On the problem of proper reparametrization for rational curves and surfaces

Authors:
Sonia Pérez-Díaz
Affiliations:
Departamento de Matemáticas, Universidad de Alcalá, Madrid, Spain
Venue:
Computer Aided Geometric Design
Year:
2006

Citing 16
Cited 6

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Abstract

A rational parametrization of an algebraic curve (resp. surface) establishes a rational correspondence of this curve (resp. surface) with the affine or projective line (resp. affine or projective plane). This correspondence is a birational equivalence if the parametrization is proper. So, intuitively speaking, a rational proper parametrization trace the curve or surface once. We consider the problem of computing a proper rational parametrization from a given improper one. For the case of curves we generalize, improve and reinterpret some previous results. For surfaces, we solve the problem for some special surface's parametrizations.