A slight improvement to my last attempt in Foxy Gets Hooked.
The difference here is that rather than have just one fixed Bezier Warp distortion applied to the whole composition, I've animated the Bezier points to constantly compensate for the barrel distortion drawn in the original layout.
The first clip is of a background "pan" without any post-production, typical of any 2D animated cartoon. The second clip is the same pan with additional distortion animated in post to compensate for the curving lines. The third is the same again, only with reference models put in the scene to test for how extreme it can be taken before it's a mess.
The bezier warp shape is like that of pincushion distortion, compensating for the barrel distortion, but as the amount of distortion in the artwork changes during the pan, the pincushion's shape changes too. At the beginning, there's no distortion on the left, but is most extreme on the right because the wall begins to curve there. Halfway through the transition, the pincushion is at its most extreme and symmetrical distorting both sides. By the end of the pan, there's hardly any distortion since the lines were mostly rectilinear.
It's rather wonky in this test because the layout was only a quick sketch. In a proper production the layout would be significantly more refined and the perspective lines would be less hazy resulting in a much more mathematically accurate distortion. For one thing the wide-angle perspective seemed to shift, with an asymmetrical distortion across the layout. I now know that doesn't really work. You'll be seeing more experiments involving this and in abundance in my next big project that being a Starfox parody (as well as in future projects in general).