Modeling with rational biquadratic splines

We develop a rational biquadratic G¹ analogue of the non-uniform C¹ B-spline paradigm. These G¹ 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.