Form and movement representation of a hexagonal plane

Question

The most basic way of representing a quadrile plane (a bunch of squares) is to use a two-dimensional array.

In C# we declare this as int[,] and can make our plane as big as we want:

string[3,3] => tic-tac-toe board (or similar)
string[8,8] => chess or checkers board

To "move" an item on the plane, we would just asign it toa new "position"

//using our tic-tac-toe board:
string[0,0] = "x"; //top-left
string[1,1] = "o"; //middle-middle

//to move
string[0,1] = bN; //Black Knight's starting positon
string[2,2] = bN; //Black Knight moves
string[0,1] = String.Empty;

So, how would you represent a hexagonal plane (a bunch of hexagons) and how would movement from one position to the next be handled?

Note: This is not purely theoretical, as I have an idea for a little game in my head which would require this kind of movement, but I can't wrap my head around how it would be done. I've looked through some of the other questions here, but can't really find a good match...

Answer 1

I do not know if this is the optimal solution but what I would do is create a new class of board the board would be a collection of "cells" each cell would contain a pointer to each of it's neighboring cell (or null if the cell is on a edge). You could implement some iterators on the board class that would walk the cells.

You would have to treat it more like a List instead of a vector. But it is at least a start.

---

Another solution is set you board up like this

and still just use the [,] to access each cell but it will take a little more math to figure out if you are traversing cells (Up Right is [+1,-1], Right is [+1,0], Down Right is [0,+1], Down Left is [-1,+1], Left is [-1,0], Up Left is [0,-1])

EDIT

If you want vertical walls instead of a slant just take make your width(X) equal X + Y*2 then on each row make the current row number (y) and make the cells 0 to Y-y and X-y to X off limits.

Example:

const int X = 10;
const int Y = 10;
int grid[,] = new int[X+(2*Y), Y];

bool IsCellOffLimits(int x, int y)
{
    return (x < Y-y || x > X-y || y < 0 || y > Y);
}

you waste a little memory space but it gives you a board like this

If you are Very Clever© you can just use the normal space but just have your code have anything in that Y-y or X-y range be on the opposite side of the board. But ill leave that code up to the reader.