Rational quadratic approximation to real algebraic curves

Computer Aided Geometric Design

Volumn 21, Issue 8, 2004, Pages 805-828

  Gao, Xiao Shan ^a   Li, Ming ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Approximation; Parametrization; Real algebraic curve; Topology determination

Indexed keywords

ALGEBRA; ALGORITHMS; APPROXIMATION THEORY; MATHEMATICAL MODELS; PROBLEM SOLVING; TOPOLOGY;

CURVE SEGMENTATION; RATIONAL QUADRATIC APPROXIMATION; REAL ALGEBRAIC CURVES; TOPOLOGY DETERMINATION;

COMPUTER AIDED DESIGN;

EID: 4544385167     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2004.07.009     Document Type: Conference Paper

References (25)

1. Abhyankar, S., Bajaj, C., 1988. Automatic parameterization of rational curves and surfaces, III: algebraic plane curves. Computer Aided Geometric Design 5 (4), 309-321.
2. Bajaj, C., Hoffmann, C., Hopcroft, J., Lynch, R., 1988. Tracing surface intersections. Computer Aided Geometric Design 5 (4), 285-307.
3. Bajaj, C., Xu, G.L., 1997. Piecewise rational approximations of real algebraic curves. J. Comput. Math. 15 (1), 55-71.
4. Bondy, J., Murty, U., 1976. Graph Theory with Applications. Macmillan Press.
5. Chang, G.Z., Sederberg, T., 1997. Over and Over Again. American Mathematical Association.
6. Chen, F.L., Wang, W.P., 2003. Computing real inflection points of cubic algebraic curves. Computer Aided Geometric Design 20 (2), 101-117.
7. Chen, F.L., Deng, L., 2003. Interval parametrization of planar algebraic curves. In: Li, Z.M., Sit, W. (Eds.), Proceeding of the 6th Asian Symposium on Computer Mathematics. World Scientific, Singapore, pp. 64-76.
8. Cheng, J., Gao, X.-S, Li, M., 2004. Topology determination of real projective plane algebraic curves. Preprint.
9. Chuang, J., Hoffmann, C., 1989. On local implicit approximation and its application. ACM Trans. Graph. 8 (4), 298-324.
10. Farin, G., 1989. Curvature continuity and offsets for piecewise conics. ACM Trans. Graph. 8 (2), 89-99.
11. Farouki, R., 1989. Hierarchical segmentations of algebraic curves and some applications. In: Lyche, T., Schumaker, L.L. (Eds.), Math. Methods in Comp. Aided Geom. Design. Academic Press, Boston, MA, pp. 239-248.
12. Gao, X.S., Chou, S.C., 1992. On the parameterization of algebraic curves. Applicable Algebra in Elementary Communication and Computing 3, 27-38.
13. Gonzalez-Vega, L., Necula, I., 2002. Efficient topology determination of implicitly defined algebraic plane curves. Computer Aided Geometric Design 19 (9), 719-743.
14. Hong, H., 1996. An efficient method for analyzing the topology of plane real algebraic curves. Math. Comput. Simulation 42 (4-6), 571-582.
15. Ihm, I., Naylor, B., 1991. Piecewise linear approximations of digitized space curves with applications. In: Patrikalakis, N. (Ed.), Scientific Visualization of Physical Phenomena. Springer-Verlag, Berlin, pp. 545-569.
16. Lee, E., 1985. Rational Bézier representation for conies. In: Farin, G. (Ed.), Geometric Modeling: Algorithm and New Trends. SIAM, Philadelphia, PA, pp. 3-19.
17. Montaudouin, Y., Tiller, W., Vold, H., 1986. Application of power series in computational geometry. Computer-Aided Design 18 (10), 93-108.
18. Piegl, L., Tiller, W., 1987. Curve and surface constructions using rational B-spline. Computer-Aided Design 19 (9), 485-498.
19. Pottmann, H., 1991. Locally controllable conic splines with curvature continuity. ACM Trans. Graph. 10 (4), 366-377.
20. Pottmann, H., Leopoldseder, S., Hofer, M., 2002. Approximation with active B-spline curves and surfaces. In: Coquillart, S., Shum, H., Hu, S.M. (Eds.), Proc. of Pacific Graphics 2002. IEEE Press, Los Alamitos, CA, pp. 8-25.
21. Sederberg, T., Zhao, J., Zundel, A., 1989. Rational approximation of algebraic curves. In: Strasser, W., Seidel, H. (Eds.), Theory and Practice of Geometric Modeling. Springer-Verlag, Berlin, pp. 33-54.
22. Sederberg, T., Zheng, J., 2002. Algebraic methods for computer aided geometric design. In: Farin, G., Hoschek, J., Kim, M.S. (Eds.), Handbook of Computer Aided Geometric Design. North-Holland, Amsterdam.
23. Sendra, J., Winkler, F., 1991. Symbolic parameterization curves. J. Symbolic Comput. 12, 607-632.
24. Walker, R., 1978. Algebraic Curves. Springer-Verlag, New York.
25. Yang, H.P., Wang, W.P., Sun, J.G., 2004. Control points adjustment for B-spline curve approximation. Computer-Aided Design 36 (7), 639-652.