In 3D Studio Max, there is special way to map image maps onto a sphere. It is an option within UVW map called ‘Shrinkwrap’.
Uses spherical mapping, but truncates the corners of the map and joins them all at a single pole, creating only one singularity. Shrink-wrap mapping is useful when you want to hide the mapping singularity.
Does Blender or any add-on for Blender have such a mapping method?