RATIONAL CURVES AND SURFACES WITH RATIONAL OFFSETS

Given a rational algebraic surface in the rational parametric represen tation s(u, v) with unit normal vectors n(u, v) = (s(u) x s(v))/parall el to s(u) x s(v) parallel to, the offset surface at distance d is s(d )(u, v) = s(u, v) + dn(u, v). This is in general not a rational repres entation, since parallel to s(u) x s(v) parallel to is in general not rational. In this paper, we present an explicit representation of all rational surfaces with a continuous set of rational offsets s(d)(u, v) . The analogous question is solved for curves, which is an extension o f Farouki's Pythagorean hodograph curves to the rationals. Additionall y, we describe all rational curves c(t) whose are length parameter s(t ) is a rational function of t. Offsets arise in the mathematical descr iption of milling processes and in the representation of thick plates, such that the presented curves and surfaces possess a very attractive property for practical use.