Real world uses of Quaternions? - Mathematics Stack Exchange
Quaternions are a way of specifying a rotation through a axis and the cosine of half the angle. They main advantage is I can pick any two quaternions and smoothly interpolate between them. Rotors …
linear algebra - How can one intuitively think about quaternions ...
Oct 19, 2010 · After a couple awesome moments of understanding, I understood it for imaginary numbers, but I'm still having trouble extending the thoughts to quaternions. How can someone …
Understanding quaternions - Mathematics Stack Exchange
May 27, 2020 · How many questions about understanding quaternions have you read on the site? This is something that people are constantly asking about, so there is plenty of material. If you're mainly …
Confusion with getting a unit quaternion from two vectors
Jun 26, 2025 · Quaternions. For me, the quaternions are a 4D algebra $\Bbb H=\Bbb R\oplus\Bbb R^3$ and every quaternion is uniquely expressible as a sum of a scalar and a 3D vector.
How to convert Euler angles to Quaternions and get the same Euler ...
Oct 29, 2018 · I am rotating n 3D shape using Euler angles in the order of XYZ meaning that the object is first rotated along the X axis, then Y and then Z. I want to convert the Euler angle to Quaternion …
Quaternions: why does ijk = -1 and ij=k and -ji=k
I think the geometric algebra interpretation of complex numbers and quaternions is the best, since it reveals more directly the fact that the "imaginary numbers" can be seen as encodings of …
inverse - Quaternions multiplication order (to rotate & unrotate ...
Feb 2, 2017 · Multiplication by quaternions in the conventional way transforms the world coordinates of whatever object you apply it to. In order to achieve the effect of first performing the parent rotation, …
How do quaternions represent rotations? - Mathematics Stack Exchange
Apr 27, 2012 · 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 $\Bbb R$, the reduced norm defines a …
How to convert a quaternion from one coordinate system to another
Jun 24, 2022 · When dealing with quaternions, there are two variations in conventions which should be stated when describing the quaternions. The first one is if the scalar element is first or last, the …
Why do we need quaternions when we already have continuous …
Jun 5, 2024 · A quaternion has $4$ components. Your matrix exponential has $9$ components. It's easier to store quaternions than matrices. It's also easier to multiply two quaternions than two …