Rotate a Vector3 direction

Question

How can i rotate a Vector3 direction 45 degrees along the y axis? So a Vector3(1,0,0) for example, would become Vector3(0.5,0,0.5).

And i cant use Transform.RotateAround, or any other Transform methos. As i am not applying this Vector3 directly to a object.

Answer 1

Best Answer

Answer by Jessy · Feb 08, 2011 at 08:04 PM

http://unity3d.com/support/documentation/ScriptReference/Quaternion.AngleAxis.html

vector = Quaternion.AngleAxis(-45, Vector3.up) * vector;

That's a general case. For rotation around a world axis, it's faster/easier:

vector = Quaternion.Euler(0, -45, 0) * vector;

For (1,0,0), this results in (sqrt(.5), 0, sqrt(.5)), not (.5,0,.5), by the way. The length of the rotated vector stays constant. To achieve a squared hypotenuse of 1, you add .5, 0, and .5, not .25, 0, and .25, which would shorten your vector.

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Mattivc · Feb 09, 2011 at 08:04 PM 0

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Thanks, this works great.

Jessy · Feb 09, 2011 at 09:47 PM 2

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Glad to hear it. Rotate those vectors like they were on the Witches' Wheel!

beneon · Sep 14, 2014 at 02:34 PM 0

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really thanks a lot

Thaoren · Nov 02, 2018 at 01:47 AM 2

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Thanks! Worked great.

One thing to note is that you cannot do:

 vector = vector * Quaternion.AngleAxis(-45, Vector3.up);

and must do

 vector = Quaternion.AngleAxis(-45, Vector3.up) * vector;

as there are some reasons internal to Unity.

Bonfire-Boy Thaoren · Jul 01, 2019 at 08:55 AM 3

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as there are some reasons internal to Unity.

Nope, reasons internal to mathematics. You wouldn't say that 2/3 and 3/2 are different "because Unity", would you?

ratneshpatel Thaoren · Sep 21, 2019 at 12:40 PM 0

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That is because Quaternion $$anonymous$$ultiplication, A x B is not B x A. This is just the tip of the iceberg when you talk about complexity and beauty of quaternions.

Bunny83 ratneshpatel · Sep 21, 2019 at 02:44 PM 3

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Right, though Unity just decides to only implement Quaternion * Vector multiplication. $$anonymous$$athematically in order to rotate a vector you have to multiply the quaternion on the left side of the vector and the complex conjugate on the right side which is all implicit in that one multiplication operator in Unity. To see an actual run-down I always recommend this Numberphile video. It does simplify the concept a lot, but you get a clue what's actually going on. I once manually derived the quaternion - vector multiplication myself by literally expanding and then simplify the following

 (q.w + q.x*i + q.y*j + q.z*k) * (v.x*i + v.y*j + v.z*k) * (q.w - q.x*i - q.y*j - q.z*k)

though always remember the rules i² = j² = k³ = ijk = -1 and the order. So i*j == k but j*i == -k. i,j and k form a "ring". Writing them in a circle clockwise and you can derive the sign easily.

 // clockwise
 i*j = k
 j*k = i
 k*i = j
 // counter clockwise
 k*j = -i
 j*i = -k
 i*k = -j

in the end the real parts should cancel and you're left with just i,j and k which is your rotated vector.

Here's my run-down. The resulting equations essentially form a 3x3 matrix.

tormentoarmagedoom · Jan 29, 2019 at 09:35 PM 3

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Good question, good answer

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Answer 2

Answer by elhispano · Feb 10, 2013 at 03:00 PM

That operation is dependent on the order. rotatedVector = Quaternion vector OK rotatedVector = vector Quaternion won´t works and will launch a compiler error

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beneon · Sep 14, 2014 at 02:35 PM 0

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ok, Got it.

Answer 3

Answer by EliasMiettinen · Apr 08 at 04:16 AM

You can set the your object rotation as Vector with euler like this:

 Vector3 newRot = new Vector(0f, 90f, 0f);
 transform.rotation = Qauternion.Euler(newRot);

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Rotate a Vector3 direction

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