Perhaps you are familiar with this survey, which seems relevant:

> Felsner, Stefan, and Jacob E. Goodman. "Psuedoline Arrangements." *Handbook of Discrete and Computational Geometry*, JE Goodman, ed., 3rd ed., CRC Press, Boca Raton, FL (2016). Soon (Oct17) to appear as 4th ed:
[PDF download](http://page.math.tu-berlin.de/~felsner/Paper/pseudol.pdf).
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[![CRC][1]][1]
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  [1]: https://i.sstatic.net/MiWjr.png