Generation of parametric Gⁿ blending surfaces based on relative direction of the base surfaces

The problem in which t-directional relative directions between both base surfaces are conflicting when generating Gⁿ blending surfaces by Erich Hartmann's method is investigated. Three new linear combinations between both base surfaces are presented when the t-directional relative directions are conflicting. And Gⁿ blending surfaces are generated by the method. When contact curves are close to the relative boundaries of the two base surfaces or the change of the curvature of partial region near the contact curves on base surface is great, Gⁿ blending surfaces can also be generated by the method. The problem that the t-directional relative direction is conflicting between two reparameterized local base surfaces is thus resolved.