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


include ..\Utilitys.pmt
 
( "16" 1 "16" 1 "16" ) var al
 
def difAngle    /# b1 b2 -- diff #/
    swap - 360 mod
    dup 180 > if 360 - endif
enddef
 
def test    /# b1 b2 -- #/
    over over difAngle >ps swap " " rot " " ps> 5 tolist
    al lalign ?
enddef
 
( "b1" " " "b2" " " "diff" ) al lalign ?
"---------------- ---------------- ----------------" ?
20 45 test
-45 45 test
-85 90 test
-95 90 test
-45 125 test
-45 145 test
29.4803 -88.6381 test
-78.3251 -159.036 test
-70099.74233810938 29840.67437876723 test
-165313.6666297357 33693.9894517456 test
1174.8380510598456 -154146.66490124757 test
60175.77306795546 42213.07192354373 test