Fitting algorithms

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  • Fitting algorithms

    I have stumbled upon a Min and Max tsebashev fit algorithm for a circle. Based on the help file : minmax - the circle is fitted halfway between two circles, with a common centre, which have the minimum distance between them which encloses all the data. This has the effect of minimising the maximum deviation of any data point from the fitted circle. Note that the two circles are not the same as those produced using Maximum inscribed and Minimum

    it seems simple enough, however I don’t understand how the two circles being constructed. It says that they are not the same as max inscr. And Min circumscribed. What are they?

    At the end of the day, I want to understand where Min and max could be used or should not be used.
    B&S One
    PC-DMIS CAD v2014

    Romer Infinity

  • #2
    Chebychev (in English, or Tchebychev in french, or ????? in Russian !) calculates the min deviation.
    It's the algo which is used to calculate the circularity.
    If you want to check it, just construct a min_sep circle, dimension the circularity and the dimension / form, and you will find the same result.

    Maximum inscribed circle is the max diameter that you can find inside the COP (I call COP all the hits of the circle, it's easier).
    If you dimension the form, you will find 3 values of 0, and all the arrows will be external.

    The min circ is the same, but on the other side.

    Max inscr and min circ should be used for datums and enveloppe requirement.

    Hope it 's clear...


    • Vladimir
      Vladimir commented
      Editing a comment
      Чебычев in Russian

  • #3
    You can play with this : (36 random hits - and different subs to calculate different circles)
    Last edited by JEFMAN; 06-14-2021, 09:26 AM.


    • #4
      Maybe this picture helps - I generated a perfect circle Ø60.5 around <0, 0>, then moved the rightmost point (PNT2) a bit to the left (10.25 mm inwards).

      The MIN_CIRCUMSCRIBED is perfect (MEAS = THEO), as it ignores the inside point, all the others differ one way or another.

      Note for example that the MAX_INSCR gets a center offset in both X and Y, even though PNT2 only errors in X - unexpected, but correct.

      Red - Min Circumscribed, Ø60.5
      Green - Least Squares, Ø57.26
      Blue - Chebychev (minsep), Ø58.241
      Black - Max Inscribed, Ø50.604

      Last edited by AndersI; 05-16-2019, 04:21 AM.
      SW support - Hexagon Metrology Nordic AB


      • #5
        Thanks guys, a lot of interesting information. What about a step measurement. I have a step depth about .250" from -A-. How do I report a Maximum and Minimum envelope ? If I am not mistaken Location dim. and distance dim. used LS algorithms correct? Outputting Min and Max is not necessary the same thing as Maximum envelope, so how does one do that? Any help appreciated.
        B&S One
        PC-DMIS CAD v2014

        Romer Infinity


        • #6
          I think you have to use the "Size" in FCF, and look at the right parameter (E, GX or GN, depends on the drawing)

          Sorry Wolfman, I didn't look at your verion software, Size option appears in 2017 or 2018.

          In this case, I think that the max height envelope could be the min distance between the step and the datum (datum as reference), so the distance of the highest point of the step to the plane.
          Last edited by JEFMAN; 05-16-2019, 03:43 PM.


          • WolfMan
            WolfMan commented
            Editing a comment
            In that case, I think that measuring the step with a bunch of. Vector points would be ideal. The highest point could be used to represent max envelope and same thing for the Min envelope. Or scan it and then using variables get the max point and max point.

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