The mu-basis of a rational ruled surface Original Research Article

The mu-basis of a planar rational curve is a polynomial ideal basis comprised of two polynomials that greatly facilitates computing the implicit equation of the curve. This paper defines a mu-basis for a rational ruled surface, and presents a simple algorithm for computing the mu-basis. The mu-basis consists of two polynomials p(x,y,z,s) and q(x,y,z,s) that are linear in x,y,z and degree μ and m−μ in s respectively, where m is the degree of the implicit equation. The implicit equation of the surface is then obtained by merely taking the resultant of p and q with respect to s. This implicitization algorithm is faster and/or more robust than previous methods.