To solve the problems in adjusting and controlling shapes of developable surfaces

following the important idea of duality between points and planes in 3D projective space

two direct explicit and efficient methods of computer-aided design for developable surfaces are proposed. Constructing a class of cubic extension Bézier(CE-Bézier)basis functions with two shape parameters α

γ

the corresponding developable CE-Bézier surfaces with multiple shape control parameters are represented. The developable CE-Bézier surfaces inherit the outstanding properties of the Bézier surfaces

with a good performance on adjusting their local shapes by changing the two shape control parameters. In the particular case where α and γ are equal to 1

the developable CE-Bézier surface is a developable Bézier surface. Finally

some applications in developable surfaces design are discussed. The modeling examples illustrate that the developable CE-Bézier surfaces provide two valuable ways for the design of developable surfaces.