Rodrigues’ rotation formula: Difference between revisions
Moved Perl entry into correct alphabetical order.
(Added Algol 68) |
(Moved Perl entry into correct alphabetical order.) |
||
Line 54:
2.232221 1.395138 -8.370829
</pre>
=={{header|JavaScript}}==
Line 207 ⟶ 145:
{{out}}
<pre>(x: 2.232221073308228, y: 1.395138170817643, z: -8.370829024905852)</pre>
=={{header|Perl}}==
<lang perl>
#!perl -w
use strict;
use Math::Trig; # acos
use JSON;
use constant PI => 3.14159265358979;
# Rodrigues' formula for vector rotation - see https://stackoverflow.com/questions/42358356/rodrigues-formula-for-vector-rotation
sub norm {
my($v)=@_;
return ($v->[0]*$v->[0] + $v->[1]*$v->[1] + $v->[2]*$v->[2]) ** 0.5;
}
sub normalize {
my($v)=@_;
my $length = &norm($v);
return [$v->[0]/$length, $v->[1]/$length, $v->[2]/$length];
}
sub dotProduct {
my($v1, $v2)=@_;
return $v1->[0]*$v2->[0] + $v1->[1]*$v2->[1] + $v1->[2]*$v2->[2];
}
sub crossProduct {
my($v1, $v2)=@_;
return [$v1->[1]*$v2->[2] - $v1->[2]*$v2->[1], $v1->[2]*$v2->[0] - $v1->[0]*$v2->[2], $v1->[0]*$v2->[1] - $v1->[1]*$v2->[0]];
}
sub getAngle {
my($v1, $v2)=@_;
return acos(&dotProduct($v1, $v2) / (&norm($v1)*&norm($v2)))*180/PI; # remove *180/PI to go back to radians
}
sub matrixMultiply {
my($matrix, $v)=@_;
return [&dotProduct($matrix->[0], $v), &dotProduct($matrix->[1], $v), &dotProduct($matrix->[2], $v)];
}
sub aRotate {
my($p, $v, $a)=@_; # point-to-rotate, vector-to-rotate-about, angle(degrees)
my $ca = cos($a/180*PI); # remove /180*PI to go back to radians
my $sa = sin($a/180*PI);
my $t=1-$ca;
my($x,$y,$z)=($v->[0], $v->[1], $v->[2]);
my $r = [
[$ca + $x*$x*$t, $x*$y*$t - $z*$sa, $x*$z*$t + $y*$sa],
[$x*$y*$t + $z*$sa, $ca + $y*$y*$t, $y*$z*$t - $x*$sa],
[$z*$x*$t - $y*$sa, $z*$y*$t + $x*$sa, $ca + $z*$z*$t]
];
return &matrixMultiply($r, $p);
}
my $v1 = [5,-6,4];
my $v2 = [8,5,-30];
my $a = &getAngle($v1, $v2);
my $cp = &crossProduct($v1, $v2);
my $ncp = &normalize($cp);
my $np = &aRotate($v1, $ncp, $a);
my $json=JSON->new->canonical;
print $json->encode($np) . "\n"; # => [ 2.23222107330823, 1.39513817081764, -8.37082902490585 ] = ok.
</lang>
=={{header|Wren}}==
| |||