Inversion, degree, reparametrization and implicitization of rational planar curves using µ-basis

The µ-basis of a rational curve/surface is a new algebraic tool which plays an important role in connecting the rational parametric form and the implicit form of a rational curve/surface. However, most results for µ-bases are presented for proper rational parametrizations. In this paper we consider the µ-basis for an improper rational planar curve. Based on the known properties and new results, we design two new proper reparametrization algorithms using µ-basis. The inversion, degree of the induced rational map and implicitization formulas are also derived.Agencia Estatal de Investigació