It’s not as simple as you’d think.

If you want to skip the small talk, the code is at the bottom. Sampling 2D rotations uniformly is simple: rotate by an angle from the uniform distribution . Extending this idea to 3D rotations, we could sample each of the three Euler angles from the same uniform distribution . This, however, gives more probability density to transformations which are clustered towards the poles:

In Fast Random Rotation Matrices (James Avro, 1992), a method for uniform random 3D rotation matrices is outlined, the main steps being:

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