Order of the rotations around the axes with Euler angles

Question

According to the documentation, with Euler angles:

rotations are performed around the Z axis, the X axis, and the Y axis, in that order.

When I try to reproduce it in the inspector and with scripts, it seems that the rotation order is "YXZ", and not "ZXY".

Do you know the reason of this behaviour ? If Unity use the "YXZ" order, do you know how to convert the euler angles to "ZXY" ?

You can check the GIF files or the script below:

 using UnityEngine;
 public class RotationTest : MonoBehaviour
 {
     public Vector3 rotation;
     public bool useYXZ = true;
     
     private void Awake()
     {
         if (useYXZ) ApplyQuaternionYXZ();
         else ApplyQuaternionZXY();
 
         Debug.Log(transform.eulerAngles);
     }
 
     private void ApplyQuaternionYXZ()
     {
         transform.RotateAround(transform.position, transform.up, rotation.y);
         transform.RotateAround(transform.position, transform.right, rotation.x);
         transform.RotateAround(transform.position, transform.forward, rotation.z);
     }
 
     private void ApplyQuaternionZXY()
     {
         transform.RotateAround(transform.position, transform.forward, rotation.z);
         transform.RotateAround(transform.position, transform.right, rotation.x);
         transform.RotateAround(transform.position, transform.up, rotation.y);
     }
 }

Example of YXZ Example of ZXY

Answer 1

Best Answer

Answer by GGsparta · Mar 31, 2020 at 05:18 PM

Rotations are performed around the global axis, not local. You can test with the following code:

 transform.RotateAround(transform.position, Vector3.forward, rotation.z);
 transform.RotateAround(transform.position, Vector3.right, rotation.x);
 transform.RotateAround(transform.position, Vector3.up, rotation.y);

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Flo_P · Mar 31, 2020 at 05:34 PM 1

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Thank you for your answer ! So if I understand well, the rotation order ZXY with global axes is equivalent to the rotation order YXZ with local axes. Interesting...

DeepDeepWoe Flo_P · Sep 11, 2021 at 08:20 PM 0

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Hello Flo! I'm encountering the same problem as you. the equivalence of global ZXY and local YXZ is really interesting. Is there a mathematical proof for it?

Flo_P DeepDeepWoe · Sep 12, 2021 at 04:36 AM 0

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Hi ! Nice to see that the question is useful for you

Currently you can consider it as an empirical result.

I suppose it may be proven by constructing the quaternions representing the two ways of rotating the axes, and by checking that they are equals.

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Flo_P · Apr 01, 2020 at 08:41 AM 0

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The real name of what I called "Zxy" with local axes (or "Yxz" with global axes) is "roll/pitch/yaw" angles.

To calculate it, use this answer

Order of the rotations around the axes with Euler angles

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