There be many a land lubber that knows naught of the pirate ways and gives direction by degree!
They know not how to box the compass!



Task description

 Create a function that takes a heading in degrees and returns the correct 32-point compass heading.
 Use the function to print and display a table of Index, Compass point, and Degree; rather like the corresponding columns from, the first table of the wikipedia article, but use only the following 33 headings as input:
[0.0, 16.87, 16.88, 33.75, 50.62, 50.63, 67.5, 84.37, 84.38, 101.25, 118.12, 118.13, 135.0, 151.87, 151.88, 168.75, 185.62, 185.63, 202.5, 219.37, 219.38, 236.25, 253.12, 253.13, 270.0, 286.87, 286.88, 303.75, 320.62, 320.63, 337.5, 354.37, 354.38]. (They should give the same order of points but are spread throughout the ranges of acceptance).


Notes;
 The headings and indices can be calculated from this pseudocode:
for i in 0..32 inclusive:
    heading = i * 11.25
    case i %3:
      if 1: heading += 5.62; break
      if 2: heading -= 5.62; break
    end
    index = ( i mod 32) + 1
 The column of indices can be thought of as an enumeration of the thirty two cardinal points (see talk page)..


defmodule Box do
  defp head do
    Enum.chunk(~w(north east south west north), 2, 1)
    |> Enum.flat_map(fn [a,b] ->
         c = if a=="north" or a=="south", do: "#{a}#{b}", else: "#{b}#{a}"
         [ a, "#{a} by #{b}", "#{a}-#{c}", "#{c} by #{a}",
           c, "#{c} by #{b}", "#{b}-#{c}", "#{b} by #{a}" ]
       end)
    |> Enum.with_index
    |> Enum.map(fn {s, i} -> {i+1, String.capitalize(s)} end)
    |> Map.new
  end
 
  def compass do
    header = head()
    angles = Enum.map(0..32, fn i -> i * 11.25 + elem({0, 5.62, -5.62}, rem(i, 3)) end)
    Enum.each(angles, fn degrees ->
      index = rem(round(32 * degrees / 360), 32) + 1
      :io.format "~2w  ~-20s ~6.2f~n", [index, header[index], degrees]
    end)
  end
end
 
Box.compass