三次可展Bezier曲面的构造

摘要

可展曲面在很多的工程领域里，尤其在机械工程设计中有着重要的作用，例如飞机机翼、汽车车身、船体、鞋和服装等的设计与制造等。在空间的一平面上分别生成2条3次Bezier曲线，该平面绕一固定轴旋转不同角度，生成两个相交的平面，这2条3次Bezier曲线跟随旋转，分别位于两相交平面上，并由这两条曲线生成直纹面。根据直纹面可展的充要条件，求解出未知的设计曲线和伴随曲线的控制顶点，最终生成3次可展Bezier曲面。%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.