Expand cylinder to a surface

LMZ

Hi!

help me please in expanding cylinder to surface.
I mean, I have cylinder:

Code:

x = 3Cos(u)
y = v
z = 3Sin(u)

u=[0;2Pi]
v=[0;2]

I guess now I need to find some functions instead of

Code:

3Cos(u), v, 3Sin(u)

that will a point on surface (not 3d space), something like this.

PS: the example of my task is a globe transformed to a surface as map.

Appreciate your help, Alexandr.

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