Manhattan Distance between tiles in a hexagonal grid

Question

For a square grid the euclidean distance between tile A and B is:

distance = sqrt(sqr(x1-x2)) + sqr(y1-y2))

For an actor constrained to mo

Answer 1

A straight forward answer for this question is not possible. The answer of this question is very much related to how you organize your tiles in the memory. I use odd-q vertical layout and with the following matlab code gives me the right answer always.

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

For mathematical details of this solution visit: http://www.redblobgames.com/grids/hexagons/ . You can get a full hextile library at: http://www.redblobgames.com/grids/hexagons/implementation.html