Issue mapping points on a (doubly) curved to a flat plane

I need help with the bottom right section of this code. I’m just trying to remap points on a surface to a flat plane but something seems to be going on with re-parameterizing the surface. If you see the points in space on the lounge chair shape and then look at them on the flat plain, it isn’t hard to see that something is off.

Surface to ball placement from lounge chair 3.gh (32.6 KB)

no surface internalized

Apologies!

Surface to ball placement from lounge chair 3.gh (28.3 KB)

i just rebuild the base surface

increase the uv divisions for more accuracy

Surface to ball placement from lounge chair_rp00.gh (31.0 KB)

Huh. Well that seemed easy. Thanks!

Without pufferfish

Surface to ball placement from lounge chair 3 no puff.gh (33.9 KB)