Pseudo-Line Arrangements: Duality, Algorithms and Applications

called a family of pseudo-lines if every pair of curves intersects
in at most one crossing point. Let P be a set of points in the plane.
We define a duality transform that maps L to a set L* of points in
the plane and P to a set P* of pseudolines so that the incidence and
the above-below relationships are preserved. We present an algorithm
for constructing the arrangement of P*, and applications.