Summary: Given a rational algebraic surface in the rational parametric representation with unit normal vectors
the offset surface at distance is
This is in general not a rational representation, since is in general not rational. We present an explicit representation of all rational surfaces with a continuous set of rational offsets . The analogous question is solved for curves, which is an extension of Farouki’s Pythagorean hodograph curves to the rationals. Additionally, we describe all rational curves whose arc length parameter is a rational function of t. Offsets arise in the mathematical description 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.