%0 Journal Article 
%A Pérez Díaz, Sonia
%A Shen, Li-Yong
%T The μ-basis of improper rational parametric surface and its application
%D 2021
%@ 2227-7390
%U http://hdl.handle.net/10017/49653
%X 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.
%K μ-basis
%K Rational surfaces
%K Inversion
%K Improper
%K Reparametrization
%K Implicitization
%K Resultant
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala