Generating and Flattening of Developable Surfaces

Abstract In this paper, methods for generating and flattening developable surfaces by means of two given directrix curves have been investigated. By finding the two end points of every generatrix, a developable surface may be formed. Such a developable surface may be flattened by rotating part of the surface about a generatrix. A new approach based on the principle of geodesic curve length preservation for flattening developable surfaces is also introduced. In this technique, an algorithm for evaluating the geodesic curvature of a point of a curve that lies on a surface is utilized.