Missing sets in rational parametrizations of surfaces of revolution

Authors
Sendra Pons, Juan RafaelUniversity of Alcalá Author; Sevilla, David; Villarino Cabellos, CarlosUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/39746
Publisher
Elsevier
Date
2015-04-01
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Keywords
Revolution surface
Rational parametrization
Critical set
Covering parametrization
Real algebraic surface
Geometric computation
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/acceptedVersion
Publisher's version
http://dx.doi.org/10.1016/j.cad.2015.04.006
Rights
© 2015 Elsevier Ltd. All rights reserved.
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
Access rights
info:eu-repo/semantics/openAccess
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Abstract
Parametric representations do not cover, in general, the whole geometric object that they parametrize.This can be a problem in practical applications. In this paper we analyze the question for surfaces of revolution generated by real rational profile curves, and we describe a simple small superset of the real zone of the surface not covered by the parametrization. This superset consists, in the worst case, of the union of a circle and the mirror curve of the profile curve.
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