Angle difference between two bearings

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Revision as of 20:21, 12 November 2017 by Thundergnat (talk | contribs) (bold instead of italics)
Task
Angle difference between two bearings
You are encouraged to solve this task according to the task description, using any language you may know.

Finding the angle between two bearings is often confusing.[1]


Task

Find the angle which is the result of the subtraction b2 - b1,   where b1 and b2 are the bearings.

Input bearings are expressed in the range   -180   to   +180   degrees.
The result  is also expressed in the range   -180   to   +180   degrees.


Compute the angle for the following pairs:

  • 20 degrees (b1) and 45 degrees (b2)
  • -45 and 45
  • -85 and 90
  • -95 and 90
  • -45 and 125
  • -45 and 145
  • 29.4803 and -88.6381
  • -78.3251 and -159.036


Optional extra
allow the input bearings to be any (finite) value.
Test cases
  • -70099.74233810938 and 29840.67437876723
  • -165313.6666297357 and 33693.9894517456
  • 1174.8380510598456 and -154146.66490124757
  • 60175.77306795546 and 42213.07192354373



AWK

<lang AWK>

  1. syntax: GAWK -f ANGLE_DIFFERENCE_BETWEEN_TWO_BEARINGS.AWK

BEGIN { 

   fmt = "%11s %11s %11s\n"
   while (++i <= 11) { u = u "-" }
   printf(fmt,"B1","B2","DIFFERENCE")
   printf(fmt,u,u,u)
   main(20,45)
   main(-45,45)
   main(-85,90)
   main(-95,90)
   main(-45,125)
   main(-45,145)
   main(29.4803,-88.6381)
   main(-78.3251,-159.036)
   main(-70099.74233810938,29840.67437876723)
   main(-165313.6666297357,33693.9894517456)
   main(1174.8380510598456,-154146.66490124757)
   main(60175.77306795546,42213.07192354373)
   exit(0)

} function main(b1,b2) { 

   printf("%11.2f %11.2f %11.2f\n",b1,b2,angle_difference(b1,b2))

} function angle_difference(b1,b2, r) { 

   r = (b2 - b1) % 360
   if (r < -180) {
     r += 360
   }
   if (r >= 180) {
     r -= 360
   }
   return(r)

} </lang>

Output:
         B1          B2  DIFFERENCE
----------- ----------- -----------
      20.00       45.00       25.00
     -45.00       45.00       90.00
     -85.00       90.00      175.00
     -95.00       90.00     -175.00
     -45.00      125.00      170.00
     -45.00      145.00     -170.00
      29.48      -88.64     -118.12
     -78.33     -159.04      -80.71
  -70099.74    29840.67     -139.58
 -165313.67    33693.99      -72.34
    1174.84  -154146.66     -161.50
   60175.77    42213.07       37.30

C

This implementation either reads two bearings from the console or a file containing a list of bearings. Usage printed on incorrect invocation. <lang C> /*Abhishek Ghosh, 3rd October 2017*/

  1. include<stdlib.h>
  2. include<stdio.h>
  3. include<math.h>

void processFile(char* name){

int i,records; double diff,b1,b2; FILE* fp = fopen(name,"r");

fscanf(fp,"%d\n",&records);

for(i=0;i<records;i++){ fscanf(fp,"%lf%lf",&b1,&b2);

diff = fmod(b2-b1,360.0); printf("\nDifference between b2(%lf) and b1(%lf) is %lf",b2,b1,(diff<-180)?diff+360:((diff>=180)?diff-360:diff)); }

fclose(fp); }

int main(int argC,char* argV[]) { double diff;

if(argC < 2) printf("Usage : %s <bearings separated by a space OR full file name which contains the bearing list>",argV[0]); else if(argC == 2) processFile(argV[1]); else{ diff = fmod(atof(argV[2])-atof(argV[1]),360.0); printf("Difference between b2(%s) and b1(%s) is %lf",argV[2],argV[1],(diff<-180)?diff+360:((diff>=180)?diff-360:diff)); }

return 0; } </lang> Invocation and output for two bearings : 

C:\rosettaCode>bearingDiff.exe 29.4803 -88.6381
Difference between b2(-88.6381) and b1(29.4803) is -118.118400

File format for bearing list : 

<Number of records>
<Each record consisting of two bearings separated by a space>

Input file : 

12
20 45
-45 45
-85 90
-95 90
-45 125
-45 145
29.4803 -88.6381
-78.3251 -159.036
-70099.74233810938 29840.67437876723
-165313.6666297357 33693.9894517456
1174.8380510598456 -154146.66490124757
60175.77306795546 42213.07192354373

