Details:
Title  The implicit equation of a canal surface  Author(s)  Marc Dohm, Severinas Zube  Type  Article in Journal  Abstract  A canal surface is an envelope of a oneparameter family of spheres. In this paper we present an efficient algorithm for computing the implicit equation of a canal surface generated by a rational family of spheres. By using Laguerre and Lie geometries, we relate the equation of the canal surface to the equation of a dual variety of a certain curve in 5dimensional projective space. We define the μ basis for arbitrary dimension and give a simple algorithm for its computation. This is then applied to the dual variety, which allows us to deduce the implicit equations of the dual variety, the canal surface and any offset to the canal surface.  Keywords  Canal surface, Implicit equation, Resultant, μ basis, Offset  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108000916 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  2  Pages  111  130  Year  2009  Edition  0  Translation 
No  Refereed 
No 
