Constrained Least Squares confusion - 2021

With "Constrained Least Squares", the used algorithm IS "Least Squares", no doubt about it, but after calculating it, a constrainment is used on it by shifting the least squares solution to the high point, giving a very stable and reproducable solution. So, yes, it is in fact named correctly.

Paganini is correct. For AMSE we now default to using constrained L2 for datum fitting as per the ASME Y14.5.1 - 2019 math standard. For ISO we default to constrained min/max as per ISO5459:2011. In either case you are able to manually over-ride by selecting least squares.

See this section of the help files: https://docs.hexagonmi.com/pcdmis/2022.2/en/helpcenter/mergedProjects/core/geometric_tolerances/How_PC-DMIS_Solves_Datums.htm#MiniTOCBookMark4

I was under the assumption from reading the manual that the new Default math type regarding 'Coinstrained Least Squares' is an external simulator then if needed does some least squares math to account for stability issues.

ASME is all about functionality and external fits, avoiding interference. I don't see PCDMIS going to a math method that could push parts thru Quality that had interference fits. Am I reading this wrong somehow?

I think you're reading it wrong. It doesn't do an external fit, then uses least square to maximise stability.

It uses constrained least square to give give an external fit, whilst maximising stability.

Correct. It does a least squared fit first, then shifts, external to material. I obviously can't share the exact algorithm on a public forum as it is Hexagon's intellectual property.

You can take a look here...
https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=921833
or here :
https://www.nist.gov/publications/constrained-l2-based-algorithm-standardized-planar-datum-establishment

Thanks all. I'll read those links you provided...I took a brief look they look intimidating.

So I read what I could on those links and re-read some areas in PC DMIS core manual. I may have not been clear on my original post....

My problem with calling the new default ASME standard 'constrained least squares' is that someone without a proper understanding and is a little sick in the head, as we all may be, could mis-understand this as a least-squared fit...In essence, they could feel comfortable that a large external hit in the MMC direction may be averaged out and the plane or cylinder datum would be allowed to interfere with this surface hit point(datum feature). This is what I first thought when I read the term 'constrained least-squares'.

A while back when I read the manual on datums, I learned that the term 'constrained' is defined in the core manual as being 'external'. So why not just call the damn thing 'external'. 'External least-squares' seems much less ambiguous than 'constrained least-squares'

So maybe I misspoke when I said I didn't think this was least squares...I just wanted to see if you all felt some of my confusion in that the critical thing with this math type is that it is 'external' being a surface plate, pin gage, hard gage type measurement, when a simple 'least-squares' can have interference hit points with the datum. I associate least-squares with allowing for this interference. Knowing that 'constrained' means 'external' is not common knowledge in my opinion. Maybe, I just am not seasoned enough to realize everyone knows this, but this wasn't intuitive to me a year ago. I ran 2021 this week and it reminded me of this issue and wanted to post my confusion.

You all are an amazing group of people and have been an unbelievable resource to me, thanks.

So I read what I could on those links and re-read some areas in PC DMIS core manual. I may have not been clear on my original post....

My problem with calling the new default ASME standard 'constrained least squares' is that someone without a proper understanding and is a little sick in the head, as we all may be, could mis-understand this as a least-squared fit...In essence, they could feel comfortable that a large external hit in the MMC direction may be averaged out and the plane or cylinder datum would be allowed to interfere with this surface hit point(datum feature). This is what I first thought when I read the term 'constrained least-squares'.

A while back when I read the manual on datums, I learned that the term 'constrained' is defined in the core manual as being 'external'. So why not just call the **** thing 'external'. 'External least-squares' seems much less ambiguous than 'constrained least-squares'

So maybe I misspoke when I said I didn't think this was least squares...I just wanted to see if you all felt some of my confusion in that the critical thing with this math type is that it is 'external' being a surface plate, pin gage, hard gage type measurement, when a simple 'least-squares' can have interference hit points with the datum. I associate least-squares with allowing for this interference. Knowing that 'constrained' means 'external' is not common knowledge in my opinion. Maybe, I just am not seasoned enough to realize everyone knows this, but this wasn't intuitive to me a year ago. I ran 2021 this week and it reminded me of this issue and wanted to post my confusion.

You all are an amazing group of people and have been an unbelievable resource to me, thanks.

I understand that it can be confused...
Now, it's called L2 constrained, maybe it's not very clear (as L infinite is minimax).
What I retain is that minimax and L2 are different only in convex planes datums, and L2 constrained is not parallel to a least square plane shift to the max point (because there are not parallels).
I hope that what I retain is true !!!!!!!