Box the compass

Box the compass is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Avast me hearties!

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

1. Create a function that takes a heading in degrees and returns the correct 32-point compass heading.
2. 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 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).

Note

• The headings and indices can be calculated from this pseudocode:

for i in 0..33 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

J

<lang j>require'strings' cardinal=: ;:'N Ne E Se S Sw W Nw N' rplc;:'N North E East e east S South W West w west' tween=:1 :'[,m,tolower@]' by=:' by 'tween points=:,2 ([;by;'-'tween;by~)&>/\ cardinal deg2pnt=: points {~ 32 | 0.5 <.@+ %&11.25</lang>

As for the required example, sometimes it's simpler to do just a small bit of "extra" work:

<lang j> ((;@~."1@deg2pnt),.' ',.":) _5.62 0 5.62 +/~11.25 * i.33 North _5.62 0 5.62 North by northeast 5.63 11.25 16.87 North-northeast 16.88 22.5 28.12 Northeast by north 28.13 33.75 39.37 Northeast 39.38 45 50.62 Northeast by east 50.63 56.25 61.87 Northeast-east 61.88 67.5 73.12 East by northeast 73.13 78.75 84.37 East 84.38 90 95.62 East by southeast 95.63 101.25 106.87 East-southeast 106.88 112.5 118.12 Southeast by east 118.13 123.75 129.37 Southeast 129.38 135 140.62 Southeast by south 140.63 146.25 151.87 Southeast-south 151.88 157.5 163.12 South by southeast 163.13 168.75 174.37 South 174.38 180 185.62 South by southwest 185.63 191.25 196.87 South-southwest 196.88 202.5 208.12 Southwest by south 208.13 213.75 219.37 Southwest 219.38 225 230.62 Southwest by west 230.63 236.25 241.87 Southwest-west 241.88 247.5 253.12 West by southwest 253.13 258.75 264.37 West 264.38 270 275.62 West by northwest 275.63 281.25 286.87 West-northwest 286.88 292.5 298.12 Northwest by west 298.13 303.75 309.37 Northwest 309.38 315 320.62 Northwest by north 320.63 326.25 331.87 Northwest-north 331.88 337.5 343.12 North by northwest 343.13 348.75 354.37 North 354.38 360 365.62</lang>

Here, I compute the name for each of the numbers, and then find the unique list of names represented in each row (which is always only one name) and convert the whole thing to characters.

Python

<lang python>majors = 'north east south west'.split() majors = majors + majors # no need for modulo later quarter1 = 'N,N by E,N-NE,NE by N,NE,NE by E,E-NE,E by N'.split(',') quarter2 = [p.replace('NE','EN') for p in quarter1]

def degrees2compasspoint(d):

   d = (d % 360) + 360/64
   majorindex, minor = divmod(d, 90.)
   majorindex = int(majorindex)
   minorindex  = int( (minor*4) // 45 )
   p1, p2 = majors[majorindex: majorindex+2]
   if p1 in {'north', 'south'}:
       q = quarter1
   else:
       q = quarter2
   return q[minorindex].replace('N', p1).replace('E', p2).capitalize()

for i in range(33):

   d = i * 11.25
   m = i % 3
   if   m == 1: d += 5.62
   elif m == 2: d -= 5.62
   n = i % 32 + 1
   print( '%2i %-18s %7.2f°' % (n, degrees2compasspoint(d), d) )</lang>

Output

 1 North                 0.00°
 2 North by east        16.87°
 3 North-northeast      16.88°
 4 Northeast by north   33.75°
 5 Northeast            50.62°
 6 Northeast by east    50.63°
 7 East-northeast       67.50°
 8 East by north        84.37°
 9 East                 84.38°
10 East by south       101.25°
11 East-southeast      118.12°
12 Southeast by east   118.13°
13 Southeast           135.00°
14 Southeast by south  151.87°
15 South-southeast     151.88°
16 South by east       168.75°
17 South               185.62°
18 South by west       185.63°
19 South-southwest     202.50°
20 Southwest by south  219.37°
21 Southwest           219.38°
22 Southwest by west   236.25°
23 West-southwest      253.12°
24 West by south       253.13°
25 West                270.00°
26 West by north       286.87°
27 West-northwest      286.88°
28 Northwest by west   303.75°
29 Northwest           320.62°
30 Northwest by north  320.63°
31 North-northwest     337.50°
32 North by west       354.37°
 1 North               354.38°

