Computing the μ-bases of algebraic monoid curves and surfaces
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49652DOI: 10.1016/j.cag.2021.04.011
ISSN: 0097-8493
Publisher
Elsevier
Date
2021-04-24Embargo end date
2023-04-24Funders
Agencia Estatal de Investigación
Bibliographic citation
Pérez Díaz, S. & Shen, L.Y. 2021, “Computing the μ-bases of algebraic monoid curves and surfaces”, Computers & Graphics, vol. 97, pp. 78-87.
Keywords
μ-basis
Conic
Quadric
Monoid curves and surfaces
Multiple point
Rational parametrization
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.cag.2021.04.011Rights
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 is a developing algebraic tool to study the expressions of rational curves and surfaces. It can play a bridge role between the parametric forms and implicit forms and show some advantages in implicitization, inversion formulas and singularity computation. However, it is difficult and there are few works to compute the μ-basis from an implicit form. In this paper, we derive the explicit forms of μ-basis for implicit monoid curves and surfaces, including the conics and quadrics which are particular cases of these entities. Additionally, we also provide the explicit form of μ-basis for monoid curves and surfaces defined by any rational parametrization (not necessarily in standard proper form). Our technique is simply based on the linear coordinate transformation and standard forms of these curves and surfaces. As a practical application in numerical situation, if an exact multiple point can not be computed, we can consider the problem of computing “approximate μ-basis” as well as the error estimation.
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