There are two familiar constructions of a developable surface from a space curve. The tangent developable is a ruled surface for which the rulings are tangent to the curve at each point and relative to this surface the absolute value of the geodesic curvature κ_g of the curve equals the curvature κ. The alternative construction is the rectifying developable. The geodesic curvature of the curve relative to any such surface vanishes. We show that there is a family of developable surfaces that can be generated from a curve, one surface for each function k that is defined on the curve and satisfies |k| ≤ κ, and that the geodesic curvature of the curve relative to each such constructed surface satisfies κ_g = k.

空间曲线有两种熟悉的可展曲面构造。可展开切线是直纹曲面，其直纹曲面在每个点与曲线相切，并且相对于该曲面，曲线的测地曲率κ _g的绝对值等于曲率κ。另一种结构是整流可开发。曲线相对于任何此类表面的测地线曲率消失。我们展示了可以从曲线生成的一系列可展曲面，一个曲面对应于在曲线上定义的每个函数k，并且满足 | ķ | ≤  κ，并且曲线相对于每个这样的构造表面的测地线曲率满足κ _g  =  k。