A Direct Approach to Computing theμ-basis of Planar Rational Curves

This paper presents an O(n2) algorithm, based on Gröbner basis techniques, to compute the μ -basis of a degree n planar rational curve. The prior method involved solving a set of linear equations whose complexity by standard numerical methods was O(n3). The μ -basis is useful in computing the implicit equation of a parametric curve and can express the implicit equation in the form of a determinant that is smaller than that obtained by taking the resultant of the parametric equations.