How to calculate the distance between rotations in quaternion?
Let q ∗ denote the quaternion conjugate. The difference rotation quaternion that represents the difference rotation is defined as r ≜ p q ∗ . The distance between rotations represented by unit quaternions p and q is the angle of the difference rotation represented by the unit quaternion r = p q ∗ .
How are the axis and the angle of rotation encapsulated?
The axis and the angle of rotation are encapsulated in the quaternion parts. For a unit vector axis of rotation [ x, y, z ], and rotation angle , the quaternion describing this rotation is Note that to describe a rotation using a quaternion, the quaternion must be a unit quaternion.
Why are quaternions and conjugates have opposite effects?
A quaternion and its conjugate have opposite effects because of the symmetry in the point and frame rotation equations. Rotating by the conjugate “undoes” the rotation. Because of the symmetry of the equations, this code performs the same rotation.
How are quaternions used to describe rotations in MATLAB?
Often rotations and orientations are described using alternate means: Euler angles, rotation matrices, and/or rotation vectors. All of these interoperate with quaternions in MATLAB. Euler angles are frequently used because they are easy to interpret.
Is the inverse of Q a unit quaternion?
The quaternion that computes this rotation is You may want to confirm that q is a unit quaternion, since that will allow us to use the fact that the inverse of q is q’ if q is a unit quaternion. Suppose we want to perform two rotations on an object.
Why are quaternions used instead of 3×3 matrix multiplication?
For quaternions versus a 3×3 rotation matrix, the quaternion has the advantage in size (4 scalars vs. 9) and speed (quaternion multiplication is much faster than 3×3 matrix multiplication). Note that all of these representations of rotations are used in practice.
Why are quaternions used instead of Euler angles?
Euler angles are still used when memory is a concern as you only need to store 3 numbers. For quaternions versus a 3×3 rotation matrix, the quaternion has the advantage in size (4 scalars vs. 9) and speed (quaternion multiplication is much faster than 3×3 matrix multiplication).