Tangent developable

The tangent developable of a space curve ${\displaystyle \gamma (t)}$ is a developable surface formed by the union of the tangent lines to the curve.

Let ${\displaystyle \gamma (t)}$ be a parameterization of a smooth space curve. That is, ${\displaystyle \gamma }$ is a twice-differentiable function with nowhere-vanishing derivative that maps its argument ${\displaystyle t}$ (a real number) to a point in space; the curve is the image of ${\displaystyle \gamma }$. Then a two-dimensional surface, the tangent developable of ${\displaystyle \gamma }$, may be parameterized by the map

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