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

✍ Scribed by Jianmin Zheng; Thomas W. Sederberg

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
265 KB
Volume
31
Category
Article
ISSN
0747-7171

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✦ Synopsis

This paper presents an O(n 2 ) 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(n 3 ). 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.

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