Invocation and output for above bearing list file : 

C:\rosettaCode>bearingDiff.exe bearingList.txt

Difference between b2(45.000000) and b1(20.000000) is 25.000000
Difference between b2(45.000000) and b1(-45.000000) is 90.000000
Difference between b2(90.000000) and b1(-85.000000) is 175.000000
Difference between b2(90.000000) and b1(-95.000000) is -175.000000
Difference between b2(125.000000) and b1(-45.000000) is 170.000000
Difference between b2(145.000000) and b1(-45.000000) is -170.000000
Difference between b2(-88.638100) and b1(29.480300) is -118.118400
Difference between b2(-159.036000) and b1(-78.325100) is -80.710900
Difference between b2(29840.674379) and b1(-70099.742338) is -139.583283
Difference between b2(33693.989452) and b1(-165313.666630) is -72.343919
Difference between b2(-154146.664901) and b1(1174.838051) is -161.502952
Difference between b2(42213.071924) and b1(60175.773068) is 37.298856

C++

<lang cpp>#include <cmath>

  1. include <iostream>

using namespace std;

double getDifference(double b1, double b2) { double r = fmod(b2 - b1, 360.0); if (r < -180.0) r += 360.0; if (r >= 180.0) r -= 360.0; return r; }

int main() { cout << "Input in -180 to +180 range" << endl; cout << getDifference(20.0, 45.0) << endl; cout << getDifference(-45.0, 45.0) << endl; cout << getDifference(-85.0, 90.0) << endl; cout << getDifference(-95.0, 90.0) << endl; cout << getDifference(-45.0, 125.0) << endl; cout << getDifference(-45.0, 145.0) << endl; cout << getDifference(-45.0, 125.0) << endl; cout << getDifference(-45.0, 145.0) << endl; cout << getDifference(29.4803, -88.6381) << endl; cout << getDifference(-78.3251, -159.036) << endl;

cout << "Input in wider range" << endl; cout << getDifference(-70099.74233810938, 29840.67437876723) << endl; cout << getDifference(-165313.6666297357, 33693.9894517456) << endl; cout << getDifference(1174.8380510598456, -154146.66490124757) << endl; cout << getDifference(60175.77306795546, 42213.07192354373) << endl;

return 0; }</lang>

Output:
Input in -180 to +180 range
25
90
175
-175
170
-170
170
-170
-118.118
-80.7109
Input in wider range
-139.583
-72.3439
-161.503
37.2989

Fortran

Rather than calculate angle differences and mess about with folding the results into ±180 and getting the sign right, why not use some mathematics? These days, trigonometrical functions are calculated swiftly by specialised hardware (well, microcode), and with the availability of functions working in degrees, matters are eased further nor is precision lost in converting from degrees to radians. So, the first step is to convert a bearing into an (x,y) unit vector via function CIS(t) = cos(t) + i.sin(t), which will handle all the annoyance of bearings specified in values above 360. Then, using the dot product of the two vectors allows the cosine of the angle to be known, and the cross product determines the sign.

However, this relies on the unit vectors being accurately so, and their subsequent dot product not exceeding one in size: given the rounding of results with the limited precision actual floating-point arithmetic, there may be problems. Proving that a calculation will not suffer these on a specific computer is difficult, especially as the desire for such a result may mean that any apparent pretext leading to that belief will be seized upon. Because calculations on the IBM pc and similar computers are conducted with 80-bit floating-point arithmetic, rounding errors for 64-bit results are likely to be small, but past experience leads to a "fog of fear" about the precise behaviour of floating-point arithmetic.

As it happens, the test data did not provoke any objections from the ACOSD function, but even so, a conversion to using arctan instead of arccos to recover angles would be safer. By using the four-quadrant arctan(x,y) function, the sign of the angle difference is also delivered and although that result could be in 0°-360° it turns out to be in ±180° as desired. On the other hand, the library of available functions did not include an arctan for complex parameters, so the complex number Z had to be split into its real and imaginary parts, thus requiring two appearances and to avoid repeated calculation, a temporary variable Z is needed. Otherwise, the statement could have been just T = ATAN2D(Z1*CONJG(Z2)) and the whole calculation could be effected in one statement, T = ATAN2D(CIS(90 - B1)*CONJG(CIS(90 - B2))) And, since cis(t) = exp(i.t), T = ATAN2D(EXP(CMPLX(0,90 - B1))*CONJG(EXP(CMPLX(0,90 - B2)))) - although using the arithmetic statement function does seem less intimidating.

