Developable Bezier function surface

Developable surface plays an important role in engineering practice. And Bezier function surfaces on the rectangular and triangular domains are common representation forms in a computer aided geometric design system. However, there are no studies about developable Bezier function surface up to now. General characterizations of developable Bezier function surfaces of arbitrary degree on the rectangular and triangular domains are presented. It is proved that a developable Bezier function surface of degree 2 on the triangular domain must be a parabolic cylinder. The construction methods of developable Bezier function surfaces of degree 3 on the triangular domain and of degree (2,2) on the rectangular domain are presented. The conclusions can be easily extended to bivariate polynomial function surface.