Finite piecewise polynomial parametrization of plane algebraic curves
We present an algorithm with the following characteristics: given a real non-polynomial rational parametrization P(t) of a plane curve and a tolerance ϵ>0 , R is decomposed as union of finitely many intervals, and for each interval I of the partition, with the exception of some isolating interval...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49598 |
| Acceso en línea: | http://hdl.handle.net/10017/49598 https://dx.doi.org/10.1007/s00200-006-0029-2 |
| Access Level: | acceso abierto |
| Palabra clave: | Piecewise polynomial parametrization Rational algebraic curves Error analysis Matemáticas Mathematics |
| Sumario: | We present an algorithm with the following characteristics: given a real non-polynomial rational parametrization P(t) of a plane curve and a tolerance ϵ>0 , 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 PI(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 CI={P(t)|t∈I} is in the offset region of C∗I={PI(t)|t∈I} at distance at most 2–√ϵ , and conversely. |
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