Optimal discrete Morse functions for 2-manifolds

Computational Geometry: Theory and Applications

Volumn 26, Issue 3, 2003, Pages 221-233

  Lewiner, Thomas ^a   Lopes, Hélio ^a   Tavares, Geovan ^a  

^a PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Computational geometry and object modeling; Computational topology; Forman theory; Morse theory

Indexed keywords

EID: 84867942371     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(03)00014-2     Document Type: Article

References (23)

1. E. Babson, P. Hersh, Discrete Morse functions from lexicographic orders, Topology, submitted for publication
2. M.K. Chari On discrete Morse functions and combinatorial decompositions Discrete Math. 217 2000 101 113
3. M.K. Chari, M. Joswig, Discrete Morse complexes, Preprint, 2001
4. F.H. Croom Basic Concepts of Algebraic Topology 1978 Springer-Verlag New York
5. C.J.A. Delfinado, and H. Edelsbrunner An incremental algorithm for Betti numbers of simplicial complexes on the 3-sphere Computer Aided Geometric Design 12 1995 771 784
6. T.K. Dey, H. Edelsbrunner, and S. Guha Computational topology B. Chazelle, J.E. Goodman, R. Pollack, Advances in Discrete and Computational Geometry, Contemporary Math. 223 1999 American Mathematical Society Providence, RI 109 143
7. H. Edelsbrunner, D. Letscher, and A. Zomorodian Topological persistence and simplification Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science 2000 454 463
8. H. Edelsbrunner, J.L. Harer, and A. Zomorodian Hierarchical Morse complexes for piecewise linear 2-manifolds Proceedings of the 17th Symposium of Computational Geometry 2001 70 79
9. Ö. Eeciolu, and T.F. Gonzalez A computationally intractable problem on simplicial complexes Computational Geometry 6 1996 85 98
10. R. Forman A discrete Morse theory for cell complexes S.T. Yau, Geometry, Topology and Physics for Raoul Bott 1995 International Press
11. R. Forman Morse theory for cell complexes Adv. Math. 134 1998 90 145
12. R. Forman, Some applications of combinatorial differential topology, in: Proc. of the SullivanFest, a conference in honor of Dennis Sullivan's 60th birthday, submitted for publication
13. R. Forman, A user's guide to discrete Morse theory, in: Proc. of the 2001 Internat. Conf. on Formal Power Series and Algebraic Combinatorics, A special volume of Advances in Applied Mathematics, submitted for publication
14. J.C. Hart Morse theory for implicit surface modeling H.-C. Hege, K. Polthier, Mathematical Visualization 1998 Springer Berlin 257 268
15. T. Lewiner, H. Lopes, and G. Tavares Visualizing Forman's discrete vector field H.-C. Hege, K. Polthier, Mathematical Visualization III 2002 Springer Berlin to appear
16. H. Lopes, Algorithm to build and unbuild 2 and 3 dimensional manifolds, PhD Thesis, Department of Mathematics, PUC-Rio, 1996 (in portuguese)
17. H. Lopes, J. Rossignac, A. Safanova, A. Szymczak, and G. Tavares Edgebreaker: a simple compression for surfaces with handles Proc. 7th ACM Siggraph Symposium on Solid Modeling and Application 2002 289 296
18. A. Lundell, and S. Weingram The Topology of CW Complexes 1969 Van Nostrand Reinhold New York
19. J.W. Milnor Morse Theory 1963 Princeton University Press Princeton, NJ
20. S. Moriyama, and F. Takeuchi Incremental construction properties in dimension two - shellability, extendable shellability and vertex decomposability Proceedings of the 12th Canadian Conference on Computational Geometry, Fredericton 2000 65 72
21. Y. Shinagawa, T.L. Kunii, and Y.L. Kergosien Surface coding based on Morse theory IEEE Computer Graphics and Applications 11 1991 66 78
22. R.E. Tarjan Data Structures and Network Algorithms 1983 Society for Industrial and Applied Mathematics Philadelphia
23. G. Vegter Computational topology J.E. Goodman, J. O'Rourke, Handlebook of Discrete Computational Geometry 1997 CRC Press 517 536