The developable surface is always a hot issue in CAGD, CAD/CAM and used in many manufacturing planning operations, e.g., for ships, aircraft wing, automobiles and garments. In some special fields, the CAD model of developable surface is designed by interpolating a given spatial characteristic curve. In this paper, we present a class of methods to construct local controlled developable H-Bezier surfaces through a given characteristic curve. First, we introduce a class of generalized cubic H-Bezier basis functions, and utilize them to design the generalized cubic H-Bezier curves with shape parameters. Then we construct generalized cubic developable H-Bezier surfaces through a given space generalized cubic H-Bezier curve which serve as the line of curvature or geodesic. The shapes of the constructed surfaces can be adjusted and altered expediently using the shape parameters. Furthermore, the sufficient and necessary conditions for the interpolating developable H-Bezier surface to be a cylinder or a cone are deduced, respectively. Finally, we give some representative examples to illustrate the convenience and efficiency of the presented methods.
