Tangent developable

is a twice-differentiable function with nowhere-vanishing derivative that maps its argument

, may be parameterized by the map The original curve forms a boundary of the tangent developable, and is called its directrix or edge of regression.

The envelope of this family of lines is a plane curve whose inverse image under the development is the edge of regression.

Intuitively, it is a curve along which the surface needs to be folded during the process of developing into the plane.

The tangent developable of a curve containing a point of zero torsion will contain a self-intersection.

[3] Until that time, the only known developable surfaces were the generalized cones and the cylinders.