Perhaps you are familiar with this survey, which seems relevant:
Felsner, Stefan, and Jacob E. Goodman. "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.
[![CRC][1]][1]