A Method of Local Design Modification of a Developable Surface

Abstract

A method to modify a developable surface locally based on the designers' demand is proposed. A developable surface, which can be flattened without stretching or expanding e.g. a cone or cylinder, widely used in many products, such as shipbuilding, clothing, and so on. Since these products are manufactured by bending, they are required not only their three-dimensional shape but also its developed shape. Nevertheless, its design process is not done by the CAD system but mainly by the experience or intuition of designers because the developable condition of a surface is complicated. Therefore, modifying a developable surface according to the designers' demand is much more difficult than doing a free-form surface, such as Bezier surface. In this study, we aim to improve efficiency of the design process and propose a method to modify a developable surface when a point of its boundary curve changes. First, we model the developable surface based on the differential geometry. Then we formulate its modification process and obtain the differential equation regarding the direction of modifying and its amount. From the features of this equation, we propose a simple algorithm, not spending much calculation time. Finally, we verify the validity of the proposed method through some examples of numeric calculation. This method can modify not only its three-dimensional shape of the surface, but also its developed shape.