dc.contributor.author | Pérez Díaz, Sonia | |
dc.contributor.author | Shen, Li-Yong | |
dc.date.accessioned | 2021-10-13T15:06:31Z | |
dc.date.available | 2021-10-13T15:06:31Z | |
dc.date.issued | 2021-03-17 | |
dc.identifier.bibliographicCitation | Pérez Díaz, S. & Shen, L.Y. 2021, "The μ-basis of improper rational parametric surface and its application", Mathematics, vol. 9, no. 6. | |
dc.identifier.issn | 2227-7390 | |
dc.identifier.uri | http://hdl.handle.net/10017/49653 | |
dc.description.abstract | The μ-basis is a newly developed algebraic tool in curve and surface representations and it is used to analyze some essential geometric properties of curves and surfaces. However, the theoretical frame of μ-bases is still developing, especially of surfaces. We study the μ-basis of a rational surface V defined parametrically by P(t¯),t¯=(t1,t2) not being necessarily proper (or invertible). For applications using the μ-basis, an inversion formula for a given proper parametrization P(t¯) is obtained. In addition, the degree of the rational map ϕP associated with any P(t¯) is computed. If P(t¯) is improper, we give some partial results in finding a proper reparametrization of V. Finally, the implicitization formula is derived from P (not being necessarily proper). The discussions only need to compute the greatest common divisors and univariate resultants of polynomials constructed from the μ-basis. Examples are given to illustrate the computational processes of the presented results. | en |
dc.description.sponsorship | Agencia Estatal de Investigación | es_ES |
dc.format.mimetype | application/pdf | en |
dc.language.iso | eng | en |
dc.publisher | MDPI | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | μ-basis | en |
dc.subject | Rational surfaces | en |
dc.subject | Inversion | en |
dc.subject | Improper | en |
dc.subject | Reparametrization | en |
dc.subject | Implicitization | en |
dc.subject | Resultant | en |
dc.title | The μ-basis of improper rational parametric surface and its application | en |
dc.type | info:eu-repo/semantics/article | en |
dc.subject.eciencia | Matemáticas | es_ES |
dc.subject.eciencia | Mathematics | en |
dc.contributor.affiliation | Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas | es_ES |
dc.date.updated | 2021-10-13T15:04:47Z | |
dc.relation.publisherversion | https://doi.org/10.3390/math9060640 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | en |
dc.identifier.doi | 10.3390/math9060640 | |
dc.relation.projectID | 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/ | en |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |
dc.identifier.uxxi | AR/0000038133 | |
dc.identifier.publicationtitle | Mathematics | |
dc.identifier.publicationvolume | 9 | |
dc.identifier.publicationissue | 6 | |