Rotation Matrices
The orthogonal matrix (post-multiplying a column vector) corresponding to a clockwise/left-handed rotation by the unit quaternion is given by the inhomogeneous expression
or equivalently, by the homogeneous expression
If is not a unit quaternion then the homogeneous form is still a scalar multiple of a rotation matrix, while the inhomogeneous form is in general no longer an orthogonal matrix. This is why in numerical work the homogeneous form is to be preferred if distortion is to be avoided.
The orthogonal matrix (post-multiplying a column vector) corresponding to a clockwise/left-handed rotation with Euler angles φ, θ, ψ, with x-y-z convention, is given by:
Read more about this topic: Conversion Between Quaternions And Euler Angles
Famous quotes containing the word rotation:
“The lazy manage to keep up with the earths rotation just as well as the industrious.”
—Mason Cooley (b. 1927)