Approximate transformation of an arbitrary curved surface into a plane using dynamic programming

Abstract This paper is concerned with the approximate transformation of curved surfaces with arbitrary shape into a plane using dynamic programming. In designing for curved shapes, CAD systems have a prominent role; in particular, methods for the transformation of arbitrary regions on the curved surface into flattened forms are indispensable for manufacturing processes. Generally, until now, in the absence of a systematic scheme for obtaining flattened forms, manual methods have needed a great deal of work. A method to transform curved surfaces using the finite element method has already been proposed. In this paper, DP is introduced into the primal problem. That is, an objective curved surface is decomposed into regions of adjacent strips. Then, each region is developed in turn into a flattened shape. The whole shape is derived by solving multi-stage decision processes. Moreover, a two-step algorithm is proposed for obtaining a good initial shape. By way of illustration, the results are then applied to the problem of transforming duct and shoe models into flattened forms.