直纹曲面是可展曲面的一个充要条件

The full and Essential Condition for a Ruled Surface Being a Developable Surface

可展曲面是直纹曲面的一种类型,可展曲面就是沿每一条直母线只有一个切平面.我们通过几何分析方法得到直纹曲面是可展曲面的充要条件是:曲面S是它的切平面族的包络面.

The developable surface, along every straight line with only one tangent plane, is a type of ruled surface. Our purpose is to give a sufficient and necessary condition for being a developable surface. In this paper, we use the methods of geometry analysis to study ruled surface, and get that developable surface S to be a developable surface if and only if S is of an enveloping surface of tangent plane families.