Flattening developable bi-parametric surfaces

Abstract

This paper describes a computer method for transforming an arbitrary developable surface into a flattened pattern. Developable surfaces are a special class of ruled surfaces. The Gaussian curvature of any point of the developable surfaces is zero. Some curves on developable surfaces are geodesic curves and the geodesic curvatures of all the points on these curves are zero. The flattening technique introduced in this paper is based on the geodesic curve length preservation and linear mapping principles. Both trimmed and untrimmed developable surfaces can be flattened by the algorithm.