Hexagonal Grid Numbering

A fundamental requirement for scientific treatment of board games is a simple and practical numbering of the map locations. With square grids, an obvious solution is coordinates along two orthogonal axes. Hexagonal grids, however, have three axes, and only one of them can be aligned with an edge of a square board. Various systems have been proposed for numbering hexagonal grids, and several remain in use. Computational tools that support games with hexagonal grids will presumably need to convert, or operate directly on, the grid coordinates. While it would be possible to write separate software for each of the different coordinate systems, a more general approach is to define a formal description of the coordinate system, which is then supplied as data, and have a single piece of software that can handle all possible hexagonal grid coordinates. Such a system is proposed here, after an exhaustive survey of the various existing coordinate systems, and a comprehensive investigation of the logical possibilities for defining a coordinate system on a hexagonal grid. The formal expression that defines any specific coordinate system consists of around ten characters in the standard 7-b ASCII alphabet, for maximum computational interoperability.