PDF(89 KB)
PDF(89 KB)
PDF(89 KB)
参数曲线的隐式化
Implicitization of parametric curves
This paper presents an efficient algorithm for the implicitization of parametric curves defined by polynomial parametric equations, which is mainly based on the theory of matrices. Initially, the upper bound of the degree of the desired implicit equation and its general representation are given, and then all of its coefficients can be obtained by the construction of null vectors of the corresponding implicit matrix. Furthermore, the desired implicit equation of the parametric curve can be obtained. Examples given in the paper demonstrate the correctness and efficiency of the method in detail.
［1］BUSE L, COX D, D'ANDREA C. Implicitization for surfaces in P3 in the presence of base points［J］. Journal of Algebra and its Application, 2003, 2(2): 189-214.
［2］GAO Xiaoshan, CHOU S C. Implicitization of rational parametric equations［J］. Journal of Symbolic Computation, 1992, 14: 459-470.
［3］ALONSO C, GUTIERREZ J, RECIO T. An implicitization algorithm with fewer variables［J］. Computer Aided Geometric Design, 1995, 12: 251-258.
［4］COX D, LITTLE J, O'SHEA D. Using Algebraic Geometry［M］. Berlin: Springer, 1998.
［5］WU Wenjun. 〖JP2〗Mathematics mechanization［M］. Beijing and Dordrecht: Science Press and Kluwer Academic, 2000.〖JP〗
［6］SHI He, SUN Yongli. Blending of triangular algebraic surfaces［J］. MMRes Preprints, 2002, 21: 200-206.
［7］CORLESS R M, GIESBRECHT M W, KOTSIREAS I S, et al. Numerical implicit
ization of parametric hypersurfaces with linear algebra［C］∥AISC'2000 Proceedings, 2000: 174-183.
［8］MACRO A, MARTINEZ J J. Using polynomial interpolation for implicitizing algebraic curves［J］. Computer Aided Geometric Design, 2001, 18:309-319.
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