Parametrization of approximate algebraic curves by lines
It is well known that irreducible algebraic plane curves having a singularity of maximum multiplicity are rational and can be parametrized by lines. In this paper, given a tolerance > 0 and an –irreducible algebraic plane curve C of degree d having an -singularity of multiplicity d−1, we provide...
| Autores: | , , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Recursos: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49616 |
| Acesso em linha: | http://hdl.handle.net/10017/49616 https://dx.doi.org/10.1016/j.tcs.2004.01.010 |
| Access Level: | acceso abierto |
| Palavra-chave: | Approximate algebraic curves Rational parametrization Hibrid symbolic-numeric methods Matemáticas Mathematics |
| Resumo: | It is well known that irreducible algebraic plane curves having a singularity of maximum multiplicity are rational and can be parametrized by lines. In this paper, given a tolerance > 0 and an –irreducible algebraic plane curve C of degree d having an -singularity of multiplicity d−1, we provide an algorithm that computes a proper parametrization of a rational curve that is exactly parametrizable by lines. Furthermore, the error analysis shows that under certain initial conditions that ensures that points are projectively well defined, the output curve lies within the offset region of C at distance at most 2√ 2 1/(2d) exp(2). |
|---|