Probably this question has been asked already but does anyone know the

equation for cylindrical mapping ?

Advanced Animation & Rendering Techniques doesn’t satisfy me:

He defined cylinder as:

I: ( x, y, z ) = ( r * cos(PHI), r * sin PHI), hz )

For the u and v texels he said:

II: ( u, v ) = ( phi / 2 * PI, z )

For PHI I get:

III: PHI = arccos ( x / r) and IV: PHI = arcsin( y / r )

If I set only one equation (III or IV) in II the mapping goes wrong.

My question is now: How do I get the correct equation ?