Rotate vector by quaternion

How do you rotate a vector by a quaternion?

Apologies for this very simple question, but I just can't find the operation in the Unity scripting reference. I would have expected the '*' operator to work, or there to be a vector.rotateBy method, or something.

As a simple example, I would expect to be able to do this:

var turnRight = Quaternion.FromToRotation(Vector3.forward, Vector3.right);

and then

v * turnRight

to rotate v by 90 degrees (clockwise, looking down) around the Y axis. I'm sure it must be there and I'm just missing it.

 

You're on the right track. The only trick is that the order matters when multiplying vectors and quaternions (matrix multiplication is not comutative).

So Quaternion * Vector3 will work, but Vector3 * Quaternion is undefined and will throw an exception.

 

Well I think I found the answer. The '*' operator simply takes the quaternion on the left. This is not documented either in Vector or Quaternion class references. I'll drop Unity a note about it.

(Edit: Simultaneous post with dawvee. Thanks dawvee!)

 

It is documented, in the Quaternion class reference (to multiply both ways the * operator would need another overload for "Vector3 * Quaternion").

Edit: haha, no problem!

 

Aha! I see what's wrong. In the class reference itself is just says "operator * Combines rotations lhs and rhs." But if you click on "operator *" then it also mentions "quaternion * vector". Still needs fixing imho, but thanks again.

 

You can get Vector3 * Quaternion from Quaternion * Vector3 by using Quaternion.Inverse.

Code (csharp):

1.     v = Quaternion.Inverse(turnRight) * v; // same as v * turnRight

So it's not really a drama.

 

You just resurrected a post that was almost 4 years old to say there was no drama.

 

With a solution that I was looking for, and found it here, after another 4 months.
Really why do it bother you that he resurrected this thread with a valid, actual information? Would you be rather if I created another thread asking another question to this topic?


dmcclurg - Thank you

 

I'm pretty sure he was just poking fun at the no drama line. No need to make drama.

 

You just resurrected a post that was over 4 years old to make a dumb joke.
Nice.

 

See you guys in 4 years!

 

I love you guys. You solved my problem, and you made me smile.

 

This worked for me too!

Jan 20, 2022

 

Just thought I'd check in to let y'all know that there's still no drama

 

I am still using this information a lot and appreciat this forum topic. Well, yes, 4 years rule... Going back to work right now...

 

Everything is looking OK in there. Keep on

 

This thread is so dramatic its amazing

 

lol really funny thread, it helped me and made me smile at the same time.

 

Thought I should just drop by now that it's 2020. Can confirm, still no drama.

 

2020, and this bug (which has a one line of code fix) is still present...

 

It is nearly the end of 2020, and I assure you there is much drama.

 

But there's no drama around Quaternion's * operator, that's for sure.

 

For the last time: THIS IS NOT A BUG. This is how quaternions work. Quaternion multiplication is NOT commutative.

Actually to rotate a vector / point by a quaternion "q" you have to do

p' = q * p * q^-1

where

q^-1

is the complex conjugate of q. It has to be done is this order. Unity does this "sandwich multiplication" internally for you when you do

q * p

. I recommend to watch this 3blue1brown video on quaternions.

 

My 5 cents.
One thing that I have experience (prove me wrong i'm not 100% sure) is that quaternions representing rotation around the same axis are commutative.

 

Helo there!

 

More or less. You can conceptualise quaternions as local rotations. You will get different results if you look up and then roll to the side, and if you roll and then look up. If you nail the rotation to a specific axis and just manipulate one Euler angle - it doesn't really matter, but it's not normally a property of multiplying quaternions and it's something to be aware of.

As for drama, last year was wild, I'm not sure what qualifies anymore. (Search engines still love this thread though.)