Angles (geometric), normalization and conversion
my @units =
{ code => 'd', name => 'degrees' , number => 360 },
{ code => 'g', name => 'gradians', number => 400 },
{ code => 'm', name => 'mills' , number => 6400 },
{ code => 'r', name => 'radians' , number => tau },
;
my Code %cvt = (@units X @units).map: -> ($a, $b) {
"{$a.<code>}2{$b.<code>}" => sub ($angle) {
my $norm = $angle % $a.<number>
- ( $a.<number> if $angle < 0 );
$norm * $b.<number> / $a.<number>
}
}
say ' Angle Unit ', @units».<name>».tc.fmt('%11s');
for -2, -1, 0, 1, 2, tau, 16, 360/tau, 360-1, 400-1, 6400-1, 1_000_000 -> $angle {
say '';
for @units -> $from {
my @sub_keys = @units.map: { "{$from.<code>}2{.<code>}" };
my @results = %cvt{@sub_keys}».($angle);
say join ' ', $angle .fmt('%10g'),
$from.<name>.fmt('%-8s'),
@results .fmt('%11g');
}
}
Output:
Angle Unit Degrees Gradians Mills Radians
-2 degrees -2 -2.22222 -35.5556 -0.0349066
-2 gradians -1.8 -2 -32 -0.0314159
-2 mills -0.1125 -0.125 -2 -0.0019635
-2 radians -114.592 -127.324 -2037.18 -2
-1 degrees -1 -1.11111 -17.7778 -0.0174533
-1 gradians -0.9 -1 -16 -0.015708
-1 mills -0.05625 -0.0625 -1 -0.000981748
-1 radians -57.2958 -63.662 -1018.59 -1
0 degrees 0 0 0 0
0 gradians 0 0 0 0
0 mills 0 0 0 0
0 radians 0 0 0 0
1 degrees 1 1.11111 17.7778 0.0174533
1 gradians 0.9 1 16 0.015708
1 mills 0.05625 0.0625 1 0.000981748
1 radians 57.2958 63.662 1018.59 1
2 degrees 2 2.22222 35.5556 0.0349066
2 gradians 1.8 2 32 0.0314159
2 mills 0.1125 0.125 2 0.0019635
2 radians 114.592 127.324 2037.18 2
6.28319 degrees 6.28319 6.98132 111.701 0.109662
6.28319 gradians 5.65487 6.28319 100.531 0.098696
6.28319 mills 0.353429 0.392699 6.28319 0.0061685
6.28319 radians 0 0 0 0
16 degrees 16 17.7778 284.444 0.279253
16 gradians 14.4 16 256 0.251327
16 mills 0.9 1 16 0.015708
16 radians 196.732 218.592 3497.47 3.43363
57.2958 degrees 57.2958 63.662 1018.59 1
57.2958 gradians 51.5662 57.2958 916.732 0.9
57.2958 mills 3.22289 3.58099 57.2958 0.05625
57.2958 radians 42.8064 47.5626 761.002 0.747112
359 degrees 359 398.889 6382.22 6.26573
359 gradians 323.1 359 5744 5.63916
359 mills 20.1938 22.4375 359 0.352447
359 radians 49.1848 54.6498 874.397 0.858437
399 degrees 39 43.3333 693.333 0.680678
399 gradians 359.1 399 6384 6.26748
399 mills 22.4438 24.9375 399 0.391717
399 radians 181.016 201.129 3218.06 3.15933
6399 degrees 279 310 4960 4.86947
6399 gradians 359.1 399 6384 6.26748
6399 mills 359.944 399.938 6399 6.2822
6399 radians 155.693 172.992 2767.88 2.71736
1000000 degrees 280 311.111 4977.78 4.88692
1000000 gradians 0 0 0 0
1000000 mills 90 100 1600 1.5708
1000000 radians 339.513 377.237 6035.79 5.92562
Alternately, implemented as a series of postfix operators:
(Much of the complexity is due to the requirement that negative angles must normalize to a negative number.)
