An algorithm to parametrize approximately space curves

Authors
Rueda Pérez, Sonia Luisa; Sendra Pons, JuanaUniversity of Alcalá Author; Sendra Pons, Juan RafaelUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20451
DOI: 10.1016/j.jsc.2013.04.002
ISSN: 0747-7171
Publisher
Elsevier B.V.
Date
2013
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Journal of Symbolic Computation, 2013, v. 56 p. 80-106
Keywords
Space curve
Rational parametrization
Hausdorff distance
Description / Notes
This is the author’s version of a work that was accepted for publication in Journal of Symbolic Computation. 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 Journal of Symbolic Computation vol. 56 pp. 80-106 (2013). DOI: 10.1016/j.jsc.2013.04.002
All authors belong to the Research Group ASYNACS (Ref. CCEE2011/R34).
Project
info:eu-repo/grantAgreement/MICINN//MTM2008-04699-C03-01/ES/VARIEDADES PARAMETRICAS: ALGORITMOS Y APLICACIONES/
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/submittedVersion
Publisher's version
http://dx.doi.org/10.1016/j.jsc.2013.04.002
Rights
© Elsevier B.V., 2013
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We present an algorithm that, given a non-rational irreducible real space curve, satisfying certain conditions, computes a rational parametrization of a space curve near the input one. For a given tolerance \epsilon > 0, the algorithm checks whether a planar projection of the given space curve is \epsilon -rational and, in the affirmative case, generates a planar parametrization that is lifted to a space parametrization. This output rational space curve is of the same degree as the input curve, both have the same structure at infinity, and the Hausdorff distance between their real parts is finite. Moreover, in the examples we check that the distance is small.
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