Implementing POV-Ray on Sphere Mazes

Understanding POV-Ray

Instead of trying to implement a 3D renderer ourselves, we will rely on a third-party tool called the Persistence of Vision Raytracer, or POV-Ray for short. It excels at drawing photorealistic 3D geometry (like spheres). All we need to do is give it something to put on that geometry. (A maze, for instance.)

To understand how this will work, consider the following world map.

Looking at that map, we think that Antarctica is enormous. It must comprise at least as much land as all the other continents combined. Of course, this isn’t true. Antarctica is actually comparable in size to North America. So why, then, is it shown so large on the map?

The answer is that the map distorts it. Because the earth is a sphere, its surface cannot be drawn—or projected—onto a flat surface very easily, and definitely not without some amount of distortion. Our map uses what’s called a cylindrical projection, which takes areas near the poles and stretches them out to fill a rectangular area.

We’ll use this same technique to draw our maze, distorting the cells near the poles in order to fit everything in a rectangular grid. POV-Ray, then, will take that projection and apply it to a sphere, wrapping it neatly around the globe like a decal on a model airplane and fixing the distortion in one go. This lets us render a maze on a 3D surface by drawing a 2D image, a technique we’re already very familiar ...