So I’ve started on a new hobby project. I’m not far enough along to go into details, but I have come up with one bit of technology that I think is cool so I’ll talk about it now.

A lot of levels in games are rectangular (from above) – being a rectangle makes a lot of things easier. Rectangles correspond to the shape of textures and regular geometric grids that can be used for terrain height fields. It’s easy to make a rectangular world wrap too by just making sure it is tileable and drawing a few extra copies of the world once you get within sight of borders. A rectangle lets you use euclidean coordinate space. If I wanted to create a world, it would be easy to draw a rectangular map.

However, it would be cool if the world was really stylized, like you are walking/flying over the surface of a mini planet. You can percieve the curvature of the world – it falls off in your peripheral vision and things climb up over the horizon as you move. Well, if your map needs to be spherical, it suddenly becomes a lot harder to draw. You have to start using spherical coordinates too, which complicates things like finding distances or even moving at a consistent speed in any direction.

The thing I came up with is a way to use a wrapping rectangular world, but give it the illusion that it is spherical – a spherical rectangle. It’s not rocket science or anything, but I think it’s a neat concept and can be kind of a brain teaser to figure out how everything can continue to line up as you move over its surface.

View of the terrain from high above

Same perspective, but without the spherical illusion

Finally, I put together some animated gifs of the world spinning in a few directions; can you tell that the rectangular world is repeating in every direction? The world still retains its rectangular proportions despite how much you spin the sphere – mysterious!