sub postfix:<t>( $t ) { my $a = $t % 1 * τ; $t >=0 ?? $a !! $a - τ }
sub postfix:<d>( $d ) { my $a = $d % 360 * τ / 360; $d >=0 ?? $a !! $a - τ }
sub postfix:<g>( $g ) { my $a = $g % 400 * τ / 400; $g >=0 ?? $a !! $a - τ }
sub postfix:<m>( $m ) { my $a = $m % 6400 * τ / 6400; $m >=0 ?? $a !! $a - τ }
sub postfix:<r>( $r ) { my $a = $r % τ; $r >=0 ?? $a !! $a - τ }
sub postfix:«->t» ($angle) { my $a = $angle / τ; ($angle < 0 and $a == -1) ?? -0 !! $a }
sub postfix:«->d» ($angle) { my $a = $angle / τ * 360; ($angle < 0 and $a == -360) ?? -0 !! $a }
sub postfix:«->g» ($angle) { my $a = $angle / τ * 400; ($angle < 0 and $a == -400) ?? -0 !! $a }
sub postfix:«->m» ($angle) { my $a = $angle / τ * 6400; ($angle < 0 and $a == -6400) ?? -0 !! $a }
sub postfix:«->r» ($angle) { my $a = $angle; ($angle < 0 and $a == -τ) ?? -0 !! $a }
for <-2 -1 0 1 2 6.2831853 16 57.2957795 359 399 6399 1000000> -> $a {
say '';
say ' Quantity Unit ', <turns degrees gradians mils radians>.fmt('%15s');
for 'turns', &postfix:«t», 'degrees', &postfix:«d», 'gradians', &postfix:«g»,
'mils', &postfix:«m», 'radians', &postfix:«r»
-> $unit, &f {
printf "%10s %-10s %15s %15s %15s %15s %15s\n", $a, $unit,
|($a.&f->t, $a.&f->d, $a.&f->g, $a.&f->m, $a.&f->r)».round(.00000001);
}
}
Output:
Quantity Unit turns degrees gradians mils radians
-2 turns 0 0 0 0 0
-2 degrees -0.00555556 -2 -2.22222222 -35.55555556 -0.03490659
-2 gradians -0.005 -1.8 -2 -32 -0.03141593
-2 mils -0.000313 -0.1125 -0.125 -2 -0.0019635
-2 radians -0.31830989 -114.59155903 -127.32395447 -2037.18327158 -2
Quantity Unit turns degrees gradians mils radians
-1 turns 0 0 0 0 0
-1 degrees -0.00277778 -1 -1.11111111 -17.77777778 -0.01745329
-1 gradians -0.0025 -0.9 -1 -16 -0.01570796
-1 mils -0.000156 -0.05625 -0.0625 -1 -0.00098175
-1 radians -0.15915494 -57.29577951 -63.66197724 -1018.59163579 -1
Quantity Unit turns degrees gradians mils radians
0 turns 0 0 0 0 0
0 degrees 0 0 0 0 0
0 gradians 0 0 0 0 0
0 mils 0 0 0 0 0
0 radians 0 0 0 0 0
Quantity Unit turns degrees gradians mils radians
1 turns 0 0 0 0 0
1 degrees 0.00277778 1 1.11111111 17.77777778 0.01745329
1 gradians 0.0025 0.9 1 16 0.01570796
1 mils 0.000156 0.05625 0.0625 1 0.00098175
1 radians 0.15915494 57.29577951 63.66197724 1018.59163579 1
Quantity Unit turns degrees gradians mils radians
2 turns 0 0 0 0 0
2 degrees 0.00555556 2 2.22222222 35.55555556 0.03490659
2 gradians 0.005 1.8 2 32 0.03141593
2 mils 0.000313 0.1125 0.125 2 0.0019635
2 radians 0.31830989 114.59155903 127.32395447 2037.18327158 2
Quantity Unit turns degrees gradians mils radians
6.2831853 turns 0.2831853 101.946708 113.27412 1812.38592 1.77930572
6.2831853 degrees 0.01745329 6.2831853 6.981317 111.701072 0.10966227
6.2831853 gradians 0.01570796 5.65486677 6.2831853 100.5309648 0.09869604
6.2831853 mils 0.00098175 0.35342917 0.39269908 6.2831853 0.0061685
6.2831853 radians 1 359.99999959 399.99999954 6399.99999269 6.2831853
Quantity Unit turns degrees gradians mils radians
16 turns 0 0 0 0 0
16 degrees 0.04444444 16 17.77777778 284.44444444 0.27925268
16 gradians 0.04 14.4 16 256 0.25132741
16 mils 0.0025 0.9 1 16 0.01570796
16 radians 0.54647909 196.73247221 218.59163579 3497.46617261 3.43362939
Quantity Unit turns degrees gradians mils radians
57.2957795 turns 0.2957795 106.48062 118.3118 1892.9888 1.85843741
57.2957795 degrees 0.15915494 57.2957795 63.66197722 1018.59163556 1
57.2957795 gradians 0.14323945 51.56620155 57.2957795 916.732472 0.9
57.2957795 mils 0.00895247 3.2228876 3.58098622 57.2957795 0.05625
57.2957795 radians 0.11890653 42.80634926 47.56261029 761.00176466 0.74711174
Quantity Unit turns degrees gradians mils radians
359 turns 0 0 0 0 0
359 degrees 0.99722222 359 398.88888889 6382.22222222 6.26573201
359 gradians 0.8975 323.1 359 5744 5.63915881
359 mils 0.056094 20.19375 22.4375 359 0.35244743
359 radians 0.13662457 49.1848452 54.649828 874.39724794 0.85843749
Quantity Unit turns degrees gradians mils radians
399 turns 0 0 0 0 0
399 degrees 0.10833333 39 43.33333333 693.33333333 0.68067841
399 gradians 0.9975 359.1 399 6384 6.26747734
399 mils 0.062344 22.44375 24.9375 399 0.39171733
399 radians 0.50282229 181.01602572 201.12891747 3218.06267946 3.15932565
Quantity Unit turns degrees gradians mils radians
6399 turns 0 0 0 0 0
6399 degrees 0.775 279 310 4960 4.86946861
6399 gradians 0.9975 359.1 399 6384 6.26747734
6399 mils 0.999844 359.94375 399.9375 6399 6.28220356
6399 radians 0.43248085 155.69310421 172.99233802 2767.87740825 2.71735729
Quantity Unit turns degrees gradians mils radians
1000000 turns 0 0 0 0 0
1000000 degrees 0.77777778 280 311.11111111 4977.77777778 4.88692191
1000000 gradians 0 0 0 0 0
1000000 mils 0.25 90 100 1600 1.57079633
1000000 radians 0.9430919 339.51308233 377.23675814 6035.78813022 5.92562114