The source style is F77 (even using the old-style arithmetic statement function) except for the convenience of generic functions taking the type of their parameters to save on the bother of DCMPLX instead of just CMPLX, etc. Floating-point constants in the test data are specified with ~D0, the exponential form that signifies double precision otherwise they would be taken as single precision values. Some compilers offer an option stating that all floating-point constants are to be taken as double precision. REAL*8 precision amounts to about sixteen decimal digits, so some of the supplied values will not be accurately represented, unless something beyond REAL*8 is available. <lang Fortran> SUBROUTINE BDIFF (B1,B2) !Difference B2 - B1, as bearings. All in degrees, not radians. 

      REAL*8 B1,B2	!Maximum precision, for large-angle folding.
      COMPLEX*16 CIS,Z1,Z2,Z	!Scratchpads.
      CIS(T) = CMPLX(COSD(T),SIND(T))	!Convert an angle into a unit vector.
       Z1 = CIS(90 - B1)	!Bearings run clockwise from north (y) around to east (x).
       Z2 = CIS(90 - B2)	!Mathematics runs counterclockwise from x (east).
       Z = Z1*CONJG(Z2)	!(Z1x,Z1y)(Z2x,-Z2y) = (Z1x.Z2x + Z1y.Z2y, Z1y.Z2x - Z1x.Z2y)
       T = ATAN2D(AIMAG(Z),REAL(Z))	!Madly, arctan(x,y) is ATAN(Y,X)!
       WRITE (6,10) B1,Z1,B2,Z2,T	!Two sets of numbers, and a result.
  10   FORMAT (2(F14.4,"(",F9.6,",",F9.6,")"),F9.3)	!Two lots, and a tail.
     END SUBROUTINE BDIFF	!Having functions in degrees saves some bother.

     PROGRAM ORIENTED
     REAL*8 B(24)	!Just prepare a wad of values.
     DATA B/20D0,45D0, -45D0,45D0, -85D0,90D0, -95D0,90D0,	!As specified.
    1      -45D0,125D0, -45D0,145D0, 29.4803D0,-88.6381D0,
    2      -78.3251D0,              -159.036D0,
    3   -70099.74233810938D0,      29840.67437876723D0,
    4  -165313.6666297357D0,       33693.9894517456D0,
    5     1174.8380510598456D0,  -154146.66490124757D0,
    6    60175.77306795546D0,      42213.07192354373D0/

     WRITE (6,1) ("B",I,"x","y", I = 1,2)	!Or, one could just list them twice.
   1 FORMAT (28X,"Bearing calculations, in degrees"//
    * 2(A13,I1,"(",A9,",",A9,")"),A9)	!Compare format 10, above.

     DO I = 1,23,2	!Step through the pairs.
       CALL BDIFF(B(I),B(I + 1))
     END DO

     END</lang>

The output shows the stages: 

                            Bearing calculations, in degrees

            B1(        x,        y)            B2(        x,        y)
       20.0000( 0.342020, 0.939693)       45.0000( 0.707107, 0.707107)   25.000
      -45.0000(-0.707107, 0.707107)       45.0000( 0.707107, 0.707107)   90.000
      -85.0000(-0.996195, 0.087156)       90.0000( 1.000000, 0.000000)  175.000
      -95.0000(-0.996195,-0.087156)       90.0000( 1.000000, 0.000000) -175.000
      -45.0000(-0.707107, 0.707107)      125.0000( 0.819152,-0.573576)  170.000
      -45.0000(-0.707107, 0.707107)      145.0000( 0.573576,-0.819152) -170.000
       29.4803( 0.492124, 0.870525)      -88.6381(-0.999718, 0.023767) -118.118
      -78.3251(-0.979312, 0.202358)     -159.0360(-0.357781,-0.933805)  -80.711
   -70099.7423( 0.984016,-0.178078)    29840.6744(-0.633734, 0.773551) -139.584
  -165313.6666(-0.959667, 0.281138)    33693.9895(-0.559023,-0.829152)  -72.340
     1174.8381( 0.996437,-0.084339)  -154146.6649(-0.918252, 0.395996) -161.510
    60175.7731( 0.826820, 0.562467)    42213.0719( 0.998565,-0.053561)   37.297

Go

Basic task solution:

