how to visualize how quaternion to a 4x4 matrix rotation work

[glossy oyster]

ik those "1-" thing for the identity matrix thing, what about the rest? like why is it those specific number and variables being multiplied and subtracted/added?

^^ how am I supposed to visualize what happen if I scale up a variable and what does it do to the rest etc how does the logic even work that actually makes a rotation

I watched the 3 blue 1 brown video abt it but like he didn't mention this formula

[modest cloak]

i dont know a single thing about quarterninion or rotation matrix

[smoky sleet]

Then don’t comment

[modest cloak]

but i lowk

want to know

i mean

[smoky sleet]

Component parallel to rotation axis stays unchanged
Component perpendicular to axis gets rotated in a circle
The circular rotation involves both the perpendicular component and and a cross product with the axis
The matrix contains all of the three effects at the same time for x, y, z coordinates

new_x = (1 - 2y^2 - 2z^2)*old_x + (2xy - 2wz)*old_y + (2xz + 2wy)*old_z

^ To get one row of the matrix

[dapper glacier]

boi what in the helly is this

[glossy oyster]

wait so ur saying that matrix has a cross product formula combined it

ion understand

make like an example with a hand or something