Perhaps you are familiar with this survey, which seems relevant:
Felsner, Stefan, and Jacob E. Goodman. "Psuedoline"Pseudoline 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.
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