.R. Schikore, Contour trees and small seed sets for iso-surface traversal, in: Proc. 13th Ann. Sympos. Comput. Geom., 1997, pp. 212-220
18. Y. Matsumoto An Introduction to Morse Theory Translated from Japanese by K. Hudson and M. Saito 2002 Amer. Math. Soc.
19. N. Max, R. Crawfis, and D. Williams Visualization for climate modeling IEEE Comput. Graphics Appl. 13 1993 34 40
20. J. Milnor Morse Theory 1963 Princeton Univ. Press NJ
21. J.R. Munkres Elements of Algebraic Topology 1984 Addison-Wesley Redwood City, CA
22. V. Pascucci, and K. Cole-McLaughlin Parallel computation of the topology of level sets Algorithmica 38 2 2003 249 268
23. G. Reeb Sur les points singuliers d'une forme de Pfaff complètement intégrable ou d'une fonction numérique Comptes Rendus de L'Académie ses Séances, Paris 222 1946 847 849
24. Y. Shinagawa, and T.L. Kunii Constructing a Reeb graph automatically from cross sections IEEE Comput. Graphics Appl. 11 1991 44 51
25. B.S. Sohn, and C.L. Bajaj Time-varying contour topology IEEE Transactions on Visualization and Computer Graphics 12 1 2006 14 25
26. A. Szymczak, Subdomain aware contour trees and contour evolution in time-dependent scalar fields, in: SMI '05: Proceedings of the International Conference on Shape Modeling and Applications 2005 (SMI' 05), 2005, pp. 136-144