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 …
conditions for quaternions to be valid - Mathematics Stack Exchange
Mar 21, 2024 · However I should answer this soon to other members of my work group. My understanding of quaternions is composed of four values w,x,y and z and that they can be used to …
ring theory - Why are the only associative division algebras over the ...
Why are the only (associative) division algebras over the real numbers the real numbers, the complex numbers, and the quaternions? Here a division algebra is an associative algebra where every …
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 …
3d - Averaging quaternions - Mathematics Stack Exchange
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...
Super confused by SQUAD algorithm for quaternion interpolation
Feb 14, 2018 · The demo generates 10 random unit quaternions and then interpolates between them indefinitely. It shows 12 WebGL canvas instances, 2 per algorithm. The top canvas displays the …
Why is quaternion algebra 4d and not 3d?
Oct 12, 2011 · There are only four normed division algebras (algebras where division by nonzero elements is possible) over the reals: the reals themselves, the complex numbers, quaternions, and a …
quaternions - Rotating a 4 dimensional point? - Mathematics Stack …
I'm trying to rotate a 4 dimensional point (w,x,y,z). So far I've been rotating around planes (wx,xy,yz,zw,wy, and xy), but the order in which I do these rotations changes the results and can …