RE: [Algorithms] Rotation Matrices

[Tom F. <to...@mu...>]

There is indeed a difference. Think of rotating an object 90 degrees about
the X, then 90 degrees about the Y. Now do it the other way. The object will
be pointing in completely different directions depending which way you do
it.

Only 2D rotations commute. 3D rotations don't.

Tom Forsyth - Muckyfoot bloke.
Whizzing and pasting and pooting through the day.

> -----Original Message-----
> From: Nik...@ao... [mailto:Nik...@ao...]
> Sent: 02 August 2000 19:25
> To: gda...@li...
> Subject: [Algorithms] Rotation Matrices
> 
> 
> Why isn't the multiplication of rotational matrices 
> commutative?  For example 
> if I have one rotation matrix which rotates 20 degrees around 
> the Z axis, and 
> another which rotates 50 degrees around the X axis, depending 
> on the order in 
> which I multiply them, I get different results.  Why is this? 
>  When rotating 
> an object there is no visible difference when it is first 
> rotated on one axis 
> and then on another, is there?  I first looked in an 
> elementary linear 
> algebra book for the answer; however it stated that the 
> multiplication of 
> rotation matrices is commutative (although it was only 
> covering 2D rotation 
> matrices). Any help would be appreciated.
> 
> Thanks,
> Nik...@ao...
> 
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