Generating Gⁿ parametric blending surfaces based on partial reparameterization of base surfaces

A method for generating parametric Gⁿ blending surfaces based on reparameterization of partial surface patches of the base surfaces is presented. In the method, partial regions, called reparameterized local base surfaces, near the contact curves on both base surfaces are reparameterized first. Then a parametric Gⁿ blending surface is generated by a linear combination of the two reparameterized local base surface patches by using Erich Hartmann's method. Here, contact curves can be arbitrarily defined by users according to practical requirements. Some methods for determining the reparameterized local base surfaces are given, and thereafter the influences of the reparameterized local base surfaces on the blending surface are discussed in detail. In addition, in order to achieve the fairness of the blending surface, a shape optimization method for minimizing the strain energy of the surface is proposed. Finally, some examples, including a G² blending surface generated with the method between an aerofoil and a missile body, are given to demonstrate the effectiveness of the proposed approach.