Quaternion.Angle is inaccurate

Question

I have a strange issue with comparing angles. I do want to detect if an object rotated during the frame, using

 if(Round(lastRotation, transform.rotation)) { // rotations are equal }
 
 bool Round(Quaternion a, Quaternion b) {
     return Quaternion.Angle(a, b) < 0.001f;
 }

However, that returns false for some quaternions that are absolutely equal. Here's a debug print of those:

 //  (first value: Quaternion.Angle(a,b); -- this should be zero! Then the Quaternions xyzw; then the eulerAngles xyz)

 diff_rot: 0.03956468; (0.02575354000000000000, 0.96469100000000000000, -0.24099940000000000000, 0.10308820000000000000) != (0.02575354000000000000, 0.96469100000000000000, -0.24099940000000000000, 0.10308820000000000000); (28.05311000000000000000, 167.80090000000000000000, 0.00000024185890000000) != (28.05311000000000000000, 167.80090000000000000000, 0.00000024185890000000)

Why on earth do two exactly equal rotations (even equal in floating point!) return a non-zero angle? And not even a small one, but 0.03 degrees, which would be a visible change in rotation?

Here's a script to test yourself this strange behaviour: link text

Answer 1

Answer by Amir1360 · Jan 14 at 02:35 PM

It seems that Quaternion.Angle function is not accurate. Try the following function instead:

 float AcurateAngle(Quaternion a, Quaternion b)
 {
      GameObject go = new GameObject();
      go.transform.rotation = a;
      Quaternion.Inverse(b).ToAngleAxis(out float angle, out Vector3 axis);
      go.transform.Rotate(axis, angle);
      go.transform.rotation.ToAngleAxis(out angle, out _);
      Destroy(go);
      return angle;
 }

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Pangamini · Jan 14 at 03:09 PM 1

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Wow, creating and destroying a gameObject just to calculate an angle seems brutally inefficient

Quaternion.Angle is inaccurate

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