Abstract: By introducing shift operator and using de Casteljau algorithm，we draw the conclusion that a Bezier ruled surface is an envelope of single-parameter plane family，compactly derive the sufficient and necessary conditions of a ruled surface taking Bezier curves of degree n and degree m as its boundary being a developable surface.Furthermore，we present the method for designing quadratic Bezier developable surface：give four corner points of developable surface and two free designing parameters，the other two control vertexes are on the line connecting the linear interpolation point between the first two control vertexes and the linear interpolation point between the last two control vertexes，and they are the linear interpolation points between these two linear interpolation points respectively，namely，these four linear interpolation points are colinear.This method is very simple and we can conveniently control the surface shape by changing the two free designing parameters.Experiment results show that it is efficient.

Key words: developable surface, Bezier surface, envelope, surface design, Computer Aided Geometic Design（CAGD）

摘要： 通过引入移位算子，利用de Casteljau算法，得到了可展Bézier直纹面是单参数平面族的包络的结论，并简洁地导出了两条边界曲线分别为n次和m次的空间Bézier曲线的直纹面为可展曲面的充分必要条件。提出了二次Bézier可展曲面的设计方法：给定可展曲面的4个角点a0、b0、a2、b2和两个自由设计参数?姿、?滋，则待求的2个控制顶点a1、b1是在前2个控制顶点a0、b0的线性插值点a*与后2个控制顶点a2、b2的线性插值点b*的连线上，并且也是a*、b*这2个线性插值点的线性插值，即这4点a*、a1、b1、b*共线。该设计方法简单，可以通过2个自由设计参数?姿、?滋方便地控制曲面的形状。实例说明设计效果良好。

关键词: 可展曲面, Bézier曲面, 包络, 曲面设计, 计算机辅助几何设计