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#ActualParadigm Shifter

Posted 06 April 2013 - 01:49 PM

q and -q represent the same rotation, unit quaternions are a double cover for the sphere.

 

The only issue is when interpolating/slerping quaternions, you want to go the quickest route rather than the long way round, but you can do that by checking that the quaternion dot product between the 2 quaternions is positive, if it is negative negate one of the quaternions before interpolation.

 

EDIT: If you think about the axis/rotation form of a quaternion it is easy to see that -q and q represent the same rotation; the axis is negated but so is the rotation angle => they represent the same rotation.

 

EDIT2: Euler angle representations aren't unique either, so converting Euler angles to a quaternion and then back again might not give you the same angles back either ;)

 

EDIT3: So in conclusion, there's nothing to worry about.


#3Paradigm Shifter

Posted 06 April 2013 - 01:47 PM

q and -q represent the same rotation, unit quaternions are a double cover for the sphere.

 

The only issue is when interpolating/slerping quaternions, you want to go the quickest route rather than the long way round, but you can do that by checking that the quaternion dot product between the 2 quaternions is positive, if it is negative negate one of the quaternions before interpolation.

 

EDIT: If you think about the axis/rotation form of a quaternion it is easy to see that -q and q represent the same rotation; the axis is negated but so is the rotation angle => they represent the same rotation.

 

EDIT2: Euler angle representations aren't unique either, so converting Euler angles to a quaternion and then back again might not give you the same angles back either ;)


#2Paradigm Shifter

Posted 06 April 2013 - 01:40 PM

q and -q represent the same rotation, unit quaternions are a double cover for the sphere.

 

The only issue is when interpolating/slerping quaternions, you want to go the quickest route rather than the long way round, but you can do that by checking that the quaternion dot product between the 2 quaternions is positive, if it is negative negate one of the quaternions before interpolation.

 

EDIT: If you think about the axis/rotation form of a quaternion it is easy to see that -q and q represent the same rotation; the axis is negated but so is the rotation angle => they represent the same rotation.


#1Paradigm Shifter

Posted 06 April 2013 - 01:38 PM

q and -q represent the same rotation, unit quaternions are a double cover for the sphere.

 

The only issue is when interpolating/slerping quaternions, you want to go the quickest route rather than the long way round, but you can do that by checking that the quaternion dot product between the 2 quaternions is positive, if it is negative negate one of the quaternions before interpolation.


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