# Unity : Hexagonal Grids

I recently started working on a project with a friend that involves a hex map. There is an amazing guide here I couldn’t possibly top. I’m going to cover a few items that were absent I needed.  I used an axial coordinate system.  I haven’t seen a better method.

This post will cover:

1) Calculating Unity world coordinates from array coords, where to instantiate

2) Trimming for a hexagonal shaped map

3) Marking a border

4) Finding neighboring hexagons within a radius

Instantiating hex pieces, calculating Unity world coordinates from array coords.

I stored my hexagons in a 2d array let’s say HexMap[,].  The picture to the left shows an example.  Please note on an axial system (aka slanted) the Z axis is slanted and the Y axis is vertical.  To find where to place hexagons at their correct ‘world coordinate:”

Create a variable that stores the hex models radius (it’s side length in Unity)
Next calculate the apothem which is :

Once you have the apothem you can easily calculate the world coordinates for any Hex based on the following :

x world coordinate = (x Array Coordinate * (1.5 * radius))
z world coordinate = ((z Array Coordinate * (2 * apothem)) + (x Array Coordinate * apothem))
.

Trimming the edges to create a Hex shaped map To accomplish this look the array (map)  needs to be an odd number of hexes and square, the example above is 5×5.  To locate of the unwanted Hexagons marked in yellow above, red to the right.

amountToTrim = xMax / 2;  (floor division)
mapSize = (xSize-1)*2

Every tile that meets the following conditions needs trimmed:
if (x+z < hexAmountToTrim || x+z > (mapSize  – hexAmountToTrim ) ) {}

Marking a Border

I marked the border for two reasons.  I felt it would look nicer to add a trim piece to the map and my path finding algorithm does not check if coordinates are valid.  To handle this I flag border pieces as invalid/non-traversable so if/when they are reached they are ignored.

When generating the map catch the pieces and flag as a border only  if they are not caught while trimming the edges above.  This will only catch a 1 hex deep border.  If you want more you’ll need to check for different conditions.

(x + z < hexAmountToTrim + 1 || (x + z > ((mapSize  – 1) * 2) – (hexAmountToTrim + 1)) || z == 0 || x == 0 || z == mapSize  – 1 || x == mapSize  – 1)

Finding a hexgons neighbor’s The example code will find the coords within a perimeter of three around the hexagon at the coordinates of 27,24.