Analysis and applications of pipe surfaces Original Research Article

A pipe (or tubular) surface is the envelope of a one-parameter family of spheres with constant radii r and centers C(t). In this paper we investigate necessary and sufficient conditions for the nonsingularity of pipe surfaces. In addition, when C(t) is a rational function, we develop an algorithmic method for the rational parametrization of such a surface. The latter is based on finding two rational functions α(t) and β(t) such that ¦C′(t)¦2 = α2(t) + β2(t) (Lü and Pottmann, 1996).