Generating blend surfaces using a perturbation method

In this paper, a method is developed for generating blend surfaces. Here, a blend is considered to be a transition surface between primary surfaces that meets those surfaces with a specified degree of continuity. They are generated as the solution of elliptic partial differential equations, perturbed by the addition of one or more higher derivatives multiplied by a small parameter. The method of matched asymptotic expansions is used to arrive at efficient analytic representations of the surfaces.