Another way to see quaternions

I share with you an article entitled “Spherical-vectors and geometric interpretation of unit quaternions”. this paper gives an algebraic structure to the vector-arcs (which I call spherical-vectors) introduced by W. R. Hamilton in his geometric model for the group of unit quaternions. It allows us first to represent geometrically the algebraic structure of unit quaternions on the unit sphere of $\mathbb{R}^3$, and then to introduce an exponential notation of quaternions that obeys the algebraic properties.

Your comments are welcome.

Here is a small summary.

 

Despite using quaternions for yeeeaaaars.... I still have no clue what they really are. Not sure if that's a... bad... thing?

 

In my opinion, the quaternions are of dimonsion 4 but it is the only way to pass from one point to another in real space IR ^ 3.That is to say :
Let A (a, b, c) and B (a ', b', c ') be two points of space associated with the numbers z1 = a + ib + jk and z2 = a' + ib '+ jc. To pass from z1 to z2 we have to multiply z1 by a quaternion q. z2 = q * z1.

 

I am somewhat familiar that they are working in 4 dimensional space. But that's about as far as I get.

 

In my opinion, paper is little to no use, in game making. Feels more self promoting, considering date of paper and joining community.

Quaternions are nothing new.
We have methods, which does all magic, and math with vectors. Also, multiple simplification methods are used, to make thing more efficient.

Representation is nothing more but nice pictures and is gibberish for any average programmer to be honest.
There are much better explanations out there, what quaternion is and how to work with. I wouldn't even attempt to read that, if I want make a game.

 

Yup it's all conveniently wrapped magic. I would, however, like to know how it all works for no other reason than curiosity.

 

There is somwhere cool video explaining quaternions in understandable way. But unfortunately I can not find it and it have been burried, by other boring quaternion related vids.

I can suggest first to watch multiple visualizations (i.e. youtube), before going into math, if that is the route you try to take.

Probably searching forum for quaternions topics, could dig you out few good responses.
Don't forget about other forums and media.

 

I've been able to understand and somehow "visualize" quaternions by watching (and understanding) these videos first:

Then following these interactive series:

https://eater.net/quaternions/