Generating G″ blending surface based on auxiliary surfaces

The influences of base surfaces, reparameterized local base surfaces, the balance factor and the thumb weight on the blending surface are analyzed when a Gⁿ blending surface is generated by linear combination. A method of generating the Gⁿ blending surface based on auxiliary surfaces is presented. First, an auxiliary surface is generated according to the design requirements and design expectation of the designer. Blending contact curves are used as boundaries of the auxiliary surface. Then two small reparameterized local base surfaces near the contact curves in both base surfaces are determined, and a mesne blending surface is generated by linear combination of the auxiliary surface and one reparameterized local base surface with large values of the given balance factor and thumb weight λ₁, and small value of the given thumb weight λ₂. Finally, a Gⁿ blending surface is generated by linear combination of the mesne blending surface and the other reparameterized local base surface with large values of the given balance factor and thumb weight λ₁, and small value of the given thumb weight λ₂. In this way, the influences of base surfaces and reparameterized local base surfaces on the blending surface are reduced. And the intent of designers for generating a blending surface is realized.