Rotations about an Arbitrary Axis using Quaternions

Go to 8:44 to skip the explanation.

Someone commented that they were interested in rotations about an arbitrary axis. I did a quick video demonstrating how Quaternions can be employed to do this.

An interesting method which can be proven using quaternions is also the Rodrigues Rotation Formula method, which I would strongly encourage looking into. Quaternions are fun, but a bit time consuming.

Around 8:44 I start doing an example using Quaternions. If you look closely, you'll see a simple math error that throws off the results.

[TheDavddd]

Way easier to understand with math than when people try to give "intuitive" explanations that just make things way harder. Thank you.

[aceofspades]

Thanks for the lesson. My doubt is: How do I isolate axis rotation when comparing the current 3x3matrix orientation (object) to the original 3x3matrix orientation (earth), if all the axis are connected to each other in a very messy way? (I've been struggling to understanding it for six days now)

[amiraliomidfar]

Shouldn't your v vector be unit length vector as you mentioned earlier. Seems to me we need to divide by 1/sqrt(3). But thanks for the video, very helpful.

[taskeenzahra]

Thanks for the video. I have a question what if a point P1 say (x1, y1, z1) needs to be rotated about a vector that doesnot originate from the origin rather its between some point P2 (x2, y2,z2) and P3(x3, y3, z3) that means the point P1 needs to be rotated about vector P2P3 ?

[WaseemAbbas-drsj]

Vectors you took in this example are these taken from the origin?
In my case i have to rotate an object along Y axis then along Z axis thorugh known angles. Note that the object is not placed at the point of rotation and point of rotation along Y axis and Z axis are not the same. Can i apply the same concept in my example ?

[WaseemAbbas-drsj]

Why did you take the scalar component of the quarternion 0 ? Why it cant be 1 or any other constant ?