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Oh please help me ...
1. Where do I find the constants in an abox thread? Esi and so on did not work!
2. Damned smooth sphere fold, i was tryin all day but unsuccessfully, looks crappy
Formula is here.
F(R) = k*(r1+rp)/(1+rp)*v+u: R=scale/F(R)
Then x*=r etc ...
Where...
R1 = abs((R-something)/uhm)
K is the sign of R-something ... Something should be u, and uhm too?...
Rp = r1**p (int pow for speed. Also exp-1 may be good? )
U = (minr+1)*0,5
V=(1-minr)*0,5
The other constants must satisfy ...
If pow is big, new r must be equal to that you find with standard method.
f(infy)=1 and f(u)=u, and f'(u)=1 (derivate)
Not much time to find the good values

I corrected the formula. You can try it for the sphere folding (it is not for the normal folding, but it should be an approx of the spheric one), but i am not 100%sure of it. Will test again later, but I am sure that your program is correct

I just have to thank you once more for the incredible work you do Luca! (And Jesse of corse) 
I have found a couple of new favorites in the last version... 

Time!, Time Luca...