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Descripción
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| The problem of parametrizing approximately algebraic plane curves goes as follows: given a plane algebraic curve C (that is the perturbation of a rational plane curve) and a tolerance ² > 0, we want to ¯nd a new curve C, being rational, as well as a rational parametrization of it such that C is in the o®set region of C, at certain small distance dependent on ², and vice-versa. In [2] and [3] we have seen how to parametrize approximately algebraic plane curves and algebraic surfaces having an ²-singularity of maximum multiplicity. In this paper, using the techniques of ²-points, we extend the results in [2] to the general case of approximate algebraic a±ne plane curves. Moreover, the rational curve output in our method has the same structure at in¯nity as the original curve, and hence asymptotically both curves are close. We have also analyzed empirically the method and checked that the output and input curves satisfy the above condition on closeness. Nevertheless, because of page limitation we omit this study. Also, we omit how to proceed when the ²-singularities are very big. In this case, one uses clusters (see Section 3) at in¯nity to decide wether the a±ne point is associated to a point at in¯nity. | |
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Internacional
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No |
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Entidad
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Universidad de Granada |
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Lugar
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Granada (España) |
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Referencia/URL
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Tipo de publicación
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Actas sin ISSN |