One of my favorite panoramas I shot recently is the atrium of the Bavarian Ministry of Justice. Why? Because I managed to capture the almost perfect symmetry in the room. See for yourself here or here. I also reprojected the full spherical panorama to the Mercator view you see in the following image.
What I don’t like about this panorama are the curved lines. It came to my mind that a rectilinear reprojection of the image would result in straight lines. However it is also not possible to reproject the full 360° field of view into one single rectilinear image. But it is possible to split the full 360° into 4×90°. The following image is the result of this technique.
All the straight lines in the panorama are also straight in the real building. The problem is now you get some discontinuities at border between the four cube faces. This is not a real problem in this panorama as the floor tiles just look fine wih the additional discontinuities.
The following image shows the four cube faces reprojected back onto the equirectangular image. You can see here clearly why the floor tiles are not curved in the final Cube Face Panorama. You can also see that the cube faces are not really cube faces, because I moved the individual cubes faces towards the zenith to see less of the floor and more of the ceiling.
The following panorama shows the extracted cube faces in an interactive view: