-- Layout:
--[[   _
	  [ ]
	   V
	   1
     __ __
1  1|  3  |2  1
|   |     |   |
|   |     |   |
2   |__4__|   2
     __ __
1   | _3_ |   1
|    1   2    |
|             |
2    1   1    2
     |   |
     2   2

     1   1
     |   |
     2   2

     1   1
    _M_ _M_

--]]



--[[        _
	       _/| (u) direction
(u,v,w)  _/ ___
	   _/  /   \
      /   /1,0,0\
      /¯¯¯\     /
     /0,0,0\___/
  |  \     /   \
  |   \___/1,0,1\
 \|/  /   \0,1,0/
 (w) /0,0,1\___/ \_
	 \     /       \_
	  \___/          \|
	                 ¯(v) direction
	That is, to normalize grid positions into rectangular coordinates transform:
		<u, v, w> -> <u + v, 0, w + v> -> <i, 0, j> -> <i, j>
		(i = u+v, j = w+v)
--]]