Line of curvature plays an important role in differential geometry. It is a useful tool in surface analysis. A developable surface is simple and frequently used in surface modeling. Many studies have investigated how to find or compute the line of curvature from a given surface; its anti-problem is rare. This paper presents an approach of designing a developable surface by interpolating the line of curvature and applying it to surface modeling. The Frenet frame is employed to express the ruling of the ruled surface. According to the necessary and sufficient conditions of line of curvature and developable surface

the equations that satisfy the ruling can be obtained. The developable surface can be adjusted flexibly by introducing control functions. The paper presents the concrete expression of a developable surface. The necessary and sufficient conditions are analyzed by classifying the developable surface. The method is validated by two representative examples. Results show that the method is suitable not only for general parametric curves but also for piecewise parametric curves. The concrete expression of a developable surface is constructed by interpolating the line of curvature through a constructive method. The proposed method is efficient and convenient

as verified by several representative examples.