I’m pleased to announce the release of this nifty little project, part math visualization, part puzzle game. You navigate a maze on the surface of a sphere, but the maze is being visualized on the screen via stereographic projection—a method for mapping the surface of a sphere onto a flat plane. Imagine a globe with a 2D plane bisecting it at the equator. If you draw a line at any downward angle from the north pole, it will pass through the surface of the sphere once, and through the equatorial plane once. Project each point on the sphere along that line onto the equatorial plane and you’ve got a stereographic projection. The southern hemisphere is projected upward into a circle in the center of the plane, and the northern hemisphere is projected outward to fill the entire remainder of the plane. The north pole itself is lost in the infinite distance.
In Stereographic Maze, our intrepid player (a dot) starts on the south pole (which is in the center of the screen), and must find its way to the north pole (marked by a modulating circle). Use the arrow keys to move along the surface of the sphere to eventually reach the north pole; or, more accurately, use the arrow keys to rotate the entire sphere to flip it upside down, getting the original north pole to be the south pole.