caa a22 4500 463203127 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00200-006-0029-2 doi (NATIONALLICENCE)springer-10.1007/s00200-006-0029-2 Finite piecewise polynomial parametrization of plane rational algebraic curves [Elektronische Daten] [S. Pérez-Díaz, J. Sendra, C. Villarino] We present an algorithm with the following characteristics: given a real non-polynomial rational parametrization $${\mathcal{P}(t)}$$ of a plane curve and a tolerance $${\epsilon > 0}$$ , $${\mathbb{R}}$$ is decomposed as union of finitely many intervals, and for each interval I of the partition, with the exception of some isolating intervals, the algorithm generates a polynomial parametrization $${\mathcal{P}_{I}(t)}$$ . Moreover, as an option, one may also input a natural number N and then the algorithm returns polynomial parametrizations with degrees smaller or equal to N. In addition, we present an error analysis where we prove that the curve piece $${{\cal C}_{I}=\{\mathcal{P}(t)\,|\,t\in I\}}$$ is in the offset region of $${{\cal C}_{I}^{\ast}=\{\mathcal{P}_{I}(t)\,|\,t\in I\}}$$ at distance at most $${\sqrt{2}\epsilon}$$ , and conversely. Springer-Verlag, 2006 Piecewise polynomial parametrization nationallicence Rational algebraic curves nationallicence Error analysis nationallicence Pérez-Díaz S. Dpto. de Matemáticas, Universidad de Alcalá, 28871, Madrid, Spain aut Sendra J. Dpto. de Matemáticas, Universidad de Alcalá, 28871, Madrid, Spain aut Villarino C. Dpto. de Matemáticas, Universidad de Alcalá, 28871, Madrid, Spain aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 91-105 0938-1279 18:1-2<91 2007 18 200 https://doi.org/10.1007/s00200-006-0029-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-006-0029-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pérez-Díaz S. Dpto. de Matemáticas, Universidad de Alcalá, 28871, Madrid, Spain aut NATIONALLICENCE 700 1- Sendra J. Dpto. de Matemáticas, Universidad de Alcalá, 28871, Madrid, Spain aut NATIONALLICENCE 700 1- Villarino C. Dpto. de Matemáticas, Universidad de Alcalá, 28871, Madrid, Spain aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 91-105 0938-1279 18:1-2<91 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer