Angles (geometric), normalization and conversion
This task is about the normalization and/or conversion of (geometric) angles using some common scales.
The angular scales that will be used in this task are:
- degree
- gradian
- mil
- radian
- Definitions
The angular scales used or referenced here:
- turn is a full turn or 360 degrees, also shown as 360º
- degree is 1/360 of a turn
- gradian is 1/400 of a turn
- mil is 1/6400 of a turn
- radian is 1/2 of a turn (or 0.5/ of a turn)
Or, to put it another way, for a full circle:
- there are 360 degrees
- there are 400 gradians
- there are 6,400 mils
- there are 2 radians (roughly equal to 6.283+)
A mil is approximately equal to a milliradian (which is 1/1000 of a radian).
There is another definition of a mil which is 1/1000 of a radian ─── this definition won't be used in this Rosetta Code task.
Turns are sometimes known or shown as:
- turn(s)
- 360 degrees
- unit circle
- a (full) circle
Degrees are sometimes known or shown as:
- degree(s)
- deg
- º (a symbol)
- ° (a symbol)
Gradians are sometimes known or shown as:
- gradian(s)
- grad(s)
- grade(s)
- gon(s)
- metric degree(s)
Mils are sometimes known or shown as:
- mil(s)
- NATO mil(s)
Radians are sometimes known or shown as:
- radian(s)
- rad(s)
- Notes
In continental Europe, the French term centigrade was used for 1/100 of a grad (grade); this was one reason for the adoption of the term Celsius to replace centigrade as the name of a temperature scale.
Gradians were commonly used in civil engineering.
Mils were normally used for artillery (elevations for ranging).
- Positive and negative angles
Although the definition of the measurement of an angle doesn't support the concept of a negative angle, it's frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference. It is this reason that negative angles will keep their sign and not be normalized to positive angles.
- Normalization
Normalization (for this Rosetta Code task) will keep the same sign, but it will reduce the magnitude to less than a full circle; in other words, less than 360º.
Normalization shouldn't change -45º to 315º,
An angle of 0º, +0º, 0.000000, or -0º should be shown as 0º.
- Task
-
- write a function (or equivalent) to do the normalization for each scale
- Suggested names:
- d2d, g2g, m2m, and r2r
- write a function (or equivalent) to convert one scale to another
- Suggested names for comparison of different computer language function names:
- d2g, d2m, and d2r for degrees
- g2d, g2m, and g2r for gradians
- m2d, m2g, and m2r for mils
- r2d, r2g, and r2m for radians
- normalize all angles used (except for the "original" or "base" angle)
- show the angles in every scale and convert them to all other scales
- show all output here on this page
For the (above) conversions, use these dozen numbers (in the order shown):
- -2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000
REXX
<lang rexx>/*REXX pgm normalizes an angle (in a scale), or converts angles from a scale to another.*/ numeric digits length( pi() ) - length(.) /*use the "length" of pi for precision.*/ parse arg x /*obtain optional arguments from the CL*/ if x= | x="," then x= '-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000' w= 20; w7= w+7 /*W: # dec digits past the dec. point.*/ @deg = 'degrees'; @grd= "gradians"; @mil = 'mils'; @rad = "radians"
- = words(x)
call hdr @deg @grd @mil @rad
do j=1 for #; y= word(x,j)
say shw(y) fmt(d2d(y)) fmt(d2g(y)) fmt(d2m(y)) fmt(d2r(y))
end /*j*/
call hdr @grd @deg @mil @rad
do j=1 for #; y= word(x,j)
say shw(y) fmt(g2g(y)) fmt(g2d(y)) fmt(g2m(y)) fmt(g2r(y))
end /*j*/
call hdr @mil @deg @grd @rad
do j=1 for #; y= word(x,j)
say shw(y) fmt(m2m(y)) fmt(m2d(y)) fmt(m2g(y)) fmt(m2r(y))
end /*j*/
call hdr @rad @deg @grd @mil
do j=1 for #; y= word(x,j)
say shw(y) fmt(r2r(y)) fmt(r2d(y)) fmt(r2g(y)) fmt(r2m(y))
end /*j*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ fmt: _= format(arg(1), 6,w); L= length(_); return left(format(_/1, 6),L) /*align a #*/ shw: _= format(arg(1),12,9); L= length(_); return left(format(_/1,12),L) /* " " "*/ pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi d2g: return d2d(arg(1)) * 10 / 9 /*convert degrees ───► gradians. */ d2m: return d2d(arg(1)) * 160 / 9 /*convert degrees ───► mils. */ d2r: return d2d(arg(1)) * pi() / 180 /*convert degrees ───► radians. */ g2d: return g2g(arg(1)) * 0.9 /*convert gradians ───► degrees. */ g2m: return g2g(arg(1)) * 16 /*convert gradians ───► mils. */ g2r: return g2g(arg(1)) * pi() * 0.005 /*convert gradians ───► radians. */ m2d: return m2m(arg(1)) * 9 * 0.00625 /*convert mils ───► degrees. */ m2g: return m2m(arg(1)) / 16 /*convert mils ───► gradians. */ m2r: return m2m(arg(1)) * pi() / 3200 /*convert mils ───► radians. */ r2d: return r2r(arg(1)) * 180 / pi() /*convert radians ───► degrees. */ r2g: return r2r(arg(1)) * 200 / pi() /*convert radians ───► gradians. */ r2m: return r2r(arg(1)) * 3200 / pi() /*convert radians ───► mils. */ d2d: return arg(1) // 360 /*normalize degrees ───► a unit circle.*/ g2g: return arg(1) // 400 /*normalize gradians───► a unit circle.*/ m2m: return arg(1) // 6400 /*normalize mils ───► a unit circle.*/ r2r: return arg(1) // (pi() * 2) /*normalize radians ───► a unit circle.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ hdr: parse arg #o #a #b #c .; _= '═'; say /* [↓] the header line*/
@n = 'normalized'
say center(#o,23 ) center(@n #o,w7) center(#a,w7 ) center(#b,w7 ) center(#c,w7 )
say center(,23,_) center(,w7, _) center(,w7,_) center(,w7,_) center(,w7,_)
return /* '↑' seperator line.*/</lang>
- output when using the default input:
degrees normalized degrees gradians mils radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2 -2 -2.22222222222222222222 -35.55555555555555555556 -0.03490658503988659154
-1 -1 -1.11111111111111111111 -17.77777777777777777778 -0.01745329251994329577
0 0 0 0 0
1 1 1.11111111111111111111 17.77777777777777777778 0.01745329251994329577
2 2 2.22222222222222222222 35.55555555555555555556 0.03490658503988659154
6.2831853 6.2831853 6.981317 111.701072 0.10966227099790767281
16 16 17.77777777777777777778 284.44444444444444444444 0.27925268031909273231
57.2957795 57.2957795 63.66197722222222222222 1018.59163555555555555556 0.9999999997716704269
359 359 398.88888888888888888889 6382.22222222222222222222 6.26573201465964318116
399 39 43.33333333333333333333 693.33333333333333333333 0.680678408277788535
6399 279 310 4960 4.86946861306417951962
1000000 280 311.11111111111111111111 4977.77777777777777777778 4.88692190558412281539
gradians normalized gradians degrees mils radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2 -2 -1.8 -32 -0.03141592653589793238
-1 -1 -0.9 -16 -0.01570796326794896619
0 0 0 0 0
1 1 0.9 16 0.01570796326794896619
2 2 1.8 32 0.03141592653589793238
6.2831853 6.2831853 5.65486677 100.5309648 0.09869604389811690553
16 16 14.4 256 0.25132741228718345908
57.2957795 57.2957795 51.56620155 916.732472 0.89999999979450338421
359 359 323.1 5744 5.63915881319367886304
399 399 359.1 6384 6.26747734391163751073
6399 399 359.1 6384 6.26747734391163751073
1000000 0 0 0 0
mils normalized mils degrees gradians radians
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2 -2 -0.1125 -0.125 -0.00196349540849362077
-1 -1 -0.05625 -0.0625 -0.00098174770424681039
0 0 0 0 0
1 1 0.05625 0.0625 0.00098174770424681039
2 2 0.1125 0.125 0.00196349540849362077
6.2831853 6.2831853 0.353429173125 0.39269908125 0.0061685027436323066
16 16 0.9 1 0.01570796326794896619
57.2957795 57.2957795 3.222887596875 3.58098621875 0.05624999998715646151
359 359 20.19375 22.4375 0.35244742582460492894
399 399 22.44375 24.9375 0.39171733399447734442
6399 6399 359.94375 399.9375 6.28220355947533966654
1000000 1600 90 100 1.57079632679489661923
radians normalized radians degrees gradians mils
═══════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════ ═══════════════════════════
-2 -2 -114.5915590261646417536 -127.32395447351626861511 -2037.18327157626029784171
-1 -1 -57.2957795130823208768 -63.66197723675813430755 -1018.59163578813014892086
0 0 0 0 0
1 1 57.2957795130823208768 63.66197723675813430755 1018.59163578813014892086
2 2 114.5915590261646417536 127.32395447351626861511 2037.18327157626029784171
6.2831853 6.2831853 359.99999958863999622298 399.99999954293332913665 6399.99999268693326618633
16 3.43362938564082704615 196.73247220931713402877 218.59163578813014892086 3497.4661726100823827337
57.2957795 0.74711173538372170767 42.80634926218202230527 47.56261029131335811697 761.00176466101372987153
359 0.85843749076357081526 49.18484519655319477054 54.64982799617021641171 874.39724793872346258733
399 3.15932564768605195371 181.01602571984602984246 201.12891746649558871385 3218.06267946392941942158
6399 2.71735729118096649006 155.69310421377129063139 172.99233801530143403488 2767.87740824482294455809
1000000 5.92562114009385143291 339.51308232087679815481 377.23675813430755350535 6035.78813014892085608558