Square tiles are the default choice because they're easy to work with. This page covers the grid coordinates only and not the transforms. The world↔screen transform will be different for a top-down or side or isometric view, but the grid↔world transform works the same. With grids, we also have to transform “grid” coordinates into “world” coordinates and back. In both 2D and 3D graphics systems, we have to transform “world” coordinates into “screen” coordinates and back. This page is an updated version of my 2006 guide to grid parts. I hope this page gives you ideas for designing your own system for your project. You might choose additional relationships. You might choose continues to include edges that aren't colinear. For example, you might choose to have neighbors and adjacent include diagonals. You'll want to adapt these for your own project. This page isn't about the way to set up relationships, but one way to set up relationships.

The names and definitions here are arbitrary. For more on square grids, see my pages on edges, line-drawing, and circle fills. For a more detailed guide to hexagons, see my guide to hexagonal grids. There are algorithms for going from a tile to its corners, an edge to its tiles, and many others. This guide will show coordinate systems for tiles (faces), vertices (corners), and edges for square, hexagon, and triangle grids.

Types of grids em