Affine equivalences of trigonometric curves
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/58553DOI: 10.1007/s10440-020-00354-6
ISSN: 0167-8019
Publisher
Springer
Date
2020-08-24Funders
Agencia Estatal de Investigación
Bibliographic citation
Alcázar Arribas, J.G. & Quintero, E. 2020, “Affine equivalences of trigonometric curves”, Acta Applicandae Mathematicae, vol. 170, pp. 691-708.
Keywords
Affine equivalence
Algebraic curves
Elliptic Fourier descriptor (EFD) representations curves
Pattern recognition
Project
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-88796-P/ES/COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1007/s10440-020-00354-6Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2020 Springer Nature
Access rights
info:eu-repo/semantics/openAccess
Abstract
We provide an efficient algorithm to detect whether two given trigonometric curves, i.e. two parametrized curves whose components are truncated Fourier series, in any dimension, are affinely equivalent, i.e. whether there exists an affine mapping transforming one of the curves onto the other. If the coefficients of the parametrizations are known exactly (the exact case), the algorithm boils down to univariate gcd computation, so it is efficient and fast. If the coefficients of the parametrizations are known with finite precision, e.g. floating point numbers (the approximate case), the univariate gcd computation is replaced by the computation of singular values of an appropriate matrix. Our experiments show that the method works well, even for high degrees.
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