One and two-parameter blending for parametric surfaces

Two formulations are proposed for computing the general blending of paradmetric 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.