Rational Hausdorff Divisors: a New approach to the Approximate Parametrization of Curves
Identificadores
Enlace permanente (URI): http://hdl.handle.net/10017/20518DOI: 10.1016/j.cam.2013.12.052
ISSN: 0377-0427
Editor
Elsevier B.V.
Fecha de publicación
2014Patrocinadores
Ministerio de Ciencia e Innovación
Cita bibliográfica
Journal of Computational and Applied
Mathematics, 2014, v. 263, pp. 445-465.
Palabras clave
Hausdorff distance
Rational Hausdorff
Hausdorff curve
Approximate parametrization problem
Rational curve
Descripción
This is the author’s version of a work that was accepted for publication in Computational and Applied Mathematics. Changes resulting from the publishing process,
such as peer review, editing, corrections, structural formatting, and
other quality control mechanisms may not be reflected in this document.
Changes may have been made to this work
since it was submitted for publication. A definitive version was
subsequently published in Computational and Applied Mathematics 263
(2014), pp. 445-465. DOI: 10.1016/j.cam.2013.12.052
Proyectos
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/submittedVersion
Versión del editor
http://dx.doi.org/10.1016/j.cam.2013.12.052Derechos
© Elsevier B.V., 2014
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
In this paper we introduce the notion of rational Hausdor divisor, we analyze
the dimension and irreducibility of its associated linear system of curves, and we
prove that all irreducible real curves belonging to the linear system are rational
and are at nite Hausdor distance among them. As a consequence, we provide
a projective linear subspace where all (irreducible) elements are solutions to the
approximate parametrization problem for a given algebraic plane curve. Further-
more, we identify the linear system with a plane curve that is shown to be rational
and we develop algorithms to parametrize it analyzing its elds of parametriza-
tion. Therefore, we present a generic answer to the approximate parametrization
problem. In addition, we introduce the notion of Hausdor curve, and we prove
that every irreducible Hausdor curve can always be parametrized with a generic
rational parametrization having coe cients depending on as many parameters
as the degree of the input curve.
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