For a spherical wrap, the u-coordinate is derived from the angle that the vector [x y 0] makes with the x-axis (as in the cylindrical map) and the v-coordinate from the angle that the vector [x y z] makes with the z-axis. Note that this mapping causes distortion of the texture at the z-axis.
This translates to the following equations:
The scaling factors and texture origin will often not be needed here as the unscaled range of u and v is already 0 through 1.