How to find a line that stabs the maximum possible number of segments?

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Suppose we are given $N$ arbitrary different angle segments in the plane that are disjoint, and we want to find a line that stabs the maximal number of segments. How to do this? I thought about quad trees but it doesn't seem to help...

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This should help:

Edelsbrunner, Herbert, Hermann A. Maurer, Franco P. Preparata, Arnold L. Rosenberg, Emo Welzl, and Derick Wood. "Stabbing line segments." BIT Numerical Mathematics 22, no. 3 (1982): 274-281. (PDF download.)

They dualize line segments to double wedges and use that representation for their algorithms.


          DoubleWedges