One feature of this solution is that if you can rely on the input bearings being in the range -180 to 180, you don't have to use math.Mod. Another feature is the bearing type and method syntax. <lang go>package main

import "fmt"

type bearing float64

var testCases = []struct{ b1, b2 bearing }{ 

   {20, 45},
   {-45, 45},
   {-85, 90},
   {-95, 90},
   {-45, 125},
   {-45, 145},
   {29.4803, -88.6381},
   {-78.3251, -159.036},

}

func main() { 

   for _, tc := range testCases {
       fmt.Println(tc.b2.Sub(tc.b1))
   }

}

func (b2 bearing) Sub(b1 bearing) bearing { 

   switch d := b2 - b1; {
   case d < -180:
       return d + 360
   case d > 180:
       return d - 360
   default:
       return d
   }

}</lang>

Output:
25
90
175
-175
170
-170
-118.1184
-80.7109

Optional extra solution:

A feature here is that the function body is a one-liner sufficient for the task test cases. <lang go>package main

import ( 

   "fmt"
   "math"

)

var testCases = []struct{ b1, b2 float64 }{ 

   {20, 45},
   {-45, 45},
   {-85, 90},
   {-95, 90},
   {-45, 125},
   {-45, 145},
   {29.4803, -88.6381},
   {-78.3251, -159.036},
   {-70099.74233810938, 29840.67437876723},
   {-165313.6666297357, 33693.9894517456},
   {1174.8380510598456, -154146.66490124757},
   {60175.77306795546, 42213.07192354373},

}

func main() { 

   for _, tc := range testCases {
       fmt.Println(angleDifference(tc.b2, tc.b1))
   }

}

func angleDifference(b2, b1 float64) float64 { 

   return math.Mod(math.Mod(b2-b1, 360)+360+180, 360) - 180

}</lang>

Output:
25
90
175
-175
170
-170
-118.11840000000001
-80.71089999999998
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

Haskell

<lang Haskell>import Text.Printf (printf)

type Radians = Float

type Degrees = Float

angleBetweenDegrees :: Degrees -> Degrees -> Degrees angleBetweenDegrees a b = degrees $ bearingDelta (radians a) (radians b)

bearingDelta :: Radians -> Radians -> Radians bearingDelta a b -- sign * dot-product 

= sign * acos ((ax * bx) + (ay * by))
 where
   (ax, ay) = (sin a, cos a)
   (bx, by) = (sin b, cos b)
   sign -- cross-product > 0 ?
    =
     if ((ay * bx) - (by * ax)) > 0
       then 1
       else (-1)

degrees :: Radians -> Degrees degrees = (/ pi) . (180 *)

radians :: Degrees -> Radians radians = (/ 180) . (pi *)

-- TEST ----------------------------------------------------------------------- main :: IO () main = 

 putStrLn . unlines $
 uncurry
   (((<*>) . printf "%6.2f° + %6.2f°  ->  %7.2f°") <*> angleBetweenDegrees) <$>
 [ (20.0, 45.0)
 , (-45.0, 45.0)
 , (-85.0, 90.0)
 , (-95.0, 90.0)
 , (-45.0, 125.0)
 , (-45.0, 145.0)
 ]</lang>
Output:
 20.00° +  45.00°  ->    25.00°
-45.00° +  45.00°  ->    90.00°
-85.00° +  90.00°  ->   175.00°
-95.00° +  90.00°  ->  -175.00°
-45.00° + 125.00°  ->   170.00°
-45.00° + 145.00°  ->  -170.00°

J

<lang j>relativeBearing=: -&360^:(180&<)@(360 | 720 + -~)/</lang> <lang j>tests=: _99&".;._2 noun define 20 45 -45 45 -85 90 -95 90 -45 125 -45 145 29.4803 -88.6381 -78.3251 -159.036 -70099.74233810938 29840.67437876723 -165313.6666297357 33693.9894517456 1174.8380510598456 -154146.66490124757 60175.77306795546 42213.07192354373 ) 

  tests ,. relativeBearing"1 tests
     20       45       25
    _45       45       90
    _85       90      175
    _95       90     _175
    _45      125      170
    _45      145     _170
29.4803 _88.6381 _118.118

_78.3251 _159.036 _80.7109 _70099.7 29840.7 _139.583 

_165314    33694 _72.3439
1174.84  _154147 _161.503
60175.8  42213.1  37.2989</lang>

