Globe Beta 1

This is not just a demo.
Its even less!

its just an Idea:
Create Bowls/Globes out of surfaces.
I realized it as far as possible, using many tricks.

Anyone could help me in math for this?
I used the curved-function:
f(x)=-sqrt((-x-1)*(x-1))
instead of the real curve function
f(x)=sqr(1-abs(sqrt(x-1)))-1
because its simpler = better performance.
This here is all I could do to create a globe out of a surface!

This is just an idea = really early beta.