[iapcbwxw] Earth clock

Display a map projection centered on the point where the sun is directly overhead.  Choose the orientation so the path of the sun proceeds exactly right to left.

Some cylindrical projection is appropriate.  Horizontal distance from center vertical indicates time from local noon.  Perhaps vertical distance from center horizontal indicates angle of the sun in the sky.

Azimuthal orthographic could be incorporated as the background of a circular traditional clock face: the sun's eye view of earth.  Or any azimuthal.