Java

Translation of: C++

<lang java>public class AngleDifference { 

   public static double getDifference(double b1, double b2) {
       double r = (b2 - b1) % 360.0;
       if (r < -180.0)
           r += 360.0;
       if (r >= 180.0)
           r -= 360.0;
       return r;
   }

   public static void main(String[] args) {
       System.out.println("Input in -180 to +180 range");
       System.out.println(getDifference(20.0, 45.0));
       System.out.println(getDifference(-45.0, 45.0));
       System.out.println(getDifference(-85.0, 90.0));
       System.out.println(getDifference(-95.0, 90.0));
       System.out.println(getDifference(-45.0, 125.0));
       System.out.println(getDifference(-45.0, 145.0));
       System.out.println(getDifference(-45.0, 125.0));
       System.out.println(getDifference(-45.0, 145.0));
       System.out.println(getDifference(29.4803, -88.6381));
       System.out.println(getDifference(-78.3251, -159.036));

       System.out.println("Input in wider range");
       System.out.println(getDifference(-70099.74233810938, 29840.67437876723));
       System.out.println(getDifference(-165313.6666297357, 33693.9894517456));
       System.out.println(getDifference(1174.8380510598456, -154146.66490124757));
       System.out.println(getDifference(60175.77306795546, 42213.07192354373));
   }

}</lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.1184
-80.7109
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

JavaScript

ES5

This approach should be reliable but it is also very inefficient.

<lang javascript>function relativeBearing(b1Rad, b2Rad) { b1y = Math.cos(b1Rad); b1x = Math.sin(b1Rad); b2y = Math.cos(b2Rad); b2x = Math.sin(b2Rad); crossp = b1y * b2x - b2y * b1x; dotp = b1x * b2x + b1y * b2y; if(crossp > 0.) return Math.acos(dotp); return -Math.acos(dotp); }

function test() { var deg2rad = 3.14159265/180.0; var rad2deg = 180.0/3.14159265; return "Input in -180 to +180 range\n" +relativeBearing(20.0*deg2rad, 45.0*deg2rad)*rad2deg+"\n" +relativeBearing(-45.0*deg2rad, 45.0*deg2rad)*rad2deg+"\n" +relativeBearing(-85.0*deg2rad, 90.0*deg2rad)*rad2deg+"\n" +relativeBearing(-95.0*deg2rad, 90.0*deg2rad)*rad2deg+"\n" +relativeBearing(-45.0*deg2rad, 125.0*deg2rad)*rad2deg+"\n" +relativeBearing(-45.0*deg2rad, 145.0*deg2rad)*rad2deg+"\n"

+relativeBearing(29.4803*deg2rad, -88.6381*deg2rad)*rad2deg+"\n" +relativeBearing(-78.3251*deg2rad, -159.036*deg2rad)*rad2deg+"\n"

+ "Input in wider range\n" +relativeBearing(-70099.74233810938*deg2rad, 29840.67437876723*deg2rad)*rad2deg+"\n" +relativeBearing(-165313.6666297357*deg2rad, 33693.9894517456*deg2rad)*rad2deg+"\n" +relativeBearing(1174.8380510598456*deg2rad, -154146.66490124757*deg2rad)*rad2deg+"\n" +relativeBearing(60175.77306795546*deg2rad, 42213.07192354373*deg2rad)*rad2deg+"\n";

}</lang>

Output:
Input in -180 to +180 range
25.000000000000004
90
174.99999999999997
-175.00000041135993
170.00000000000003
-170.00000041135996
-118.1184
-80.71089999999998
Input in wider range
-139.5833974814558
-72.34414600076728
-161.50277501127033
37.2988761562732

ES6

<lang JavaScript>(() => { 

   // bearingDelta :: Radians -> Radians -> Radians
   const bearingDelta = (ar, br) => {
       const [ax, ay] = [sin(ar), cos(ar)], [bx, by] = [sin(br), cos(br)],

       // Cross-product > 0 ?
       sign = ((ay * bx) - (by * ax)) > 0 ? +1 : -1;

       // Sign * dot-product
       return sign * acos((ax * bx) + (ay * by));
   };

   // Pi, sin, cos, acos :: Function
   const [Pi, sin, cos, acos] = ['PI', 'sin', 'cos', 'acos']
   .map(k => Math[k]),
       degRad = x => Pi * x / 180.0,
       radDeg = x => 180.0 * x / Pi;



   // TEST ------------------------------------------------------------------

   // justifyRight :: Int -> Char -> Text -> Text
   const justifyRight = (n, cFiller, strText) =>
       n > strText.length ? (
           (cFiller.repeat(n) + strText)
           .slice(-n)
       ) : strText;

