Unified spheric propability

[yetar]

Lets say we have as much as 1D uniform random variables we want.
How from these 1D uniform random variable, we can create a uniform random variable upon the shell of a sphere?

 

[yetar]

I have solved the problem.
To get a unified spherical surface random variable you need to do the following:
Given Y and teta are unified random variables each.
The random variable F(Y, teta) = (Sqrt(r^2-Y^2)*sin(teta), Y, Sqrt(r^2-Y^2)*cos(teta))
Gives a unified sphere surface random variable.