Abstract
We give a proper reparametrization theorem for a set of rational parametric equations which is proper for all but one of its parameters. We also give an algorithm to determine whether a set of rational parametric equations belongs to this class, and if it does, we reparametrize it such that the new parametric equations are proper.
Similar content being viewed by others
References
A. Schinzel, Polynomials with Special Regard to Reducibility, Cambridge University Press, 2000.
E. W. Chionh and R. N. Goldman, Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants, Computer Aided Geometric Design, 1992, 9: 93–108.
R. J. Walker, Algebraic Curves, Princeton University Press, 1950.
D. M. Y. Sommerville, Analytical Geometry of Three Dimensions, The University Press, 1934.
T. W. Sederberg, Improperly parametrized rational curves, Computer Aided Geometric Design, 1986, 3: 67–75.
X. S. Gao and S. C. Chou, Computations with Parametric Equations, in Proc. of International Symposium on Symbolic and Algebraic Computation (ISSAC-91), ACM Press, New York, 1991, 122–127.
X. S. Gao and S. C. Chou, Implicitization of rational parametric equations, Journal of the Symbolic Computation, 1992, 14: 459–470.
W. T. Wu, Basic Principles of mechanical theorem-proving in elementary geometries, Journal of Systems Science and Mathematical Sciences, 1984, 4: 207–235.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper is partially supported by National Key Research Program of People’s Republic of China under Grant No. 2004CB318000.
Rights and permissions
About this article
Cite this article
Li, J., Gao, X. The Proper Parametrization of a Special Class of Rational Parametric Equations. Jrl Syst Sci & Complex 19, 331–339 (2006). https://doi.org/10.1007/s11424-006-0331-x
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11424-006-0331-x