Symbolic parametrization of pipe and canal surfaces

A canal surface S, generated by a parametrized curve m(t), in R3 is the envelope of the set of spheres with radius r(t) centered at m(t). This concept generalizes the classical offsets (for r(t) = const) of plane curves. In this paper we develop elementary symbolic methods for generating a rational parametrization of canal surfaces generated by rational curves m(t) with rational radius variation r(t). In a pipe surface r(t) is constant.

• Type: Conference
• Year: 2000
• Where: ISSAC
• Authors: Günter Landsmann, Josef Schicho, Franz Winkler, Erik Hillgarter
• Keywords: Canal Surfaces, Elementary Symbolic Methods, ISSAC 2000, Mathematics, Rational Radius Variation