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TitleThe implicit equation of a canal surface
Author(s) Marc Dohm, Severinas Zube
TypeArticle in Journal
AbstractA canal surface is an envelope of a one-parameter 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 5-dimensional 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.
KeywordsCanal surface, Implicit equation, Resultant, μ -basis, Offset
URL http://www.sciencedirect.com/science/article/pii/S0747717108000916
JournalJournal of Symbolic Computation
Pages111 - 130
Translation No
Refereed No