Numerical proper reparametrization of parametric plane curves

Authors
Shen, Li-Yong; Pérez Díaz, SoniaUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49553
DOI: 10.1016/j.cam.2014.09.012
ISSN: 0377-0427
Publisher
Elsevier
Date
2015-03-15
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Bibliographic citation
Shen, Li-Yong & Pérez Díaz, S. 2015, “Numerical proper reparametrization of parametric plane curves”, Journal of Computational and Applied Mathematics, vol. 277, pp. 138-161.
Keywords
Rational curve
Approximately improper
Proper reparametrization
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2014.09.012
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2014 Elsevier
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. More precisely, given a tolerance ϵ>0 and a rational parametrization P of a plane curve C with perturbed float coefficients, we present an algorithm that computes a parametrization Q of a new plane curve D such that Q is an ϵ –proper reparametrization of D. In addition, the error bound is carefully discussed and we present a formula that measures the “closeness” between the input curve C and the output curve D.
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