Design and G1 connection of developable surfaces through Bézier geodesics

For potential application in shoemaking and garment manufacture industries, the G1 connection of (1, k) developable surfaces with abutting geodesic is important. In this paper, we discuss the developable surface which contains a given 3D Bézier curve as geodesic and prove the corresponding conclusions in detail. Primarily we study G1 connection of developable surfaces through abutting cubic Bézier geodesics and give some examples.