A Direct Approach to Computing the μ-basis of Planar Rational Curves

摘要

This paper presents an O(n2) algorthm, based on Grobner 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.