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

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
       If testD > 32 Then testD -= 32
       Return _points(CInt(Math.Floor(testD)))
   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°