Inversion, degree, reparametrization and implicitization of rational planar curves using µ-basis
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49535DOI: 10.1016/j.cagd.2021.101957
ISSN: 0167-8396
Publisher
Elsevier
Date
2021-02-11Embargo end date
2023-02-11Funders
Agencia Estatal de Investigación
Bibliographic citation
Pérez Díaz, S. & Shen, L.Y. 2021, “Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using μ-basis”, Computer Aided Geometric Design, vol. 84, art. no. 101957.
Keywords
µ-basis
Inversion
Rational parametrization
Algebraic curves
Proper reparametrization
Implicitization
Fibre
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/10.1016/j.cagd.2021.101957Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2021 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
The µ-basis of a rational curve/surface is a new algebraic tool which plays an important role in connecting the rational parametric form and the implicit form of a rational curve/surface. However, most results for µ-bases are presented for proper rational parametrizations. In this paper we consider the µ-basis for an improper rational planar curve. Based on the known properties and new results, we design two new proper reparametrization algorithms using µ-basis. The inversion, degree of the induced rational map and implicitization formulas are also derived.
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