Spherical mapping was done after cylindrical. I chose spherical rather than box/ISN because I did not like the results that box/ISN provided. Box/ISN tends to leave gaps if the intermediate surface is smaller than the textured surface, and parts of the texture are missing if the converse is true. I like spherical because it has complete coverage on each face, and rather than shrinkwrap, it can provide coverage on surfaces perpendicular to the cylinder intermediate surface. Though, there is distortion of the image (compression) as you near the poles. Theta is solved for from acosine y, and phi is solve from theta and x. Phi is mapped into u and theta is mapped into v.

A spherical/ISN mapping is applied to a cube. The texture is slightly shifted to show off clamping. The texture becomes more distorted as we near the poles of the intermediate surface. The centroid is in the middle of the cube. One normal per face.

The same spherical mapping but with tiling. Severe distortion at the poles, but not as much of a hidrance as shrinkwrap mapping, as a texture can now be applied over the face that would be perpendicular to a cylinder intermediate surface.

The spherical mapping applied to a tetrahedron. The centroid is halfway up the height of the tetrahedron. Interpolated normals per face.

The spherical mapping tiled across the tetrahedron. More distortion near the base of the tetrahedron and of course, near the pole of the sphere intermediate surface.

What image gallery would be complete without the Utah teapot? The centroid is at (0, 0, 0), so I believe that is the base of the teapot, but I am uncertain. Interpolated normals per face.