Determining the topology of real algebraic surfaces

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3604 LNCS, Issue , 2005, Pages 121-146

  Cheng, Jin San ^a   Gao, Xiao Shan ^a   Li, Ming ^b  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; COMPUTER GRAPHICS; SURFACE PROPERTIES;

ALGEBRAIC SURFACE; CURVILINEAR POLYGONS; PROJECTION CURVE TOPOLOGY;

ALGEBRA;

EID: 33646122694     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11537908_8     Document Type: Conference Paper

References (26)

1. Arnborg, S. and Feng, H., Algebraic decomposition of regular curves. J. Symbolic Comput., 5(1,2)(1988): 131-140.
2. Arnon, D. S., Collins, G. and McCallum S., Cylindrical algebraic decomposition I: the basic algorithm. Quantifier Elimination and Cylindrical Algebraic Decomposition, Edited by B. Buchberger and G. E. Collins, Springer: 136-151.
3. Arnon, D. S. and McCallum, S., A polynomial-time algorithm for the topological type of a real algebraic curve, J. Symbolic Comput., 5(1,2)(1988): 213-236.
4. Bajaj, G., Hoffmann, C. M., Lynch, R. E. and Hopcroft, J. E. H., Tracing surface intersection, Computer Aided Geometric Design, (1988)5: 285-307.
5. Bajaj, C. and Xu, G. L., Spline approximations of real algebraic surfaces, J. Symbolic Comput., (1997)23: 315-333.
6. Basu, S., Pollack, R. and Roy, M.-F., Algorithms in real algebraic geometry. Algorithms and Computat. in Mathematics, (2003)10. Springer-Verlag.
7. Feng, H., Decomposition and computation of the topoplogy of plane real algebraic curves, PhD Thesis. (1992) The Royal Institute of Technology, Stockholm, Sweden.
8. Fortuna, E., Gianni, P., Parenti, P. and Traverse, Algorithms to compute the topology of orientable real algebraic surfaces, J. Symbolic Comput., 36(2003)343-364.
9. Gao, X. S. and Li, M., Rational quadratic approximation to real algebraic curves, Computer Aided Geometric Design, (2004)21: 805-828.
10. Gatellier G., Labrouzy A., Mourrain. B. and Técourt. J. P., Computing the topology of three dimensional algebraic curves. Computational Methods for Algebraic Spline Surfaces, (2004), Springer-Verlag: 27-44.
11. Geismann, N., Hemmer, M. and Schömer, E., Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually. Symposium on Computational Geometry, 2001: 264-273.
12. Gianni, P. and Traverse, C., Shape determination for real curves and surfaces. Ann. Univ. Ferrara Sez. VII(N.S.), (1983)29, 87-109.
13. Gonzalez-Vega, L. and El Kahoui, M., An improve upper complexity bound for the topology computation of a real algebraic plane curve. J. Complexity, (1996)12: 527-544.
14. Gonzalez-Vega, L. and Necula, I., Efficient topology determination of implicitly defined algebraic place curves, Computer Aided Geometric Design, 19(2002): 719-743.
15. Hart. J. C., Morse theory for implicit surface modeling. Mathematical Visualization, H-C Hege and K. Polthier, Eds., Springer-verlag, Oct. 1998: 257-268.
16. Hong, H., An efficient method for analyzing the topology of plane real algebraic curves. Math. Comput. Simulation, (1996) 42(4-6): 571-582.
17. Johnson, J. R., Algorithms for polynomial real root isolation. Ph.d. Thesis. The Ohio state University. 1991.
18. Keyser, J., Culver, T. and Krishnan, S., Efficient and exact manipulation of algebraic points and curve. Computer Aided Design, (2000) 32(11): 649-662.
19. Massey, W. S., A basic course in algebraic topology. Springer-verlag, 1991.
20. Ni, X. L., Garland, M. and Hart, J. C., Fair morse functions for extracting topological structure of a surface mesh. Proc. SIGGRAPH 2004.
21. Sakkalis, T., The topological configuration of a real algebraic curve. Bull. Australian Math. Soc., (1991) 43(1): 37-50.
22. Stander, B. T. and Hart, J. C., Guaranteeing the topology of an implicit surface polygonization for interactive modeling. Proc. SIGGRAPH 97 Aug. 1997: 279-286.
23. Walker, R. J., Algebraic curves, Springer-Verlag, 1978.
24. Wu, W. T., Mathematics Mechanization, Science Press/Kluwer, Beijing, 2000.
25. Yang, L., Zhang, J. Z. and Hou X. R., Nonlinear Algebraic Equation System and Automated Theorem Proving, Shanghai Scientific and Technological Education Publishing House, Shanghai, 1996.
26. Zhang, S. G., Liu, D. Z. and Feng, G. C., Computer Mathematics: an introduction(in Chinese), Juin University Press, 1997.