Abstract: This paper proposes an algorithm to design almost developable meshes interpolating a given discrete line of curvature. First of all, compute the discrete Frenet frame of the given curve. Then rotate this frame to get the rotation minimizing frames. Select one of them by assigning the normal vector of the resulting surface at some vertex of the given discrete line. Finally, use it to construct an almost developable mesh in real time. This algorithm has very good interactivity, and the obtained interpolatory meshes possess good developability and smoothness. The experiment results show that this algorithm is very simple and efficient, and it has big potential value in practical application.