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Proper Reparametrization of Rational Ruled Surface

Jia Li, Li-Yong Shen, and Xiao-Shan Gao   

  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing 100080, China
  • Revised:2008-01-15 Online:2008-03-15 Published:2008-03-10

In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.

Key words: painting; direct 3D manipulation; configuration space; metaball;



[1] Walker R J. Algebraic Curves. Princeton University Press, 1950.

[2] Gao X S, Chou S C. Implicitization of rational parametric equations. -\it Journal of the Symbolic Computation}, 1992, 14(5): 459--470.

[3] Schinzel A. Polynomials with Special Regard to Reducibility. Cambridge University Press, 2000.

[4] Sederberg T W. Improperly parametrized rational curves. -\it Computer Aided Geomeric Design}, 1986, 3(1): 67--75.

[5] Sonia P D. On the problem of proper reparametrization for rational curves and surfaces. -\it Computer Aided Geometric Design}, 2006, 23(4): 307--323.

[6] Chionh E W, Goldman R N. Degree, multiplicity, and inversion formulas for rational surfaces using U-resultants. -\it Computer Aided Geometric Design}, 1992, 9(2): 93--108.

[7] Li J, Gao X S. The proper parametrization of a special class of rational parametric equations. -\it Journal of Systems Science and Complexity}, 2006, 19(3): 331--339.

[8] Chionh E W, Gao X S, Shen L Y. Inherently improper surface parametric supports. -\it Computer Aided Geometric Design}, 2006, 23(8): 629--639.

[9] Chen F L, Zheng J M, Sederberg T W. The $\mu$-basis of a rational ruled surface. -\it Computer Aided Geometric Design}, 2001, 18(1): 61--72.

[10] Chen F L, Wang W P. Revisiting the $\mu$-basis of a rational ruled surface. -\it Journal of Symbolic Computation}, 2003, 36(5): 699--716.

[11] B L Van der Waerden. Einf\"-u}rung in Die Algebraischen Geometrie. Berlin: Springer-Verlag, 1973.
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ISSN 1000-9000(Print)

         1860-4749(Online)
CN 11-2296/TP

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