G1 continuity of four pieces of developable surfaces with Bézier boundaries

For potential applications in geometric design and manufacturing of material, the G1 connection of many pieces of developable surfaces is an important issue. In this paper, by using de Casteljau algorithm we study the G1 connection of four pieces of developable surfaces with Bézier boundary curves. We convert these surfaces to tensor form firstly, then characterize the constrains of the control points of the surfaces need to satisfy when G1 connecting them. This method can also be extended to the case when the developable surfaces possess Bézier boundary curves with different degrees.