I think the nomenclature isn't so bad. Coordinate transformations often leave you with something that doesn't make sense if you think of it in the new frame or orientation, and if you walk up to them cold take a lot of time reading detailed specs to make sense of. They're tedious to read through and make sense of and easy to mess up when tracing through. I've had to work with stuff that had 7 C-sized sheets packed with notes (and some figures) to define the "base" coordinate system and the transformations to get to mine. You've got what looks like a relatively straightforward set of routines and a lot of detailed description, so I don't think I'd complain about your naming. Most of my experience with nomenclature for this is based on sitting next to someone saying "show me it sliced at the yz plane at x = 'about here' finger point looking from putting +x pointing this way another finger point." Where the finger points would refer to the global coordinates or vectors if I had to write code.