Math for Game Developers - Axis-Angle Rotation

Axis-angle rotations can help us improve our abilities to rotate vectors and objects.

[JorgeVinoRodriguez]

If you want to see a text version of it, you should check out the book "3D Primer for Graphics and Game Development" by Dunn and Parberry. It's a great book, it's basically the textbook that I've been basing most of these lessons out of.

[anzatzi]

Great play list on quaternions.  I dont now if i still really have an intuition of quaternions beyond the angle axis model, but I do see the interpolation issue and I have more momentum to peck away at this topic.  Thanks again--grreat job

[alenagy]

Thanks a lot Jorge. It took me a while but with your video and the comments on it I could finally wrap my head around the Rodrigues formula. It was hard for me to break the paradigm of x, y, z and realise this was an axis independent from those three and possibly located anywhere in a 3d space coordinate system. Also had to bring down to numbers to help me align my thoughts with the concepts. Just some advice in case someone else is having a hard time on the subject.

[fjsfnehfwhxbfid]

For 2D rotation, we actually rotate about the z axis. In the angle-axis rotation, think about it as being given a z-axis and constructing an x(e from v1) and y(f) axis from there. From there, we can use the to axis for our basis for rotation as per the case for an xy rotation (x cos0 + ysin0). We add the result to p because the result is just a direction vector relative to the origin we used in the new axis(p). We add p to the result to make it relative to the actual origin(0, 0, 0).

[dandymcgee]

It's spherical and linear at the same time because the slerp factor is a 1-dimensional scalar.

[ollicron]

Things I never want to see or deal with ever, but I know I'll have to eventually. :D

[DarkDrakman]

mmm got everything except why e' is equal to (e cosO + f sin O)...i whatched the two rotation videos, but i don;t understand how you get that 

[voxeledphoton]

*E Prime* .. _the rotated one_ said by many to have originated from the _rejection vector_ in the dark ages. He waits in search for the almighty *V Prime* _the rotated vector_ that points at this point right here .

[rayforceaddict]

This rotation was named after you, you know! :)

[mboog]

very good tutorial. the way it's presented helps a lot. what program did you use to make it?

[gfetco]

You want a vector perpendicular to the e and n axis at 4:20, wouldn't that account to e x n and NOT n x v like you've proposed later at 6:10?
EDIT: Answer: Since f = e x n and e = v - p. e x n = (v - p) x n = (v x n) - (p x n). Since p and n are parallel that means that their cross product is equal to the zero vector.
p x n = 0 hence f = e x n = v x n.

[satori_mountian_station]

I think this is what I'm looking for in regard to (AWES)

[jovanrakocevic]

Could the second part be v*cos(theta) * (1-cos(theta)) around 7:07 mark? I am getting back into this stuff after years without maths at uni (nothing for the last two years sadly, other areas of maths before it...)

[MrGameengineer]

I have seen that book but I was wondering if you had thoughts about Eric Lengyel's book "Mathematics for 3d Game Programming and Computer Graphics, 3rd Ed."

[meetjatin]

Great lecture however I have a question why did you wrote f vector to be cross product of n and v vectors in the equation. Earlier in the video you stated that f vector is perpendicular to both e and n vectors then shouldn't f be cross product of n and e .

[JorgeVinoRodriguez]

Yeah I know, my sarcastic side got the better of me :P The term made me go O.o when I first saw it.

[JorgeVinoRodriguez]

All of these are made with Photoshop, Visual Studio, and some screen recording software.

[procrastinator]

I would expect the n x v vector to have to be normalized, unless the v vector is.
edit: on the other hand, if n is unit then f would have the same scale as e so maybe it evens out?

[JorgeVinoRodriguez]

Haven't read it myself, I hear mixed things.

[NeilRoy]

Starting to hate math again. 2D game programming is looking better and better all the time.