   // showMap :: Degrees -> Degrees -> String
   const showMap = (da, db) =>
       justifyRight(6, ' ', `${da}° +`) +
       justifyRight(11, ' ', ` ${db}°  ->  `) +
       justifyRight(7, ' ', `${(radDeg(bearingDelta(degRad(da), degRad(db))))
           .toPrecision(4)}°`);

   return [
           [20, 45],
           [-45, 45],
           [-85, 90],
           [-95, 90],
           [-45, 125],
           [-45, 145]
       ].map(xy => showMap(...xy))
       .join('\n');

})();</lang>

Output:
 20° +  45°  ->   25.00°
-45° +  45°  ->   90.00°
-85° +  90°  ->   175.0°
-95° +  90°  ->  -175.0°
-45° + 125°  ->   170.0°
-45° + 145°  ->  -170.0°

Kotlin

<lang scala>// version 1.1.2

class Angle(d: Double) { 

   val value = when {
      d in -180.0 .. 180.0 -> d
      d > 180.0            -> (d - 180.0) % 360.0 - 180.0
      else                 -> (d + 180.0) % 360.0 + 180.0
   }

   operator fun minus(other: Angle) = Angle(this.value - other.value)

}

fun main(args: Array<String>) { 

   val anglePairs = arrayOf(
        20.0 to 45.0,
       -45.0 to 45.0,
       -85.0 to 90.0,
       -95.0 to 90.0,
       -45.0 to 125.0,
       -45.0 to 145.0,
        29.4803 to -88.6381,
       -78.3251 to -159.036,
       -70099.74233810938 to 29840.67437876723,
       -165313.6666297357 to 33693.9894517456,
        1174.8380510598456 to -154146.66490124757,
        60175.77306795546 to 42213.07192354373
   )
   println("       b1            b2           diff")
   val f = "% 12.4f  % 12.4f  % 12.4f"
   for (ap in anglePairs) {
       val diff = Angle(ap.second) - Angle(ap.first)
       println(f.format(ap.first, ap.second, diff.value))
   }

}</lang>

Output:
       b1            b2           diff
     20.0000       45.0000       25.0000
    -45.0000       45.0000       90.0000
    -85.0000       90.0000      175.0000
    -95.0000       90.0000     -175.0000
    -45.0000      125.0000      170.0000
    -45.0000      145.0000     -170.0000
     29.4803      -88.6381     -118.1184
    -78.3251     -159.0360      -80.7109
 -70099.7423    29840.6744     -139.5833
-165313.6666    33693.9895      -72.3439
   1174.8381  -154146.6649     -161.5030
  60175.7731    42213.0719       37.2989

Perl 6

Works with: Rakudo version 2016.11

<lang perl6>sub infix:<∠> (Real $b1, Real $b2) { 

  (my $b = ($b2 - $b1 + 720) % 360) > 180 ?? $b - 360 !! $b;

}

  1. TESTING

for 20, 45, 

  -45, 45,
  -85, 90,
  -95, 90,
  -45, 125,
  -45, 145,
  29.4803, -88.6381,
  -78.3251, -159.036,
  -70099.74233810938, 29840.67437876723,
  -165313.6666297357, 33693.9894517456,
  1174.8380510598456, -154146.66490124757,
  60175.77306795546, 42213.07192354373

 -> $b1, $b2 { say "$b1 ∠ $b2 = ", $b1 ∠ $b2 }</lang>
Output:
20 ∠ 45 = 25
-45 ∠ 45 = 90
-85 ∠ 90 = 175
-95 ∠ 90 = -175
-45 ∠ 125 = 170
-45 ∠ 145 = -170
29.4803 ∠ -88.6381 = -118.1184
-78.3251 ∠ -159.036 = -80.7109
-70099.74233810938 ∠ 29840.67437876723 = -139.58328312339
-165313.6666297357 ∠ 33693.9894517456 = -72.3439185187
1174.8380510598456 ∠ -154146.66490124757 = -161.5029523074156
60175.77306795546 ∠ 42213.07192354373 = 37.29885558827

