Finite piecewise polynomial parametrization of plane rational algebraic curves

We present an algorithm with the following characteristics: given a real non-polynomial rational parametrization of a plane curve and a tolerance , 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 . 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 is in the offset region of at distance at most , and conversely. Authors partially supported by the Spanish “Ministerio de Educación y Ciencia” under the Project MTM2005-08690-C02-01, and by the “Dirección General de Universidades de la Consejería de Educación de la CAM y la Universidad de Alcalá” under the project CAM-UAH2005/053.