Two formulations are proposed for computing the general blending of parametric surfaces. The first is an exact formulation that extends the concept of the affine potential method [11] and represents the blend exactly in a high dimensional space as the sweeping surface of the intersection between offsets of the base surfaces with radii satisfying a specific one-parameter curve. The second is a relatively complex formulation that defines the blend as the sweeping surface of the intersection between offsets of base surfaces with radii satisfying a specific two-parameter surface. To improve the interactive performance of these formulations, procedural approaches are proposed. Both formulations provide users with not only a simple and intuitive blending specification, but also a flexible shape control of the blending surface. Moreover, the formulations take the underlying geometry of the base surfaces into consideration.