Construction of Developable Surface with Geodesic or Line of Curvature Coordinates

In this paper, a developable surface with geodesic or line of curvature coordinates is constructed in the Euclidean 3-space. A coordinated by two families parametric curves, base curves (directrices) and lines (rulings). Since any part straight on curvature, we only need to show that directrices are geodesics ensure parameterized coordinates. The necessary sufficient conditions for be studied. main results paper generalized cylinder, tangent surface.