One of the central design principles in my still extremely early space shooter Hexeline (read: has neither space nor shooting) is that spacecraft will be defined in terms of a hexagonal grid, rather than cells of varying shape, which simplifies things for both the software and the player while still allowing more interesting shapes than a square grid.

A useful property of regular grids is that they are directly addressable; i.e., you can put the elements of an array and immediately access an element just by knowing its coordinate. Ideally, it’s also efficient to go from continuous spatial coordinates to a grid coordinate. This is trivial in a square grid: depending on how you define your coordinates, you can usually just divide spatial coordinates by the cell size to get the coordinate of the cell a point falls within.

In effort to get a similar property for hexagonal grids, I’ve taken the unusual step of basing a Newtonian physics engine on non-cartesian coordinates. It turns out this is not as bad as it sounds, and quite a few useful properties fall out of it.

Note: This post is going to be comparatively math-heavy and assumes some familiarity with linear algebra.