Do one quaternion multiplication and you rotate the circular component just that far around, and the quaternion axis gives you the rest of the location, and the fourth dimension says how far ahead or …

Aug 5, 2015 · Every quaternion multiplication does a rotation on two different complex planes. When you multiply by a quaternion, the vector part is the axis of 3D rotation. The part you want for 3D rotation. …

Oct 27, 2022 · A quaternion can be thought of as a scalar plus a 3D vector (also known as real and imaginary parts). The product of a scalar and a 3D vector is the usual scalar multiplication. The …

Aug 11, 2014 · We use unit length Quaternion to represent rotations. Following is a general rotation matrix obtained ⎡⎣⎢m00 m10 m20 m01 m11 m21 m02 m12 m22⎤⎦⎥3×3 (1) (1) [m 00 m 01 m 02 m 10 …

Apr 13, 2017 · A rotation about the $z$-axis is a rotation about the unit vector $k$. And we know that $\pi/ 6 = 30^\circ$, but we actually want half of that for the quaternion so $\pi /12$.

In the quaternion case, reduced means that instead of taking this as the norm, you take its square root. Since the quaternions are 4-dimensional over R R, the reduced norm defines a quadratic form, which …

If I combine 2 rotation quaternions by multiplying them, lets say one represents some rotation around x axis and other represents some rotation around some arbitrary axis. The order of rotation ma...

Feb 2, 2017 · Part 1 Suppose you have a "parent" rotation with quaternion qp, q p, and you want to combine this with a "child" rotation with quaternion qc q c that will rotate an object relative to the …

Mar 2, 2019 · It seems we can describe every rotation in SO(3) S O (3) by at least one unit vector axis u u and angle θ θ pair. Each of these pairs can also be described by a rotation matrix: I've heard …

Jan 16, 2017 · You could generalize the quaternion to be non-unit. I don't see any reason why generating a new rotation quaternion should work. - Do you want to take only the time derivative of …