Programming a Hexagon Board

I received an e-mail asking about programming hexagon-based board games. I wrote a quick explanation, which I am posting here just in case any other people are wondering but aren't brave enough to send e-mail.

A hexagon-based board is just a staggered grid. Each row is offset 1/2 hexagon from the rows above and below it.

Figure 1 contains a pattern of Xs that should roughly represent a hex board. (Ignore the Row Y business until you read the text preceding Figure 2).

Figure 1.

Row Y: X X X X X
Row Y:  X X X X X
Row Y: X X X X X
Row Y:  X X X X X

Below is a representation of the above pattern using a value for each horizontal hexagon position (X) and row (Y):

Figure 2.

Row 0: 0 1 2 3 4
Row 1:  0 1 2 3 4
Row 2: 0 1 2 3 4
Row 3:  0 1 2 3 4

As a hexagon identified by X and Y, the rules for identifying neighbors are:

• On row Y (my own row), my neighbors are X-1 and X+1.
• If Y is even, my neighbors are X-1 and X on rows Y-1 and Y+1.
• If Y is odd, my neighbors are X and X+1 on rows Y-1 and Y+1.

If you choose to reverse the rules for even and odd rows, it will result in the grid represented by Figure 3.

Figure 3.

Row 0:  0 1 2 3 4
Row 1: 0 1 2 3 4
Row 2:  0 1 2 3 4
Row 3: 0 1 2 3 4

To see an example, visit my programming page. Source code is not currently available.