Re: [Algorithms] Rotation about arbitrary axis

[Jamie F. <j.f...@re...>]

Quaternions are the baby :)

Unit quaternions can be very simply mapped to / from an axis and angle.

If your axis of rotation is ( x , y , z ) and your angle is r, an associated
quaternion is

{ x * sin ( r / 2 ) , y * sin ( r / 2 ) , z * sin ( r / 2 ) , cos ( r / 2 ) }

There are 2 quaternions for any given axis and angle, because rotating around
the negative vector by the negative angle is equivalent to the original
rotation.

But I don't have any code for the stuff I can give away, I'm afraid :)

I'm sure there are plenty of references to appropriate stuff in the archives of
the list... if they're working. :)

Jamie


Pierre Terdiman wrote:

> Hi,
>
> Since I needed a piece of code to do that I searched the web and found:
> http://www.iuk.tu-harburg.de/hypgraph/modeling/mod_tran/3drota.htm
>
> I used the final matrix at the bottom of the page, but it seems to fail when
> the arbitrary axis actually is the Z axis. The third column gets erased
> where it should at least contain a 1. This is obvious when looking at the
> provided matrix, since the third column of the third row depends on the
> rotation angle - and of course if the input axis already is the Z axis, it
> shouldn't.
>
> Now, it sounds normal regarding the underlying method (mapping the rotation
> axis to Z, etc). But I wonder whether there's an easy way to perform a real
> arbitrary rotation about any arbitrary axis without using different code
> paths according to the input axis.
>
> I think it can probably be done by introducing quaternions or better,
> angle-axis, in the story. But err.... maybe there's something simpler.
>
> Pierre
>
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