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

This paper presents an O(n2) algorithm, based on Grobner basis techniques, to compute the ? -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 ? -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.

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