multiply quaternion by vector

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Hi all, I have seen in Unity's third person tutorial (and in other scripts) the multiplication of quaternion by vector, that is quaternion*vector3. I don't understand what it means multiply quaternion by vevtor? After all to rotate a point via quaternion one need to do quaternion***vector3*inverse quaternion

thank u in advance

Answer 1

Best Answer

Answer by aldonaletto · Nov 15, 2011 at 10:01 AM

In the quaternion world, multiplication is the way to apply the rotation to something - when you multiply quaternion by vector3, you're actually rotating the vector. For instance:

   var rot = Quaternion.Euler(0, 45, 0); // rot = 45 degrees rotation around Y
   var v45 = rot * Vector3.forward; // rotate vector forward 45 degrees around Y

I didn't understand your question about point rotation - maybe a typo, but what we can read is a quaternion ** vector3 Quaternion.Inverse(quaternion), what makes no sense (this sequence isn't even allowed: Vector3 must be at the right of the quaternions).
In practice, multiplying a quaternion by a point rotates this point relative to the origin (0,0,0).
Finally, Quaternion.Inverse(quaternion) returns the inverse rotation (same rotation, but to the opposite side).

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eyal · Nov 15, 2011 at 10:14 AM 0

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thank you for your answer.Does the rotation tskes place in world or local coordinate system? say in your example

thank you in advance

aldonaletto · Nov 15, 2011 at 04:50 PM 0

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The vector will be rotated in the world space. The quaternion actually represents a single rotation of some angle around an arbitrary axis (not necessarily XYZ), but this axis is relative to the world. If a more complex rotation is specified - like Euler(15, 45, 60), for instance - Unity converts it to a single rotation: the equivalent axis and angle are calculated and encoded in the quaternion format.

dogzerx2 · Sep 04, 2013 at 09:45 PM 0

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This was extremely helpful. THAN$$anonymous$$ YOU!!

kubajs · Oct 23, 2018 at 09:45 PM 0

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Thank you, very helpful answer!

Answer 2

Answer by m16a · Mar 17, 2014 at 06:18 PM

Hi, I had the same problem too. I figured out that notation quaternion * vector uses overloaded multiply operator which incapsulate mathematical multiplying quaternion * vector * quaternion^(-1) similar question

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Answer 3

I know this is quite old post but I believe this visualisation might help a lot to those who are still struggling, just play with it a bit, it's intuitive. I had similar problems with Quaternions and then hpjohn sent me his sample code (https://forum.unity.com/threads/compare-rotation-of-matrix-with-initial-direction.572440/#post-3811600) I played with a bit and added local rotations, now I can understand that much better:

 using UnityEngine;
 
 public class RotationTest : MonoBehaviour
 {
     Quaternion currentState;
     private void Start()
     {
         //store initial state
         currentState = Quaternion.identity;
     }
 
     private void Update()
     {
         //draw axes tripod in viewport for demo
         Debug.DrawRay(Vector3.zero, currentState * Vector3.up, Color.green);
         Debug.DrawRay(Vector3.zero, currentState * Vector3.right, Color.red);
         Debug.DrawRay(Vector3.zero, currentState * Vector3.forward, Color.blue);
     }
 
     private void OnGUI()
     {
         RotateOnGlobalAxis();
         RotateOnLocalAxis();
         CompareCurrentPositionWithInitialState();
     }
 
     private void RotateOnGlobalAxis()
     {
         GUILayout.BeginArea(new Rect(100, 100, 200, 100));
         if (GUILayout.Button("Rotate around global X"))
         {
             currentState = Quaternion.Euler(90, 0, 0) * currentState;
         }
         if (GUILayout.Button("Rotate around global Y"))
         {
             currentState = Quaternion.Euler(0, 90, 0) * currentState;
         }
         if (GUILayout.Button("Rotate around global Z"))
         {
             currentState = Quaternion.Euler(0, 0, 90) * currentState;
         }
         GUILayout.EndArea();
     }
 
     private void RotateOnLocalAxis()
     {
         GUILayout.BeginArea(new Rect(350, 100, 200, 100));
         if (GUILayout.Button("Rotate around local X"))
         {
             currentState = currentState * Quaternion.Euler(90, 0, 0);
         }
         if (GUILayout.Button("Rotate around local Y"))
         {
             currentState = currentState * Quaternion.Euler(0, 90, 0);
         }
         if (GUILayout.Button("Rotate around local Z"))
         {
             currentState = currentState * Quaternion.Euler(0, 0, 90);
         }
         GUILayout.EndArea();
     }
 
     private void CompareCurrentPositionWithInitialState()
     {
         GUILayout.BeginArea(new Rect(225, 200, 200, 20));
         if (GUILayout.Button("Check State"))
         {
             Vector3 currentUp = currentState * Vector3.up;
             if (Vector3.Dot(currentUp, Vector3.up) > 0.9f)
             {
                 Debug.Log("Current State has up pointing up");
             }
             else
             {
                 Debug.Log("Current State has up pointing somewhere else");
             }
         }
         GUILayout.EndArea();
     }
 }

multiply quaternion by vector

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