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.
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)
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.
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.
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.
I think that's a good shortcut. Converting from axis-angle to quaternions is similar to switching from an angle to a vector (cos angle, sin angle). However I didn't really grok quaternions until looking at geometric algebra, and I haven't used them since then so I can't be sure my intuition is right.
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"
(I know there's weird historical oddities like branching laser disks but they are unusual enough to warrant a category all of their own)
If you can rotate around it then it's not a video. :-)
Maybe I'm pedantic on this because I work with VR a lot where the terminology is a mess. (Are 360 videos "VR"? Then what do we call actual VR videos? etc etc.)
I recall Quicktime VR videos could be one of two types: you rotate around to see a 360 scene (inside of car), or you rotate an object to see 360 (outside of car). VR360 is the first kind, I haven't seen VR360 videos that let you rotate objects on YouTube. That would be pretty cool to see an 'actual VR' roomscale VR video, walk around while scrubbing it.
Take a look at what they've done. The basic idea is that the video is "on rails", moving forward on its own, but at any point you can pause and move around the objects from the video. Then you can go back to the video and it interpolates back to the recorded track. I loved what they did, but it didn't help me understand quaternions ;(
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[ 2.9 ms ] story [ 44.1 ms ] threadeventually 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)
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.
This helped me recover the intuition around scaling and rotating from the complex numbers to quats.
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.
https://marctenbosch.com/quaternions/
(I know there's weird historical oddities like branching laser disks but they are unusual enough to warrant a category all of their own)
Maybe I'm pedantic on this because I work with VR a lot where the terminology is a mess. (Are 360 videos "VR"? Then what do we call actual VR videos? etc etc.)
Visualizing quaternions: An explorable video series - https://news.ycombinator.com/item?id=18310788 - Oct 2018 (32 comments)