7-ish hours 💀💀💀

this is nowhere near a concise description of how quaternions work

Happy to hear it!

yeah, it seems like quaternions' popularity comes from a fair amount of misinformation being passed around, and perhaps some hipster-like infatuation with complex numbers and 4d math.

Thanks for the feedback & corrections! A slight clarification regarding speed: while you're right about the number of operations, that's assuming that you already have all the matrix elements pre-computed for use. If you only have the three angles describing your rotation, then you still have to compute a big mess of trigonometric products, sums, and differences in order to construct your 3D rotation matrix, which ends up being many more (and more expensive) operations overall. I probably should've mentioned this somewhere in the video.

@@CovenantTurtle That may be true but there are very good and well optimized libraries that provide good use of quaternions for you. A couple of really good math libraries are GLM, Eigen and a few others. GLM is easier to use as it's a templated headers only library, no need for compilation, or linking, just point to appropriate folders with the needed include directives. As for Eigen it does take a little bit more work to set up as you'll have to install the Library - API, and then you'll have to make sure you're properly linking against it's compiled libraries depending on if you're linking it dynamically or statically at least with C/C++ that is... And I'm sure that either Boost or GNU has some good libraries. Quaternions when implemented correctly are still fairly fast and efficient even at the hardware level especially if their using the vector intrinsic registers such as MMX... sure it might be a few more instructions than a basic rotation matrix, but when you're working with 3D graphics you typically don't use a 2x2 or 3x3 matrix, you typically use a 4x4 MVP matrix. And quaternions translates and works well with 4x4 matrices, and they're quite easy to convert to a vector4 object. They're still fairly efficient these days and if you start to target the graphics cards that support 1/2 precision floating points... you can do a lot of amazing tricks with them. They are a very versatile and powerful tool to have in one's toolbox.

1) But aren't position vectors just a mapping *from* (i.e. tail) your initial point *to* (i.e. head) your final point? 2) I completely agree that the jump from the definition of Q to the definition of the Hamilton product isn't intuitive - but, for the purposes of this video being a quick introduction to how and why you might use quaternions for rotation, I don't think it matters. There are links in the description for more information, and I imagine anyone who's really looking into the various representations of rotations will come across the 4x4 matrix equivalents of quaternions sooner or later.

I drew all of these diagrams myself in paint.net (which despite its name is actually a program, not a website).

It's not that linear is jerky, it's that it already includes ramping up and ramping down! I highly suggest you check out the interpolation comparison animation I've linked in the description. As for getting arbitrary changes of angular velocity, instead of linearly increasing the value of the interpolation parameter (usually labelled "t"), you can increase it slower or faster at different points of the animation.

​@@CovenantTurtle thanks for replying. I saw the 3d difference lerp and slerp. good visual btw from the link. Let me pinpoint my problem exactly. I am using blender a 3d software that I am trying to animate eyes moving. Eye movemebt has to ramp up or down in speed not in location or eye orientation. so for the Lerp slerp example you posted, both are linear speed in turning to 3 o clock. lets say on the first third I want it to move at speed x and x2 on the second third of the movmement from 12o clock to 2 oclock. the x4 speed at 2 o clock to 3 o clock. Here is tge question. using quat controls and not time. how do I use the 4 quats to control the ramps speed of tge eye ball?