If I have 4 skew lines in $\mathbb{R}^3$, how can I find the line $L_c$, that is closest to all of them?

I know that with 3 skew lines, there is always a line that intersects all of them, in fact infinite many:

  • Construct a plane with $L_1$ and and arbitrary point on $L_2$,
  • intersect the plane with $L_3$ to get a second point,
  • the line through both points intersects $L_1$,$L_2$ and $L_3$

With 4 skew lines, there is at most two intersecting lines (I think, though I have not found a way to construct that yet). Assuming there is none, how do I find the line that is closest to them all?

This is related to a previous question by me: I am trying to find the axis for a surface of rotation, given 4 random points on the surface and some measurement error.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.