Need help aligning a ring with flats on the ID

[[Gr...]]

I need to inspect a small ring that has an unusual shape. Most of the alignment is easy, using the top plane and OD. The unusual part is what should be the ID. It's two pairs of opposing flat spots with an arc segment joining them.

Where I'm struggling is locking in planar rotation. I've got the programming scanning the ID as a continuous curve, then use the OD and the inner curve to do an "Alignment from Several Curves" / "Curve Best Fit" where it can only rotate around the Z axis. Is this the best method?

(Attached drawing has been changed from the actual part, but is close enough to get the point across)

[[Ma...]]

Gregory,
If you have the Curve option, this is the best option for rotation.
To cross check, you can perhaps make small straight lines with two points on the left and right and check the angles.

[[Ma...]]

Inform workers about placement of a part and scan at least 2x radius 21 with locked radius to get their center point to get rotation locked ( or perhaps would one be enough ).

Curve would be the best.

[[Ri...]]

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I would think that two-point lines could be achieved even if it was on the R21?
I suggest line scans then check for parallelism of opposing lines (2 places), if the parallelism fails at some value, check your alignment.
If you have PCM you may be able to use a loop with IF Then logic.

[[Ni...]]

Have you tried using a symmetry of two points on both flat sides?
The flat seems small enough that if you eyeball the middle, it should be able to pick up the flat planes.