Public readonly Vertex Vertices = new Vertex This way you can represent the board with nothing but arrays and do lookups with simple math to transform between 'hexagon coordinates', 'edge coordinates', and 'vertex coordinates'.īecause the board will not fit a (rectangular) matrix perfectly, you will need to fill a couple of cells with some 'empty' or 'invalid' value, to represent the couple of borderline cells that have mismatch the hexagonal shape of the board.Īsymptotically, this method uses memory linear on the number of hexes, and gives constant time for any lookup. With some more simple formulas you can lookup edges from vertices, hexes from vertices, and other lookups you may need to play the game. This gives you constant time random access to edges and vertices given an hexagon (and you can work out the coordinate transformations to do the reverse lookup as well). The edges surrounding it are those at (2x,2y), (2x,2y+1), (2x+1, 2y), (2x+1,2y+2), (2x+2,2y), and (2x+2,2y+1), with an additional adjustment to y by adding one if x is odd. You add two other matrices to this: one for edges, and another for vertices. We can evolve this idea to allow fast lookup of edges and vertices.

A simple structure to store an hexagonal grid when you care only about hexagons, is a matrix, with an hexagon at (x,y) being a neighbor of hexagons at (x, y☑), (x☑,y), and (x☑,y+1) for even xs or (x☑,y-1) for odd xs.

Catan board randomizer