We develop a rational biquadratic G 1 analogue of the non-uniform C 1 B-spline paradigm. These G 1 splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, and combine them into one smoothly-connected structure. This enables a design process that starts with basic shapes, re-represents them in spline form and uses the spline form to provide shape handles for localized free-form modification that can preserve, in the large, the initial fair, basic shapes. Highlights? Rational biquadratic G 1 analogue of the non-uniform C 1 splines. ? Exact reproduction of multiple basic shapes, such as cyclides and quadrics. ? Combining multiple basic shapes into one smoothly-connected structure.