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### When is the hull of a space curve composed of developable patches?

Let $C$ be a smooth curve in $\mathbb{R}^3$ that lies entirely on its convex hull,
$\cal{H}(C)$.
Under what conditions on $C$ is $\cal{H}(C)$ the union of developable surface patches?
I believe ...

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**3**answers

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### Surface analog of clothoid: curvatures covering $\mathbb{R}$

The clothoid $C$, a.k.a. the Euler spiral,
is one among many curves with
the property that its curvatures cover $\mathbb{R}$
in the sense that, for every $x \in \mathbb{R}$,
there is a point $p \in C$ ...