transform.exs

defmodule Transform do
  def calculate do
    origin = {3, 3}

    [
      {:n_nw, {-1,  2}, {2, 1}},
      {:nw_w, {-1,  2}, {1, 2}},
      {:w_sw, {-1,  2}, {1, 4}},
      {:sw_s, {-1,  2}, {2, 5}},
      {:s_se, {-1,  2}, {4, 5}},
      {:se_e, {-1,  2}, {5, 4}},
      {:e_ne, {-1,  2}, {5, 2}},
      {:ne_n, {-1,  2}, {4, 1}}
    ]
    |> Enum.map(fn({direction, {local_x, local_y}, {global_x, global_y}}) ->
      {origin_x, origin_y} = origin

      [
        {1, 0, 0, -1},
        {-1, 0, 0, 1},
        {-1, 0, 0, -1},
        {0, 1, -1, 0},
        {0, -1, -1, 0},
        {0, 1, 1, 0},
        {0, -1, 1, 0},
        {1, 0, 0, 1}
      ]
      |> Enum.find(fn({xx, xy, yx, yy} = transformation) ->
         {test_x, test_y} = {
           (origin_x + (local_x * xx) + (local_y * xy)),
           (origin_y + (local_x * yx) + (local_y * yy)),
         }

         if test_x == global_x and test_y == global_y do
           IO.inspect({
             direction,
             transformation,
             test_x,
             test_y
           })
         end
      end)
    end)
  end
end

Transform.calculate