Calculating distance on a hexagon grid

Question

What I am trying to do is find how many hexagons are in between two points on a hex grid. I have tried searching online for a formula but I have not been able to find one that matches the type of hex grid I am using.

The hex grid is laid out like this one with the same coordinate system: http://www.gamedev.net/index.php?app=core&module=attach&section=attach&attach_rel_module=ccs&attach_id=1962

I am aware that this may not be possible with this coordinate system but this is a last ditch effort before I go back and change it. Thank you very much in advance.

Answer 1

Thanks @user2709663 and @jonathankoren for providing answers. I spend a lots of time with your answers, but found both of this has some problems. Or at least the type of grid considered for those answers are not stated clearly. However, I found a very nice tutorial and code implementation of this problem, along with a library for managing hex grid at: http://www.redblobgames.com/grids/hexagons/ (library code: http://www.redblobgames.com/grids/hexagons/implementation.html). I also implement a matlab version of the distance code for the "odd-q" vertical layout as follows:

function f = offset_distance(x1,y1,x2,y2)
    ac = offset_to_cube(x1,y1);
    bc = offset_to_cube(x2,y2);
    f = cube_distance(ac, bc);
end

function f = offset_to_cube(row,col)
    %x = col - (row - (row&1)) / 2;
    x = col - (row - mod(row,2)) / 2;
    z = row;
    y = -x-z;
    f = [x,z,y];
end

function f= cube_distance(p1,p2)
    a = abs( p1(1,1) - p2(1,1));
    b = abs( p1(1,2) - p2(1,2));
    c = abs( p1(1,3) - p2(1,3));
    f =  max([a,b,c]);
end

Here is a matlab testing code

sx = 6;
sy = 1;
for i = 0:7
    for j = 0:5
        k = offset_distance(sx,sy,i,j);
        disp(['(',num2str(sx),',',num2str(sy),')->(',num2str(i),',',num2str(j),')=',num2str(k)])
    end
end