Rodrigues’ rotation formula: Difference between revisions

===Task-specific===

<lang perl>#!perl -w

print $json->encode($np) . "\n";</lang>

{{out}}

<pre>[2.23222107330823,1.39513817081764,-8.37082902490585]</pre>

===Generalized===

<lang perl>use strict;

use warnings;

use feature <say signatures>;

no warnings 'experimental::signatures';

use Math::Trig;

use List::Util 'sum';

use constant PI => 2 * atan2(1, 0);

sub norm ($v) { sqrt sum map { $_*$_ } @$v }

sub normalize ($v) { [ map { $_ / norm $v } @$v ] }

sub dotProduct ($v1, $v2) { sum map { $v1->[$_] * $v2->[$_] } 0..$#$v1 }

sub getAngle ($v1, $v2) { 180/PI * acos dotProduct($v1, $v2) / (norm($v1)*norm($v2)) }

sub mvMultiply ($m, $v) { [ map { dotProduct($_, $v) } @$m ] }

sub crossProduct ($v1, $v2) {

[$v1->[1]*$v2->[2] - $v1->[2]*$v2->[1], $v1->[2]*$v2->[0] - $v1->[0]*$v2->[2], $v1->[0]*$v2->[1] - $v1->[1]*$v2->[0]]

}

sub aRotate ( $p, $v, $a ) {

my $ca = cos $a/180*PI;

my $sa = sin $a/180*PI;

my $t = 1 - $ca;

my($x,$y,$z) = @$v;

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]

];

mvMultiply($r, $p)

}

my($v1,$v2) = ([5, -6, 4], [8, 5, -30]);

say join ' ', @{aRotate $v1, normalize(crossProduct $v1, $v2), getAngle $v1, $v2};</lang>

{{out}}

<pre>2.23222107330823 1.39513817081764 -8.37082902490585</pre>