unity - In Unity3D, what is the relation between inertiaTensor and inertiaTensorRotation?

In unity3d there are two properties on rigidbody that correspond to the moment of inertia tensor.

One of them is: rigidbody.inertiaTensor, which I know is the diagonal of the inertia tensor,
The other is rigidody.inertiaTensorRotation, which I don't quite understand. I have, though, created a rigidbody in such a way that I get it to be other number than Quatenion.identity, but I still don't see the connection.

Can I describe the products of inertia tensor with the rotation or ... what is the relation between them and where would I require them?

Answer

inertiaTensor is a Vector3, inertiaTensorRotation is a Quaternion. And from the docs for inertiaTensor:

The inertia tensor is rotated by the inertiaTensorRotation.

Essentially, inertiaTensor is the moment of inertia (defined as a tensor) and the inertiaTensorRotation is how that tensor is rotated.

If you'd like them to be calculated automatically, you don't set them. Or you can call Rigidbody.ResetInertiaTensor which:

After calling this function, the inertia tensor and tensor rotation will be updated automatically after any modification of the rigidbody.