Re: [Algorithms] Scaled quaternion rotations

[Jon W. <jw...@gm...>]

Marc B. Reynolds wrote:
> Cayley in [1,2] demonstrates general 3D rotations via quaternions, 
> (left-handed and right-handed respectively).

I'm sorry, but what separates a "left-handed" from a "right-handed" 
rotation? In what space interpretation?

It should be obvious that a rotation in left-handed space interpretation 
is exactly equal to that same rotation in right-handed space 
interpretation, but, because of the differences in interpretation, if 
rendered into a fixed device space they will appear as mirror images.

More directly: rotation the Z unit vector around the Y unit vector as 
axis by PI/2 radians always generates the X unit vector, no matter 
whether you choose to interpret your coordinates left-handed, or 
right-handed. In a left-handed coordinate space, you use the left hand 
to visualize the rotation; in a right-handed coordinate space, you use 
the right hand to visualize the rotation, but the actual math is exactly 
the same in both cases!

Maybe what you (or the original paper author) mean to say is "both 
forward and inverse rotations" ? Rotation math, in itself, has no 
handedness; it is only the interpretation of the coordinates in the 
coordinate space that is handed. That should be obvious to anyone who 
does computer graphics, but time and again, I hear the mis-nomers 
"left/right-handed rotation" and it drives me nuts! It's as bad as 
talking about "row major matrices" without specifying whether you're 
using row vectors (on the left) or column vectors (on the right).

Sincerely,

jw