I always had a hard time trying to visualize these higher dimension objects. I think its because I actually have quite good visualization and spacial awareness. But going to 4d it just breaks and all the concrete ability isn't so useful.<p>eventually after looking at the math and understanding more about complex numbers, i got some intuition for the multiplication of the basis vectors and i feel like I can sort of extend the intuition by linear decomposition (distributivity)<p>multplication by a complex basis vector is like a pair of rotations one of the rotations is in plane spanned by the reals and vector itself and the other is a rotation "orthogonal" to the vector spanned by the 2 other basis vectors.<p>This helped me recover the intuition around scaling and rotating from the complex numbers to quats.
Despite using quaternions all the time as a game developer, I’ve never really taken the time to fully understand them mathematically.<p>My shortcut has been to think of them as a rotation around an axis. Once I thought of them that way, I was able to use them for all kinds of purposes and situations despite not having a deeper mathematical understanding.
Discussed at the time:<p><i>Visualizing quaternions: An explorable video series</i> - <a href="https://news.ycombinator.com/item?id=18310788" rel="nofollow">https://news.ycombinator.com/item?id=18310788</a> - Oct 2018 (32 comments)
Is it just me that thinks "interactive videos" sounds like an oxymoron? Being interactive is pretty much the feature that makes something "Not just a video"<p>(I know there's weird historical oddities like branching laser disks but they are unusual enough to warrant a category all of their own)