关键词: Bezier曲线, 展曲面, Bezier曲面, 直纹面, 控制顶点

Abstract: Developable surfaces have an important role in many engineering fields, especially in the design of mechanical engineering such as aircraft wing, auto body, hull, shoes and clothing. In the three-dimensional space, two cubic Bezier curves are generated in a plane. The plane rotates different angles by a fixed axis to generate two intersecting planes. The two cubic Bezier curves located on the two intersecting planes follow the plane rotating. Then, a ruled surface is generated. According to the necessary and sufficient conditions of developable ruled surface, the unknown control vertices of design curve and accompanied curve are calculated. Finally, developable cubic Bezier surfaces are generated.

Key words: Bezier curve, developable surfaces, Bezier surfaces, ruled surfaces, control points