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 …

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 …

May 27, 2020 · Quaternions have real and imaginary parts, or one may call them a scalar and vector part. That is, we can interpret $\mathbb {H}$ (named after Hamilton) as $\mathbb {R}\oplus\mathbb …

My goal is to understand rotation quaternions specifically. I don't want to just memorize the formulas for using rotation quaternions, I want to truly understand them. It's the most difficult thing I've ever tried …

Aug 27, 2015 · Quaternions exist because someone drempt them up, and decided which properties they wanted applied to them. The answer to the question you didn't ask is: quaternions are important …

Nov 16, 2023 · And from this perspective, I am interested in the similarity between sectonions as an algebra over the quaternions by comparison with octonions as an algebra over the complex numbers.

From my understanding, in spatial applications (3D rendering, games and similar applications) quaternions can only be used to describe rotations/orientations and not translations (like a transforma...

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 …

Given multiple quaternions representing orientations, and I want to average them. Each one has a different weight, and they all sum up to one. How can I get the average of them? Simple multiplicat...

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 …