Algorithm for iterating over an outward spiral on a discrete 2D grid from the origin

Question

For example, here is the shape of intended spiral (and each step of the iteration)

          y
          |
          |
   16 15 14 13 12
   17  4  3  2 11
--         


        

Answer 1

Here's the algorithm. It rotates clockwise, but could easily rotate anticlockwise, with a few alterations. I made it in just under an hour.

// spiral_get_value(x,y);
sx = argument0;
sy = argument1;
a = max(sqrt(sqr(sx)),sqrt(sqr(sy)));
c = -b;
d = (b*2)+1;
us = (sy==c and sx !=c);
rs = (sx==b and sy !=c);
bs = (sy==b and sx !=b);
ls = (sx==c and sy !=b);
ra = rs*((b)*2);
ba = bs*((b)*4);
la = ls*((b)*6);
ax = (us*sx)+(bs*-sx);
ay = (rs*sy)+(ls*-sy);
add = ra+ba+la+ax+ay;
value = add+sqr(d-2)+b;
return(value);`

It will handle any x / y values (infinite).

It's written in GML (Game Maker Language), but the actual logic is sound in any programming language.

The single line algorithm only has 2 variables (sx and sy) for the x and y inputs. I basically expanded brackets, a lot. It makes it easier for you to paste it into notepad and change 'sx' for your x argument / variable name and 'sy' to your y argument / variable name.

`// spiral_get_value(x,y);

sx = argument0;  
sy = argument1;

value = ((((sx==max(sqrt(sqr(sx)),sqrt(sqr(sy))) and sy !=(-1*max(sqrt(sqr(sx)),sqrt(sqr(sy))))))*((max(sqrt(sqr(sx)),sqrt(sqr(sy))))*2))+(((sy==max(sqrt(sqr(sx)),sqrt(sqr(sy))) and sx !=max(sqrt(sqr(sx)),sqrt(sqr(sy)))))*((max(sqrt(sqr(sx)),sqrt(sqr(sy))))*4))+(((sx==(-1*max(sqrt(sqr(sx)),sqrt(sqr(sy)))) and sy !=max(sqrt(sqr(sx)),sqrt(sqr(sy)))))*((max(sqrt(sqr(sx)),sqrt(sqr(sy))))*6))+((((sy==(-1*max(sqrt(sqr(sx)),sqrt(sqr(sy)))) and sx !=(-1*max(sqrt(sqr(sx)),sqrt(sqr(sy))))))*sx)+(((sy==max(sqrt(sqr(sx)),sqrt(sqr(sy))) and sx !=max(sqrt(sqr(sx)),sqrt(sqr(sy)))))*-sx))+(((sx==max(sqrt(sqr(sx)),sqrt(sqr(sy))) and sy !=(-1*max(sqrt(sqr(sx)),sqrt(sqr(sy))))))*sy)+(((sx==(-1*max(sqrt(sqr(sx)),sqrt(sqr(sy)))) and sy !=max(sqrt(sqr(sx)),sqrt(sqr(sy)))))*-sy))+sqr(((max(sqrt(sqr(sx)),sqrt(sqr(sy)))*2)+1)-2)+max(sqrt(sqr(sx)),sqrt(sqr(sy)));

return(value);`

I know the reply is awfully late :D but i hope it helps future visitors.