I am just investigating and confused the implicit handness of an Unit Quaternion(Quat), which will be used to represent a Rotation around an Axis U and rotation angle A.
But in which direction should we rotate around Axis U?
From the definition:
Quat : cos(A/2) + U*sin(A/2)
We know that angle must be CCW, because positive angle is got from a CCW rotation.
And if we use this Quat to rotate a Point P we can use
Q * P * Q^ with Q^ is the conjugate of Quat Q
I think all above is nothing to do with the Handness of Coordinate System.
Right now if we are in Left Handed System(LHS).
we use CW angle as positive angle and want to create a Quat using this CW angle A.
And after using Q * P * Q^, we will get the CW rotated point P'.
But how about that in Right Handed System(RHS)?
if P is defined in RHS at the beginning
and A is CCW angle(Positive Angle),
we almost can get the same Quat(as in LHS, just y,z components swapped).
but if we rotate P in RHS using Quat Q, it will transform P to the same P' as in LHS
or mirrored position P'' ?
I hope i have made my purpose clearly.
I just want to using quaternion all the time(NO conversion to matrix).
I want to create the rotation(represented using quaternion) from an Axis and an Angle.
I am just confused here, why Q * P * Q^ can always transform P into the correct spatial position as expected, even if we have treated CW angle as positive in LHS and CCW angle in RHS.
Please help. and correct my errors in the above explanation.
thank you a lot
Somebody has told me, Quaternion does have any kind of handness, just the conversion from Quat to Matrix does.
But how can quaternion handle the rotation using its product?