Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis
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.
scientific article; zbMATH DE number 7337232
scientific article