Hi,
I have some code that constructs a transformation matrix like so:

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double a = sqrt(1 - (b*b + c*c + d*d));
Quaterniond Q1(a, b, c, d);
Affine3d S; S = Scaling<double>(u, v, w);
Affine3d T; T = Translation3d(x, y, z);
Affine3d Transformation = T*S*Q1;


Where b, c, d, u, v, w, x, y, z are all sensible doubles read in from a data file. If I then try to recalculate the Quaternion coefficients like so:

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Affine3d R; R = Transformation.rotation();
Quaterniond Q2(R);


and then compare the coefficents (.vec()) of Q1 and Q2 they are precisely the negative of each other. However, Quaternions with opposite coefficients are not equivalent. Am I missing something about Quaternion maths, or is this a bug?

q and -q do represent the same rotation.

Yes, you are right. Thank you.

I was dealing with a data format that only stores the x, y, z Quaternion coefficients, and then requires w >= 0 to save space. If you reverse x, y, z, but not w you do get a different rotation, which is what I was seeing. All fixed now and definitely a bug in my thinking, not in Eigen.