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arXiv · 0912.2986

On the convex hull of a space curve

Kristian Ranestad·Bernd Sturmfels
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Abstract

The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We express the degree of this surface in terms of the degree, genus and singularities of the curve. We present algorithms for computing their defining polynomials, and we exhibit a wide range of examples.

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Kristian Ranestad, Bernd Sturmfels. 2011-01-18. On the convex hull of a space curve. https://arxiv.org/abs/0912.2986

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