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)..


(ns boxing-the-compass
  (:use [clojure.string :only [capitalize]]))
 
(def headings
     (for [i (range 0 (inc 32))]
       (let [heading (* i 11.25)]
	 (case (mod i 3)
	       1 (+ heading 5.62)
	       2 (- heading 5.62)
	       heading))))
 
(defn angle2compass
  [angle]
  (let [dirs ["N" "NbE" "N-NE" "NEbN" "NE" "NEbE" "E-NE" "EbN"
	      "E" "EbS" "E-SE" "SEbE" "SE" "SEbS" "S-SE" "SbE"
	      "S" "SbW" "S-SW" "SWbS" "SW" "SWbW" "W-SW" "WbS"
	      "W" "WbN" "W-NW" "NWbW" "NW" "NWbN" "N-NW" "NbW"]
	unpack {\N "north" \E "east" \W "west" \S "south" \b " by " \- "-"}
	sep  (/ 360 (count dirs))
	dir  (int (/ (mod (+ angle (/ sep 2)) 360) sep))]
    (capitalize (apply str (map unpack (dirs dir))))))
 
(print
 (apply str (map-indexed #(format "%2s %-18s %7.2f\n"
				  (inc (mod %1 32)) (angle2compass %2) %2)
			 headings)))