C ++ / Matlab native quaternion criterion and matrix matrices
I noticed that there is a difference in Eigen C ++ and Matlab when computing with quaternions. In Eigen C ++ the code is
Eigen::Quaterniond q;
q.x() = 0.270598;
q.y() = 0.653281;
q.z() = -0.270598;
q.w() = 0.653281;
Eigen::Matrix3d R = q.normalized().toRotationMatrix();
std::cout << "R=" << std::endl << R << std::endl;
gives the rotation matrix:
R= -2.22045e-16 0.707107 0.707107 0 0.707107 -0.707107 -1 0 -2.22045e-16
In Matlab (which uses wxyz), however, I get the following output:
q = 0.6533 0.2706 0.6533 -0.2706 >> quat2dcm(q) ans = -0.0000 0 -1.0000 0.7071 0.7072 0 0.7072 -0.7071 -0.0000
which is transposition! Can someone explain to me what is going on? I have verified that wxyz's positions are correct.
thank
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With Matlab, you compute the cosine matrix . It is indeed a rotation matrix like the one you calculate with Eigen C ++ and as such is also unitary (all rows and all columns are norm 1 and form either a perpendicular set of vectors).
So, it so happened that the inverse unit of a unitary matrix is equal to its conjugate transposition (*), i.e.
U * U = UU * = I
In other words, what should be happening is that the Matlab convention is the opposite of the C ++ Eigen convention.
From Wikipedia :
The coordinates of the P point can change due to the rotation of the CS coordinate system (alias) or the rotation of the P point (alibi).
In most cases, the effect of ambiguity is equivalent to the effect of inverting the rotation matrix (for these orthogonal matrices, transposition of the matrix is equivalent).
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