Approximate parametrization of plane algebraic curves by linear systems of curves.
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance ² > 0 and an ²-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ²-rationality, and we provide an algorithm...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49579 |
| Acceso en línea: | http://hdl.handle.net/10017/49579 https://dx.doi.org/10.1016/j.cagd.2009.12.002 |
| Access Level: | acceso abierto |
| Palabra clave: | Approximate Parametrization Plane algebraic curves Linear systems of curves Matemáticas Mathematics |
| Sumario: | It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance ² > 0 and an ²-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ²-rationality, and we provide an algorithm to parametrize approximately affine ²-rational plane curves by means of linear systems of (d−2)-degree curves. The algorithm outputs a rational parametrization of a rational curve C of degree d which has the same points at infinity as C. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that C and C are close in practice. |
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