The mu-basis of a rational ruled surface

✍ Scribed by Falai Chen; Jianmin Zheng; Thomas W. Sederberg

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 101 KB
• Volume: 18
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/s0167-8396(01)00012-7

✦ Synopsis

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 mµ 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.