Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using μ-basis
作者： Sonia Pérez-Díaz , Li-Yong Shen
DOI: 10.1016/J.CAGD.2021.101957
关键词: Inversion (discrete mathematics) 、 Parametric equation 、 Degree (graph theory) 、 Planar curve 、 Mathematics 、 Basis (linear algebra) 、 Algebraic number 、 Applied mathematics 、 Planar 、 Surface (mathematics)
摘要: Abstract The μ-basis of a rational curve/surface is new algebraic tool which plays an important role in connecting the parametric form and implicit curve/surface. However, most results for μ-bases are presented proper parametrizations. In this paper we consider improper planar curve. Based on known properties results, design two reparametrization algorithms using μ-basis. inversion, degree induced map implicitization formulas also derived.
sci-hub.st 参考文章(27)
Dario A. Bini, Paola Boito, A Fast Algorithm for Approximate Polynomial GCD Based on Structured Matrix Computations Numerical Methods for Structured Matrices and Applications. pp. 155- 173 ,(2010) , 10.1007/978-3-7643-8996-3_6
Joe Harris, Algebraic Geometry: A First Course ,(1992)
J. Rafael Sendra, Franz Winkler, Sonia Prez-Diaz, Rational Algebraic Curves: A Computer Algebra Approach ,(2007)
Li-Yong Shen, Sonia Pérez-Díaz, Numerical proper reparametrization of parametric plane curves Journal of Computational and Applied Mathematics. ,vol. 277, pp. 138- 161 ,(2015) , 10.1016/J.CAM.2014.09.012
GEORGE FIX, CHIH-PING HSU, TIE LUO, Implicitization of rational parametric surfaces Journal of Symbolic Computation. ,vol. 21, pp. 329- 336 ,(1996) , 10.1006/JSCO.1996.0015
Jaime Gutierrez, Rosario Rubio, David Sevilla, On Multivariate Rational Function Decomposition Journal of Symbolic Computation. ,vol. 33, pp. 545- 562 ,(2002) , 10.1006/JSCO.2000.0529
Liyong Shen, Chunming Yuan, Implicitization using univariate resultants Journal of Systems Science & Complexity. ,vol. 23, pp. 804- 814 ,(2010) , 10.1007/S11424-010-7218-6
Thomas W. Sederberg, Improperly parametrized rational curves Computer Aided Geometric Design. ,vol. 3, pp. 67- 75 ,(1986) , 10.1016/0167-8396(86)90025-7
J.Rafael Sendra, Franz Winkler, Tracing index of rational curve parametrizations Computer Aided Geometric Design. ,vol. 18, pp. 771- 795 ,(2001) , 10.1016/S0167-8396(01)00069-3
Sonia Pérez-Díaz, On the problem of proper reparametrization for rational curves and surfaces Computer Aided Geometric Design. ,vol. 23, pp. 307- 323 ,(2006) , 10.1016/J.CAGD.2006.01.001