A new approach in designing of local controlled developable H-Bézier surfaces

To solve the problem of shape adjustment for developable surfaces, we propose a novel method for constructing local controlled generalized developable H-Bézier surfaces with shape parameters. The generalized developable H-Bézier surfaces are designed by using control planes with generalized H-Bézier basis functions and their shapes can be adjusted by altering the values of shape parameters. When the shape parameters assume different values, a family of developable H-Bézier surfaces can be constructed, which retain the characteristics of the developable Bézier surfaces. Furthermore, we derive the necessary and sufficient conditions for G1 continuity, Farin-Boehm G2 continuity and G2 Beta continuity between two adjacent generalized developable H-Bézier surfaces. Finally, some properties of the new developable surfaces are discussed, and the influence rules of shape parameters on the new developable surfaces are studied. Modeling examples provided show that the proposed methods are effective and hence can greatly improve problem-solving abilities in engineering appearance design by adjusting the position and shape of developable surfaces.