A survey of the representations of rational ruled surfaces
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/50574DOI: 10.1007/s11424-020-0018-8
ISSN: 1009-6124
Publisher
Springer
Date
2021-01-12Funders
Agencia Estatal de Investigación
Bibliographic citation
Yuan, Chun-Ming, Pérez-Díaz, S. & Shen, Li-Yong. 2021, “A survey of the
representations of rational ruled surfaces”, Journal of Systems Science and
Complexity, vol. 34, pp. 2357-2377.
Keywords
Birational transformation
Characterization
Implicitization
Parametrization
Rational ruled surface
Reparametrization
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/s11424-020-0018-8Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2020 The Editorial Office of JSSC & Springer-Verlag GmbH
Access rights
info:eu-repo/semantics/openAccess
Abstract
The rational ruled surface is a typical modeling surface in computer aided geometric design.
A rational ruled surface may have different representations with respective advantages and disadvantages. In this paper, the authors revisit the representations of ruled surfaces including the parametric
form, algebraic form, homogenous form and Pl¨ucker form. Moreover, the transformations between
these representations are proposed such as parametrization for an algebraic form, implicitization for a
parametric form, proper reparametrization of an improper one and standardized reparametrization for
a general parametrization. Based on these transformation algorithms, one can give a complete interchange graph for the different representations of a rational ruled surface. For rational surfaces given
in algebraic form or parametric form not in the standard form of ruled surfaces, the characterization
methods are recalled to identify the ruled surfaces from them.
Files in this item
Files | Size | Format |
|
---|---|---|---|
A_Survey_Yuan_J_Syst_Sci_Compl ... | 530.6Kb |
|
Files | Size | Format |
|
---|---|---|---|
A_Survey_Yuan_J_Syst_Sci_Compl ... | 530.6Kb |
|
Collections
- MATEMATIC - Artículos [172]