The partial differential equation (PDE) method for surface generation yields surfaces as solutions to elliptic boundary value problems. The method was introduced by Bloor and Wilson [1], and Hoschek and Lasser [2]. Lowe et al. [3] used it for the automatic design of ship hulls.

In this paper, the authors use the PDE method to generate smooth surfaces. They discuss the solution of a biharmonic elliptic equation with three vector-valued shape parameters, instead of one as done by Bloor and Wilson. The use of this generalized PDE in vase design was discussed by the authors in a separate paper [4]. Here, the authors allow a combination of the analytic closed form solution and a collocation method to minimize the residuals. They demonstrate the accuracy and efficiency of the new method with several examples, including the modeling of a claw.