I tore down a heavy truck PTO hydro pump many years back that had a series of sections. each section was a repeat of the one in front & behind. The vane chambers were kind of elliptical and also angled.
I had figured the shape of the chamber corresponded to where the oil entered & exited, like it exited on the wide side of the chamber with more volume, or vice versa with more pressure? Maybe?
Been quite a while now. I'll ask our heavy equipment mechanic to explain it to me when he comes in a couple days, and report back.