Python

Translation of: C++

<lang python>from __future__ import print_function

def getDifference(b1, b2): r = (b2 - b1) % 360.0 # Python modulus has same sign as divisor, which is positive here, # so no need to consider negative case if r >= 180.0: r -= 360.0 return r

if __name__ == "__main__": print ("Input in -180 to +180 range") print (getDifference(20.0, 45.0)) print (getDifference(-45.0, 45.0)) print (getDifference(-85.0, 90.0)) print (getDifference(-95.0, 90.0)) print (getDifference(-45.0, 125.0)) print (getDifference(-45.0, 145.0)) print (getDifference(-45.0, 125.0)) print (getDifference(-45.0, 145.0)) print (getDifference(29.4803, -88.6381)) print (getDifference(-78.3251, -159.036))

print ("Input in wider range") print (getDifference(-70099.74233810938, 29840.67437876723)) print (getDifference(-165313.6666297357, 33693.9894517456)) print (getDifference(1174.8380510598456, -154146.66490124757)) print (getDifference(60175.77306795546, 42213.07192354373))</lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.11840000000001
-80.71089999999998
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

Racket

see my comments in discussion regards bearing-heading or vice versa

<lang racket>#lang racket (define (% a b) (- a (* b (truncate (/ a b)))))

(define (bearing- bearing heading) 

 (- (% (+ (% (- bearing heading) 360) 540) 360) 180))

(module+ main 

 (bearing- 20 45)
 (bearing- -45 45)
 (bearing- -85 90)
 (bearing- -95 90)
 (bearing- -45 125)
 (bearing- -45 145)
 (bearing- 29.4803 -88.6381)
 (bearing- -78.3251 -159.036)

 (bearing- -70099.74233810938 29840.67437876723)
 (bearing- -165313.6666297357 33693.9894517456)
 (bearing- 1174.8380510598456 -154146.66490124757)
 (bearing- 60175.77306795546 42213.07192354373))

(module+ test 

 (require rackunit)

 (check-equal? (% 7.5 10) 7.5)
 (check-equal? (% 17.5 10) 7.5)
 (check-equal? (% -7.5 10) -7.5)
 (check-equal? (% -17.5 10) -7.5))</lang>
Output:
-25
-90
-175
175
-170
170
118.11839999999995
80.71090000000004
139.58328312338563
72.34391851868713
161.50295230740448
-37.29885558826936

REXX

A little extra coding was added for a better visual presentation;   the angles were centered,   the answers were aligned. <lang rexx>/*REXX pgm calculates the difference between 2 angles (degrees), normalizes the result. */ numeric digits 25 /*use enough decimal diigits for angles*/ call show 20, 45 /*display the angular difference (deg).*/ call show -45, 45 /* " " " " " */ call show -85, 90 /* " " " " " */ call show -95, 90 /* " " " " " */ call show -45, 125 /* " " " " " */ call show 45, 145 /* " " " " " */ call show 29.4803, -88.6361 /* " " " " " */ call show -78.3251, -159.036 /* " " " " " */ call show -70099.74233810938, 29840.67437876723 /* " " " " " */ call show -165313.6666297357, 33693.9894517456 /* " " " " " */ call show 1174.8380510598456,-154146.66490124757 /* " " " " " */ call show 60175.773067955546, 42213.07192354373 /* " " " " " */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ show: parse arg a,b; d=digits(); $='º' /*obtain the 2 angles (are in degrees).*/ 

     x=format( ( ( ((b-a) // 360) + 540) // 360) - 180, 4, d-4) /*compute and format.  */
     if pos(., x)\==0  then x=strip( strip(x, 'T', 0), "T", .)  /*strip trailing chaff.*/
     say center(a || $, d)      '─'      center(b || $, d)         "───►"         x || $
     return                                     /* [↑]  display the angular difference.*/</lang>

output 

           20º            ─            45º            ───►   25º
          -45º            ─            45º            ───►   90º
          -85º            ─            90º            ───►  175º
          -95º            ─            90º            ───► -175º
          -45º            ─           125º            ───►  170º
           45º            ─           145º            ───►  100º
        29.4803º          ─         -88.6361º         ───► -118.1164º
        -78.3251º         ─         -159.036º         ───►  -80.7109º
   -70099.74233810938º    ─    29840.67437876723º     ───► -139.58328312339º
   -165313.6666297357º    ─     33693.9894517456º     ───►  -72.3439185187º
   1174.8380510598456º    ─   -154146.66490124757º    ───► -161.5029523074156º
   60175.773067955546º    ─    42213.07192354373º     ───►   37.298855588184º