Tcl

<lang tcl>proc angle2compass {angle} {

   set 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

   }
   set unpack {N north E east W west S south b " by "}

   # Compute the width of each compass segment
   set sep [expr {360.0 / [llength $dirs]}]

   # Work out which segment contains the compass angle
   set dir [expr {round((fmod($angle + $sep/2, 360) - $sep/2) / $sep)}]

   # Convert to a named direction
   return [string totitle [string map $unpack [lindex $dirs $dir]]]

}

for {set i 0} {$i < 33} {incr i} {

   set heading [expr {$i * 11.25}]
   if {$i % 3 == 1} {set heading [expr {$heading + 5.62}]}
   if {$i % 3 == 2} {set heading [expr {$heading - 5.62}]}
   set index [expr {$i % 32 + 1}]
   puts [format "%2i %-18s %7.2f°" $index [angle2compass $heading] $heading]

}</lang> Output:

 1 North                 0.00°
 2 North by east        16.87°
 3 North-northeast      16.88°
 4 Northeast by north   33.75°
 5 Northeast            50.62°
 6 Northeast by east    50.63°
 7 East-northeast       67.50°
 8 East by north        84.37°
 9 East                 84.38°
10 East by south       101.25°
11 East-southeast      118.12°
12 Southeast by east   118.13°
13 Southeast           135.00°
14 Southeast by south  151.87°
15 South-southeast     151.88°
16 South by east       168.75°
17 South               185.62°
18 South by west       185.63°
19 South-southwest     202.50°
20 Southwest by south  219.37°
21 Southwest           219.38°
22 Southwest by west   236.25°
23 West-southwest      253.12°
24 West by south       253.13°
25 West                270.00°
26 West by north       286.87°
27 West-northwest      286.88°
28 Northwest by west   303.75°
29 Northwest           320.62°
30 Northwest by north  320.63°
31 North-northwest     337.50°
32 North by west       354.37°
 1 North               354.38°

Visual Basic .NET

<lang visual basic .net>Module BoxingTheCompass

   Dim _points(32) As String

   Sub Main()
       BuildPoints()

       Dim heading As Double = 0D

       For i As Integer = 0 To 32
           heading = i * 11.25
           Select Case i Mod 3
               Case 1
                   heading += 5.62
               Case 2
                   heading -= 5.62
           End Select

           Console.WriteLine("{0,2}: {1,-18} {2,6:F2}°", (i Mod 32) + 1, InitialUpper(GetPoint(heading)), heading)
       Next
   End Sub

   Private Sub BuildPoints()
       Dim cardinal As String() = New String() {"north", "east", "south", "west"}
       Dim pointDesc As String() = New String() {"1", "1 by 2", "1-C", "C by 1", "C", "C by 2", "2-C", "2 by 1"}

       Dim str1, str2, strC As String

       For i As Integer = 0 To 3
           str1 = cardinal(i)
           str2 = cardinal((i + 1) Mod 4)
           strC = IIf(str1 = "north" Or str1 = "south", str1 & str2, str2 & str1)
           For j As Integer = 0 To 7
               _points(i * 8 + j) = pointDesc(j).Replace("1", str1).Replace("2", str2).Replace("C", strC)
           Next
       Next
   End Sub

   Private Function InitialUpper(ByVal s As String) As String
       Return s.Substring(0, 1).ToUpper() & s.Substring(1)
   End Function

   Private Function GetPoint(ByVal Degrees As Double) As String
       Dim testD As Double = (Degrees / 11.25) + 0.5
       Return _points(CInt(Math.Floor(testD Mod 32)))
   End Function

End Module </lang> Output:

 1: North                0.00°
 2: North by east       16.87°
 3: North-northeast     16.88°
 4: Northeast by north  33.75°
 5: Northeast           50.62°
 6: Northeast by east   50.63°
 7: East-northeast      67.50°
 8: East by north       84.37°
 9: East                84.38°
10: East by south      101.25°
11: East-southeast     118.12°
12: Southeast by east  118.13°
13: Southeast          135.00°
14: Southeast by south 151.87°
15: South-southeast    151.88°
16: South by east      168.75°
17: South              185.62°
18: South by west      185.63°
19: South-southwest    202.50°
20: Southwest by south 219.37°
21: Southwest          219.38°
22: Southwest by west  236.25°
23: West-southwest     253.12°
24: West by south      253.13°
25: West               270.00°
26: West by north      286.87°
27: West-northwest     286.88°
28: Northwest by west  303.75°
29: Northwest          320.62°
30: Northwest by north 320.63°
31: North-northwest    337.50°
32: North by west      354.37°
 1: North              354.38°