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David Eppstein
David Eppstein
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This doesn't seem close to tight, but there's an easy lower bound of $\pi$. If you have a curve shorter than $\pi$, choose any projection direction perpendicular to the midpoint of the curve at its midpoint. The resulting projected curve will be monotonic and therefore non-self-intersecting.

This doesn't seem close to tight, but there's an easy lower bound of $\pi$. If you have a curve shorter than $\pi$, choose any projection direction perpendicular to the midpoint of the curve. The resulting projected curve will be monotonic and therefore non-self-intersecting.

This doesn't seem close to tight, but there's an easy lower bound of $\pi$. If you have a curve shorter than $\pi$, choose any projection direction perpendicular to the curve at its midpoint. The resulting projected curve will be monotonic and therefore non-self-intersecting.

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David Eppstein
David Eppstein
  • 18.6k
  • 2
  • 55
  • 127

This doesn't seem close to tight, but there's an easy lower bound of $\pi$. If you have a curve shorter than $\pi$, choose any projection direction perpendicular to the midpoint of the curve. The resulting projected curve will be monotonic and therefore non-self-intersecting.