Fill your square with a checkerboard pattern and try free transform warp once more - so you can see, what's going on...
My square has a pattern (not really visible on sreenshots) but it doesn't really help with figuring out of weird AM numbers.
I've only had a chance to look at it for a little bit, and I haven't had a chance to see it in a cleaner form, but here's my speculation.
There are also four points that define the the basic corner-pin type transform (idTop, idBtom...).
The coordinates of the 16 points are relative to those points, so if you change the the coordinates of the four points from (100, 100, 200, 200) to (0,0,1,1) and then change all the points correspondingly eg. (133.3333... to 0.33333333) they would still perform the same function.
Now, as to the 16 points, they're named 'rationalPoint', googling which lead me here: Elliptic curve - Wikipedia
I'm not familiar with the math myself, but looking at the pictures leads me to believe it might be related, some sort of coordinate system within the previously defined rectangle, that would also have to account for the Bezier-curve-looking handles that don't seem to be represented in the code.
Or, I think Bézier surface - Wikipedia this might be of use.