This was my first go laying out a sliding background, with all the maths, fields and stuff. It was what motivated me to come up with a DIY sliding pegbar bodge in the first place.
One trick I found especially tricky was keeping the vanishing point in the same place. Gwonams animated on unmoving top pegs and the background scrolls on bottom pegs. So I animated the first arch moving with one point perspective, but the wall had to connect in the same place the whole time since its panning. Basically it was a matter of having the vanishing point move the opposite direction the same amount that the pegbar moves. To simplify that, I was easing in/out in divisions of inches (1/8" x2 to 1/4" x2 to 1/2" x2 to 1" for the rest of the pan). It turned out okay! Although I wonder how the hell I'm going to scan these long backgrounds and get inch rulers in After Effects (might just draw the progressing centre positions on the paper).
Another last second change so I'm not misinforming anyone; don't have East/West coordinates in pans, just say where the new "centre" is relative to the round peg. In this case the pan started on POS A (meaning the first round peg hole) and ended 1" LO POS C (meaning the third round peg hole is 1 inch Left Of the ending pan position). I can see why we moved over to computers, but still handy knowing this stuff.