A developable surface is a surface which can be created by bending a flat surface without any distortion - stretching, shrinking or shearing. All developable surfaces are ruled surfaces (though not all ruled surfaces are developable surfaces) which can be described as a straight line swept through space. The straight lines of a ruled surface are “ruling lines”. A developable surface is a special case of a ruled surface. Along any ruling line of a developable surface the surface normals are parallel so that there is no twist along the ruling line.
Developable surfaces are useful for objects which are created by bending thin sheets; for example boats made of metal or plywood, metal ducts for air, etc. Thin material will bend more easily into a developable surface than other shapes because the material does not have significant stretching, shrinking or shearing when bent.
Frequently when designing an object to be built using sheet materials two edge curves are known, and there is a need to determine several ruling lines of the developable surface which conforms to those edge curves. Creation of a developable surface based on edge curves can often be easier and more accurate if certain ruling lines are available. The method I described above is a method to exactly determine the ruling lines of a developable surface from the edge curves.