A minor point: A number of the on-set extensions are TRANSLIGHTS, which are large backlit transparencies. The source image for these might be a painting or might be a photo. I suspect the one that extends the radial corridor might actually be a photographic enlargement of the actual corridor, but I've not studied it closely enough to be certain.
There are design tricks for avoiding the telltale "jogs" you see when the camera gets off-axis, but they're rarely used.
The floor extension in the TMP engine room isn't a matte painting. The camera move on that down-shot pretty much guarantees that, reinforced by a photo in the book The Making of Star Trek The Motion Picture
which is taken slightly off-axis and features the caption "The Enterprise
engine core extends many decks downward thanks to forced-perspective painting on the stage floor."
And then there's THIS tell, re the "crack" Robert mentions: