A canal surface is the envelope of a one-parameter set of spheres with radii r(t) and centers m(t). It is shown that any canal surface to a rational spine curve m(t) and a rational radius function r(t) possesses rational parametrizations. We derive algorithms for the computation of these parametrizations and put particular emphasis on low degree representations.
It was proved in REF that any canal surface with a rational spine curve (a set of all centers of moving spheres) and a rational radius function possesses a rational parameterization.
Computing Rational Parametrizations of Canal Surfaces
International Conference on Computational Science (2)
Mathematics Computer Science