Ring

<lang ring>

  1. Project : Angle difference between two bearings
  2. Date  : 2017/10/06
  3. Author  : Gal Zsolt (~ CalmoSoft ~)
  4. Email  : <calmosoft@gmail.com>

decimals(4) see "Input in -180 to +180 range:" + nl see getDifference(20.0, 45.0) + nl see getDifference(-45.0, 45.0) + nl see getDifference(-85.0, 90.0) + nl see getDifference(-95.0, 90.0) + nl see getDifference(-45.0, 125.0) + nl see getDifference(-45.0, 145.0) + nl see getDifference(-45.0, 125.0) + nl see getDifference(-45.0, 145.0) + nl see getDifference(29.4803, -88.6381) + nl see getDifference(-78.3251, -159.036) + nl

func getDifference(b1, b2) 

    r = (b2 - b1) % 360.0
    if r >= 180.0
       r = r - 360.0
    end
    return r

</lang> Output: 

Input in -180 to +180 range:
25
90
175
-175
170
-170
170
-170
-118.1184
-80.7109

Ruby

Translation of: C++

<lang ruby>def getDifference(b1, b2) r = (b2 - b1) % 360.0 # Ruby modulus has same sign as divisor, which is positive here, # so no need to consider negative case if r >= 180.0 r -= 360.0 end return r end

if __FILE__ == $PROGRAM_NAME puts "Input in -180 to +180 range" puts getDifference(20.0, 45.0) puts getDifference(-45.0, 45.0) puts getDifference(-85.0, 90.0) puts getDifference(-95.0, 90.0) puts getDifference(-45.0, 125.0) puts getDifference(-45.0, 145.0) puts getDifference(-45.0, 125.0) puts getDifference(-45.0, 145.0) puts getDifference(29.4803, -88.6381) puts getDifference(-78.3251, -159.036)

puts "Input in wider range" puts getDifference(-70099.74233810938, 29840.67437876723) puts getDifference(-165313.6666297357, 33693.9894517456) puts getDifference(1174.8380510598456, -154146.66490124757) puts getDifference(60175.77306795546, 42213.07192354373) end</lang>

Output:
Input in -180 to +180 range
25.0
90.0
175.0
-175.0
170.0
-170.0
170.0
-170.0
-118.11840000000001
-80.71089999999998
Input in wider range
-139.58328312338563
-72.34391851868713
-161.50295230740448
37.29885558826936

Sidef

<lang ruby>func bearingAngleDiff(b1, b2) { 

   (var b = ((b2 - b1 + 720) % 360)) > 180 ? (b - 360) : b

}

printf("%25s %25s %25s\n", "B1", "B2", "Difference") printf("%25s %25s %25s\n", "-"*20, "-"*20, "-"*20)


for b1,b2 in ([ 

                      20,                       45
                     -45,                       45
                     -85,                       90
                     -95,                       90
                     -45,                      125
                     -45,                      145
                 29.4803,                 -88.6381
                -78.3251,                 -159.036
      -70099.74233810938,        29840.67437876723
      -165313.6666297357,         33693.9894517456
      1174.8380510598456,      -154146.66490124757
       60175.77306795546,        42213.07192354373
   ].slices(2)

) { 

   printf("%25s %25s %25s\n", b1, b2, bearingAngleDiff(b1, b2))

}</lang>

Output:
                       B1                        B2                Difference
     --------------------      --------------------      --------------------
                       20                        45                        25
                      -45                        45                        90
                      -85                        90                       175
                      -95                        90                      -175
                      -45                       125                       170
                      -45                       145                      -170
                  29.4803                  -88.6381                 -118.1184
                 -78.3251                  -159.036                  -80.7109
       -70099.74233810938         29840.67437876723          -139.58328312339
       -165313.6666297357          33693.9894517456            -72.3439185187
       1174.8380510598456       -154146.66490124757        -161.5029523074156
        60175.77306795546         42213.07192354373            37.29885558827

zkl

Translation of: Perl 6

<lang zkl>fcn bearingAngleDiff(b1,b2){ // -->Float, b1,b2 can be int or float 

 ( (b:=(0.0 + b2 - b1 + 720)%360) > 180 ) and b - 360 or b;

}</lang> <lang zkl>T( 20,45, -45,45, -85,90, -95,90, -45,125, -45,145 ) .pump(Console.println,Void.Read, 

     fcn(b1,b2){ "%.1f\UB0; + %.1f\UB0; = %.1f\UB0;"
                 .fmt(b1,b2,bearingAngleDiff(b1,b2)) });</lang>
Output:
20.0° + 45.0° = 25.0°
-45.0° + 45.0° = 90.0°
-85.0° + 90.0° = 175.0°
-95.0° + 90.0° = -175.0°
-45.0° + 125.0° = 170.0°
-45.0° + 145.0° = -170.0°

References

  1. ↑ [1]
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