Sign up ×  Given is a finite set $S$ of line segments in the
plane. I am interested in finding a line $l$ which splits some
segments in $S$ into two, thus yielding a new set of line
segments $S'$. Here splitting means that if $l$ intersects a
line segment $xy$ in a point $z$ then $xy$ gets replaced by two
new line segments $xz$ and $zy$.  The goal is to chose $l$ such
that it minimizes the length of the longest line segment in
$S'$.  I would be interested to know if this problem has been
studied before. What confuses me is that the problem does seem
to be continuous and not discrete.  share|cite|improve this
question Suppose you knew the optimal length $\ell$. Then on any
line of length $L \ge 2\ell$, there's an interval (centered at
the midpoint) that the optimal line must pass through. Now you
have the problem of determining whether a single line can
simultaneously pass through a collection of line segments, which
can be solved using the dual space (is there a point in the
intersection of a collection of do