Parametric G ⁿ blending of curves and surfaces

We introduce a simple blending method for parametric curves and surfaces that produces families of parametrically defined, G ⁿ–continuous blending curves and surfaces. The method depends essentially on the parameterizations of the curves/surfaces to be blended. Hence, the flexibility of the method relies on the existence of suitable parameter transformations of the given curves/surfaces. The feasibility of the blending method is shown by several examples. The shape of the blend curve/surface can be changed in a predictable way with the aid of two design parameters (thumb weight and balance).