Computing rational parametrizations of canal surfaces

Abstract

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. © 1997 Academic Press Limited.