This one is pretty simple, you should use a method invented by a famous US military office, statesman, and rapper, Alexander Hamilton. It's called quaternions and they use a four dimensional associative representation which adds enough slack to nice represent all 3d rotations. But that's not important because "quaternion" is latin for 4, which is what all the numbers in your rotation matrix are, and for simplicity we just call that matrix "4".

I can actually provide an example to show that this is always true.

Let's say your starting point is (3.14, 0.1, -2.4759644585494356), that's just any point in 3 space, I didn't pick it for any specific reasons. Now let's pick a quaternion, I chose a random one: (0.43232215, 0, 0.54826778, 0.71589105). If you apply that rotation to our totally random starting point, we end up with a y component of 4.

[–] chuck@lemmy.ca 2 points 9 months ago* (last edited 9 months ago)

Now I want that version of Hamilton! Quick get Lin-Manuel Miranda I need some catchy tune about the bridge where Hamilton figured it all out.

But who is the villain his kid asking if he figured out how to multiply vectors ( been a while since I read the story about this )

[–] Smorty@lemmy.blahaj.zone 2 points 9 months ago

Ah, I see. Thanks, oh wise pancake.

[–] Mechaguana@programming.dev 1 points 9 months ago (1 children)

How many featherless legs does a chicken have?

[–] wise_pancake@lemmy.ca 1 points 9 months ago (1 children)

In the Z2 integer group, 4 = 0 = 2

[–] Mechaguana@programming.dev 1 points 9 months ago

Well you win this one