Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis
type: Item
instance of: scholarly article
title: Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis
zbMATH Open document ID: 1465.14056
author: Sonia Pérez Díaz
author: Li-Yong Shen
published in: Computer Aided Geometric Design
publication date: 2021-04-23T00:00:00Z
review text: Rational parametrizations of algebraic curves and surfaces play an important role in computer aided geometric design, but also in other areas such as the symbolic solution of algebraic differential equations. In most of these applications we are interested in so-called proper parametrizations; i.e., parametrizations which describe a 1-1 correspondence (almost everywhere) between parameter values and points of the algebraic variety. Such reparametrizations from an improper into a proper parametrization exist. In this paper the authors revisit the problem of reparametrization, and they propose new algorithms based on \(\mu\)-bases of curves and surfaces. \(\mu\)-bases for rational curves have been introduced about 20 years ago, and they are determined by moving lines. The concept has been extended to rational surfaces. Such bases present a bridge between implicit and parametric representations of varieties. Their use in reparametrization in new.
reviewed by: Franz Winkler
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 68U07
zbMATH DE Number: 7337232
zbMATH Keywords: \(\mu\)-basis
zbMATH Keywords: inversion
zbMATH Keywords: rational parametrization
zbMATH Keywords: algebraic curves
zbMATH Keywords: proper reparametrization
zbMATH Keywords: implicitization
zbMATH Keywords: fibre
describes a project that uses: CASA
MaRDI profile type: Publication
full work available at URL: j.cagd.2021.101957
OpenAlex ID: W3132285960
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DOI: 10.1016/J.CAGD.2021.101957
description: scientific article; zbMATH DE number 7337232