RE: [Algorithms] Quaternion handedness

[Michael P. <MPo...@cy...>]

Be aware that different books will use or not use a transposed
quat->matrix.

i.e.
	"3D Game Engine Design", Page 17, Section 2.3.5, Eqn 2.13
	    and
	 "Rotating Objects Using Quaterions" (Corrected matrix)
	 Game Developer, Feb 98, Nick Bobick

RHCS?
	         2    2                               =20
	 [ 1 - 2y - 2z    2xy + 2wz      2xz - 2wy    ]
	 [                      2    2                ]
	 [ 2xy - 2wz      1 - 2x - 2z    2yz + 2wx    ]
	 [                                     2    2 ]
	 [ 2xz + 2wy      2yz - 2wx      1 - 2x - 2y  ]

	 Used by Watt&Watt, Parameetrization of orientation, Page 362
LHCS?
	         2    2                               =20
	 [ 1 - 2y - 2z    2xy - 2wz      2xz + 2wy    ]
	 [                      2    2                ]
	 [ 2xy + 2wz      1 - 2x - 2z    2yz - 2wx    ]
	 [                                     2    2 ]
	 [ 2xz - 2wy      2yz + 2wx      1 - 2x - 2y  ]


Cheers


-----Original Message-----
From: Tyson Jensen [mailto:twj...@sa...]=20
Sent: Friday, November 22, 2002 1:41 PM
To: gda...@li...
Subject: RE: [Algorithms] Quaternion handedness


Huh?  We wrote an entire game in left-handed coordinates and we never
noticed any "magic" preference for right-handedness in matrices.  I am
unclear as to why arithmetic would care what hand humans tend to prefer.

What happens is that care must be taken when copying algorithms out of
books that might be making handed-ness assumptions.  I'd bet money that
lhA * lhB =3D right handed space is a result of a bias in code, not in =
the
math.

If you have a left-handed world and use left-handed transforms your
stuff will remain left-handed.

I recommend a constant matrix that can be applied to convert a matrix
from left-handed to right-handed and another one that goes in reverse.
I'd recommend doing all your quaternion stuff in (pick a hand) space. If
a matrix is (other-handed) then convert the matrix to the
(correct-handed) space, convert to quaternion, do whatever, convert
back, and then convert the (correct-handed) matrix back into an
(other-handed) matrix.

Trying to maintain left-handed quaternions and right-handed quaternions
is just compounding the problem of having both left-handed coordinate
spaces and right handed coordinate spaces.

-----Original Message-----
From: gda...@li...
[mailto:gda...@li...] On Behalf Of
Joseph, William
Sent: Friday, November 22, 2002 9:55 AM
To: 'gda...@li...'
Subject: RE: [Algorithms] Quaternion handedness

If I understand matrix stuff correctly, a rotation-only matrix is always
right-handed - even when working in a left-handed coordinate system. If
your rotation matrix is left-handed, transforming a space by it will
cause that space to switch handedness. For example.. object space A is
left-handed and object->world rotation matrix B is left-handed. Applying
B to A will result in the object appearing right-handed in
world-space... I think. To construct the rotation matrix correctly, you
have to do it in the correct space. I'm not familiar with tangent-space
transforms.. but you may be able to do this by converting the
left-handed basis to right-handed, extracting the rotation, then
converting back to left-handed. I suggest experimenting..

-Will

-----Original Message-----
From: Joe Ante [mailto:jo...@li...]
Sent: 22 November 2002 16:23
To: gda...@li...
Subject: [Algorithms] Quaternion handedness


Hi,

I am trying to convert tangent space 3x3 matrices for dot3 product
bumpmapping to quaternions.

I want to convert these 3x3 matrices into quaternions to do the
objectspace-
tangentspace transformation, because I need to slerp my tangentspace
transform when doing geomorphing on my chunk lod mesh. The tangentspace
orthonormal bases are sometimes right handed, sometimes left handed.

Unfortunately my matrix to quaternion algorithm seems not to work on
left handed matrices. (I am using the algorithm availible at
magic-software)


Is there any way to represent a left-handed matrix as a quaternion?

What do I have to do to convert my left-handed orthonormal matrix into a
quaternion?

Joe Ante