Detecting Symmetries of Rational Plane Curves

Authors
Alcázar Arribas, Juan GerardoUniversity of Alcalá Author; Hermoso Ortíz, CarlosUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20452
DOI: 10.1016/j.cagd.2014.02.004
ISSN: 0167-8396
Publisher
Elsevier
Date
2013
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Computer Aided Geometric Design, 2014, v. 31, n. 3-4, pp. 199-209.
Keywords
Rational planar curve
Rational space curve
Symmetry
Central symmetry
Mirror symmetry
Rotation symmetry
Symmetry center
Symmetry axis
Involution
Project
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.cagd.2014.02.004
Rights
© Elsevier, 2014
Access rights
info:eu-repo/semantics/openAccess
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Abstract
Given a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide effective methods for solving these questions without any conversion to implicit form. The underlying idea is the existing relationship between two proper parametrizations of a same curve, which in turn leads to algorithms where only univariate polynomials are involved. These methods have been implemented and tested in the computer algebra system Maple 15; evidence of their applicability, as well as a detailed theoretical analysis, is given.
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