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### Re: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?

by salva (Abbot)
 on Jun 26, 2012 at 21:51 UTC ( #978519=note: print w/ replies, xml ) Need Help??

Math::Vector::Real provides the method rotate_3d that already does what you want:

```use Math::Vector::Real;

\$offset = V(\$x, \$y, \$z);
\$p_rotated_1deg = \$axis->rotate_3d(1*\$pi/180, \$p - \$offset) + \$offset;

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Re^2: Polar Co-Ordinates: Rotating a 3D cartesian point around a fixed axis?
by fraizerangus (Sexton) on Jun 28, 2012 at 10:11 UTC
I've used this module before and been very impressed with it :) but where would you input the line unit vector to state the point at which you'd like to rotate? thanks
The line is defined by two vectors:

The first vector defines the direction of the line; it corresponds to \$axis on the code from my previous post.

The second vector indicates the positions of some point of the line relative to the origin (it can be any point on the line). It is what I have called \$offset.

The rotate_3d performs the rotation around a line passing through the origin and with the given direction, so to use it to rotate a vector \$p around a line that does not pass through the origin, we have to perform a translation, rotate the vector and undo the translation.

In practice, that means, subtracting the vector \$offset to \$p, performing the rotation, and then adding \$offset to the resulting value.

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