You might see if this paper helps:

> Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). ([arXiv abstract link](http://arxiv.org/abs/0912.2986))

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![CurveHull][1]
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The yellow surface is $z - 4x^3 + 3x = 0$.
The green surface has degree $16$.
The pink triangle is planar.
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If an approximate hull would suffice, it is "easy" to compute the 3D convex hull
of many points along your curves.


  [1]: https://i.sstatic.net/zPJpr.png