Quaternions and rotation vector.

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To calculate a normalized 3D vector from a quaternion's orientation, the vector part of the quaternion should be extracted and normalized. The vector part consists of the imaginary components associated with i, j, and k. A quaternion can be expressed in the form q = q0 + q1*i + q2*j + q3*k, where q0 is the scalar part and (q1, q2, q3) represents the 3-vector part. It's important to note that a quaternion is considered a 4-vector within a vector space. Understanding these components is essential for accurate quaternion manipulation in 3D rotations.
pjhphysics
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Hi,
I'm trying to calculate a normalized 3d vector representing the quaternion's orientation. Can anyone give me a hand?
Thanks!
 
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It's easy. Take the vector part of the quaternion and then normalize it.
 
What constitutes the vector part of the quaternion?
 
He means use the imaginary elements associated with i, j, and k of course.

BTW, technically a quaternion is itself a vector, since it's a member of a vector space.
 
A quaternion can be expressed as

q = q0 + q1*i + q2*j + q3*k

It's a 4-vector, (q0,q1,q2,q3) that can be decomposed into a scalar part, q0, and a 3-vector part (q1,q2,q3).
 
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