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The way he animated points with an increasing z value made it click for me. Now, when I look at the formula it makes sense. The larger the value of z, the smaller your projected x and y will be. This checks out because things get smaller as they move farther away. Something that’s twice as far away will seem half as big.

The rotation formula eludes me.

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> The rotation formula eludes me.

Interestingly, in a way, rotation is less mystical than the perspective projection. The rotation is linear: x' = Rx, but the perspective projection is non-linear.

This is where things become fun. Next up are homogeneous coordinates or quaternions. Takes a few years of your life to actually enjoy this though :)

I get how quaternions beat Euler angles, but I still can't visualize the damn things 8-/

> I get how quaternions beat Euler angles, but I still can't visualize the damn things 8-/

And spin groups beat quaternions since they work in every (finite) dimension. :-)

I recently appreciated this vid explaining that 3D translation using the traditional 4x4 transform matrix is performing a shear operation in 4D.

https://youtu.be/x1F4eFN_cos

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