Treasure Planet Map

Have you ever seen Treasure Planet? then you might recognize this thing. it's the map that Jim gets at the start, and is basically the central plot device of the whole movie.

It is 100 mm in diameter, or slightly less than 4 inches, and of course it requires support material and some degree of infill to print. Also, this model was a pain in the butt to make. have any of you guys ever tried to draw straight lines on a sphere?