Given a cloud P of data points, we present techniques and algorithms to decide whether P could be measurements of a developable surface and to reconstruct the original shape of the surface. We will use the dual approach to developable surfaces, which says that a developable surface can be considered as envelope of a one-parameter family of planes. A classification will be given which detects cones, cylinders, and developable surfaces of constant slope. Finally we discuss the problems occurring in this context.