Symbolic parametrization of pipe and canal surfaces

Authors:
Günter Landsmann;Josef Schicho;Franz Winkler;Erik Hillgarter
Affiliations:
Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria;Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria;Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria;Research Institute for Symbolic Computation, Johannes Kepler University, A-4040 Linz, Austria
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

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Abstract

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.