Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds

Discrete and Computational Geometry

Volumn 30, Issue 1, 2003, Pages 87-107

  Edelsbrunner, Herbert ^a,b   Harer, John ^c   Zomorodian, Afra ^d  

^a Duke University   (United States)

^b Raindrop Geomagic   (United States)

^c DUKE UNIVERSITY   (United States)

^d University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037971839     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-003-2926-5     Document Type: Conference Paper

References (18)

1. Bajaj, C. L., Pascucci, V., and Schikore, D. R. Visualization of scalar topology for structural enhancement. In Proc. 9th Ann. IEEE Conf. Visualization (1998), pp. 18-23.
2. Banchoff, T. F. Critical points and curvature for embedded polyhedral surfaces. Amer. Math. Monthly 77 (1970), 475-485.
3. Carr, H., Snoeyink, J., and Axen, U. Computing contour trees in all dimensions. In Proc. 11th Ann. Sympos. Discrete Algorithms (2000), pp. 918-926.
4. de Berg, M., and van Kreveld, M. Trekking in the alps without freezing and getting tired. In Proc. 1st Europ. Sympos. Algorithms (1993), pp. 121-132.
5. de Leeuw, W., and van Liere, R. Collapsing flow topology using area metrics. In Proc. 10th Ann. IEEE Conf. Visualization (1999), pp. 349-354.
6. Delfinado, C. J. A., and Edelsbrunner, H. An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere. Comput. Aided Geom. Design 12 (1995), 771-784.
7. Edelsbrunner, H., Letscher, D., and Zomorodian, A. Topological persistence and simplification. Discrete Comput. Geom. 28 (2002), 511-533.
8. Edelsbrunner, H., and Mücke, E. P. Simulation of Simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Trans. Graphics 9 (1990), 66-104.
9. Garland, M., and Heckbert, P. S. Surface simplification using quadric error metrics. In SIGGRAPH 97 Conf. Proc. (1997), pp. 209-216.
10. Guibas, L., and Stolfl, J. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graph. 4 (1985), 74-123.
11. Milnor, J. Morse Theory. Princeton University Press, Princeton, NJ, 1963.
12. Mischaikow, K., and Mrozek, M. Conley index theory. In Handbook of Dynamical Systems II, B. Fiedler, Ed. Elsevier, Amsterdam, 2002.
13. Moore, I. D., Grayson, R. B., and Ladson, A. R. Digital terrain modeling: a review of hydrological, geomorphological, and biological applications. Hydrological Process. 5 (1991), 3-30.
14. NOAA. Announcement 88-mgg-02, digital relief of the surface of the earth, 1988. http://www.ngdc.noaa.gov/mgg/global/seltopo.html.
15. Palis, J., and de Melo, W. Geometric Theory of Dynamical Systems. Springer-Verlag, New York, 1982.
16. Tricoche, X., Scheuermann, G., and Hagen, H. A topology simplification method for 2D vector fields. In Proc. 11th Ann. IEEE Conf. Visualization (2000), pp. 359-366.
17. van Kreveld, M., van Oostrum, R., Bajaj, C., Pascucci, V., and Schikore, D. Contour trees and small seed sets for iso-surface traversal. In Proc. 13th Ann. Sympos. Computational Geometry (1997), pp. 212-220.
18. Wallace, A. Differential Topology. First Steps. Benjamin, New York, 1968.