Question

I’m sure there’s a clean way to do this, but I’m probably not using the right keywords for find it.

So let’s say I have a grid. Starting from a position on the grid, return all of the grid coordinates that fall within a given distance. So I call something like:

getCoordinates( currentPosition, distance )

And for each coordinate, starting from the initial position, add all cardinal directions, and then add the spaces around those and so forth until the distance is reached. I imagine that on a grid this would look like a diamond. The function would return that array of coordinates. Can someone point me to a routine that will do this efficiently ( I’m working in AS3, for what it’s worth )?

In the desired output, iteration 1 would be:

.x.
xxx
.x.

Iteration 2 would be:

..x..
.xxx.
xxxxx
.xxx.
..x..

Iteration 3:

...x...
..xxx..
.xxxxx.
xxxxxxx
.xxxxx.
..xxx..
...x...

and so on…

Answer 1

Edit: Updated the algorithm to reflect what the OP wanted.

Iteration 1:

.x.
xxx
.x.

Iteration 2:

..x..
.xxx.
xxxxx
.xxx.
..x..

…
Iteration 4:

....x....
...xxx...
..xxxxx..
.xxxxxxx.
xxxxxxxxx
.xxxxxxx.
..xxxxx..
...xxx...
....x....

Clearly, you can determine the coordinates without iterating.

If the starting point is (X, Y), and the iteration is n

for(int i = x - n; i <= x + n; i++)
{
    for(int j = y - n; j <= y + n; j++)
    {
        int dx = abs(i - x);
        int dy = abs(j - y);
        if(dx + dy <= n) //Produces a diamond, n+1 would produce a diamond with cut corners
        {
            //The point at (i, j) is within the marked area.
        }
    }
}