creative checkerboard positioning

[VXGrid]

I thought they just estimate two lines from the black to white fields and where they intersect is the middle point.
Of course this might create issues on rounded surfaces, namely if the lines are not lines (straight) but splines.

I'd be willing to bet that most software is extracting checkerboard centers using entirely 2D image analysis very similar to this approach:

https://theailearner.com/2021/10/14/fin ... -accuracy/

Both Faro Scene and Agisoft Metashape ship with OpenCV so I wouldn't be surprised at all if they're actually using the exact function that author describes.

That procedure is going to give you a subpixel 2D target center from which you're going to need to extract the 3D coordinates. If I was doing that I would interpolate the 3D position based on a small number of the immediately surrounding pixels, in which case, putting a checkerboard on a curved surface might not be as bad as you would initially expect compared to trying to do a full 3D plane fit from the beginning.

I don't use checkerboards much and when I have they've been flat so I don't know if that actually works out in practice, but it would be interesting to test out.

This is a really good assumption and explanation.
I totally forgott the 3d part and was only thinking in 2d, but right with the sampling Leandre mentioned there won't be a 3d point where you'd need one, so you either interpolate or you are off. And given that the sampling bias happens from different scan positions the interpolation area shouldn't be too small.