Maya actually works like it shows, unlike max (which has several poly types) but make a new triangulation scheme in maya that reads some blind per face point data to define cut order (read the sdk examples not hard to do at all) then use the poly display-> display trangles. And make tool for setting this.
They are triangulated for view on the fly but not all renderer's make triangles out of primitives! And even wne they do its left for the render so the displayed triangulation do0e snot apply to MR for instance.
And yes theres plenty of reasons tho have native ngons, for one prman renders them faster. Tahts why even max implements this scheme.
QUOTE
Specifically, can you manually define the triangulation of a mesh and remember it, so the triangles can be turned back into quads for further editing?
Well thats just the deal a max mesh type quad is made out of triangles at all times its just that the cut is hidden from the user, its not a quad at all ever! You can also do this in maya make a uvmap that reacts to gons and use the border edges only display. Api aloso prowides a way to make a new poly based shape thats allways triangles and then you could draw edges as you wish!
Theres actually no need to classify edges like this but...