Coordinate transforms doubt

So I am reading up on Coordinate Transforms and I stumbled upon this post on Stackoverflow.
At the bottom the author(Dan Getz) says that “transform takes the standard coordinates of the points in the volume (1:3 x 1:3 x 1:3 in this case), applies tfm on them, and looks in v for the result.”
From an image perspective does this mean that the position of the extremities of the image coordinates like [1,1], [end,end] are found first after transformation and then the intensities of the intermediate pixels are then interpolated from the original image(using inverse transform?
I am not sure if my understanding is correct!