One issue with 2d Marching Cubes (i.e. Marching Squres) that I glossed over in my original tutorial is the issue of ambiguity. Later I talk about how dual contouring avoids this problem. But it turns out there’s actually a well known, but little documented way of resolving those ambiguities called the Asymptotic Decider, which I’ll explain below.

2d Marching cubes (sometimes called marching squares) is a way of drawing a contour around an area. Alternatively, you can think of it as a drawing a dividing line between two different areas. The areas are determined by a boolean or signed number value on each vertex of a grid:

But what if we didn’t have a boolean value? What if we had n possible colors for each vertex, and we wanted to draw separating lines between all of them?

Many years ago I started looking at different sorts of tiles sets used by artists. A good tile set is flexible enough to allow tiles to be re-used in a lot of situation, but simple enough that the tiles can be easily created. Ideally, it would enable autotiling or otherwise be easy to design levels with.

Though I covered a few different techniques back then, I fell short of any systematic discussion of tiles. Here I plan to take a more rigorous approach, in the hopes of making a common language for referring to different tile sets, and pointing out the key variations in design. Maybe we’ll even discover something new, like Mendelev predicting new elements for the periodic table.

You can explore many of the tilesets discussed using the Tileset Creator tool I made.