The implicit equation of a canal surface

Details The implicit equation of a canal surface The implicit equation of a canal surface

2008-06-25

arxiv.org/abs/0806.4127v1

Mathematics

Algebraic Geometry

26 pages, to be published in Journal of Symbolic Computation

Scientific paper

10.1016/j.jsc.2008.06.001

A 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 \mu-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 the dual variety, the canal surface and any offset to the canal surface.

Affiliated with

Also associated with

No associations

Rating

The implicit equation of a canal surface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The implicit equation of a canal surface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The implicit equation of a canal surface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162913