Best fit on profile of a line (technical question)

[mespejel]

Hello,

Does anyone have a useful link to learn more about the least squares best fit. I'm looking forward to do manual calculations for a line profile data set.

Thanks,

[JEFMAN]

Could you describe a little more.
The line is on the flat section, or is it an edge ?
Do you "cut" the COP construct a line ?
I would say profile in front of standards should use minmax vector.

[JEFMAN]

The deviations can be calculated by different ways :
- least square (alone) just uses distances between measured values and theo values :
ASSIGN/V1=SQRT(DOT(SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ,SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ))
and then minimizes the sum of the square of deviations.
- least square vector uses the definition of the deviation, which is the projection of the deviation along the theo vector :
ASSIGN/V2=DOT(SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ,SCN1.HIT[1..SCN1.NUMHITS].TIJK)
and then minimizes the sum of the square of deviations.
- minmax vector uses also the definition of deviations, but the algorithm search to minimize the difference between the max deviation and the min deviation.

You can try using the excel sheet in the #6 here, I'm not sure it works fine in english...

https://www.pcdmisforum.com/forum/pc...ares-vs-vector

[JEFMAN]

That's different values that I find (different than yours !):

Minimax	0.4933
max	0.5157
min	0.0224
LS vector	0.6377
max	0.2516
min	-0.3270
LS only	1.7577278
max	0.4933
min	-0.3738

[JEFMAN]

Yep, values are approximately the same (can change after the 4 decimal place)
Init is used to start the calculation with 0 on each displacement.
LS only is the minimization of distances with least squares, LS vector is distances along the vector and minmax also.

[JEFMAN]

I think it's because of the deviations along z.
On theo values, there's a variation between 5 and 33 mm, so the vectors shouldn't be <0,0,1>.
Projecting along the vector or calculating the distance "point to point" (meas to theo) give very different results because the distance are not measured along the same direction.

[JEFMAN]

I would use minmax vector...
LS vector is intersting if there are some outliers hits...
I can't answer to your question without seeing the part, the method...
I just would say that you can give the result that you want if you add to the result the algo used...

[JEFMAN]

I think it should be the same,exept if my prog is wrong !

[JEFMAN]

I made it on my own, just applying what I know...
I know that a french teacher wrote something about it, I don't know if he did it in english (Bernard Anselmetti).
You can try a google search with "using excel solver in gd&t" ?

[Cumofo]

https://docs.hexagonmi.com/pcdmis/20...nt_Methods.htm