A strange mapping

I have been experimenting with the panorama function on my camera. I have to spin gently holding the camera whilst it tales photograph after photograph and stitches them together in one big picture. So it is taking a curved 3D world and mapping it onto a straight 2D space. It must be related to those maps of the world where the globe has been cut like orange peel and squashed flat onto the page. Things get stretched and warped. Just so with this picture. Look at how the straight railway line in the bottom right of the picture has been pulled into a curve. This is similar to stuff I was reading in Roger Penrose's book The Road to Reality. He is dealing with how we cope with curved space-time in at least 4D.