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DGR_Carter1-Visitor
1-Visitor
November 5, 2020
Solved

Find an equation of a curve between two known curves

  • November 5, 2020
  • 2 replies
  • 5362 views

I have two data sets that I can curve fit to get polynomial equations for. These are 2D data sets for temperatures of 23C nd 65C. I want to find the equation of a curve at 52C based on these two curves. I could interpolate between each value and generate a new data set piece by piece, but hopefully there is a better solution? Any help woudl be greatly appreciated. The data sets are attached in Prime 6.0

 

Thanks in advance!

Best answer by Werner_E

I added spline interpolation to give you an idea what it looks like and why I suggested to stay with linear interpolation.

You could change "cspline" to "lspline" for a less oscillating curve, but I guess that there is no benefit in using spline interpolation.

Werner_E_0-1604607928584.png

Remark: You talked about "polynomial fit" and even though I called my function (wrongly) "fit" it is NOT a fit but rather an interpolation, no matter if linear or spline. A polynomial fit could be obtained using polyfit, but the resulting curve normally would not run through a single single one of the 15 given data points (unless you chose a polynomial of order 14) but will be a good overall fit. Here an example to fit the data with a simple quadratic parabola:

Werner_E_0-1604611372660.png

 

One additional remark: Luckily the x values were the same for both data sets (vx=vx65). If the data would have been sampled at different x values, an additional step would have been necessary.

 

 

Modified P6 worksheet attached

 

2 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
November 5, 2020

May be so

1-2-New.png

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
November 5, 2020

1-2-New-Plot.png

W
Werner_E25-Diamond I
25-Diamond I
November 5, 2020

Here is an utility function you might find useful.

It uses linear interpolation only and I think thats all you need as you don't gain any value by spline interpolation. But of course it would be easy to replace the linear interpolation by a spline interpolation. Only the first one, as for the temperature you would have to stay with linear interpolation as you only have two values.

Werner_E_0-1604606369208.png

Werner_E_1-1604606419645.png

P6 worksheet attached

 

    W
    Werner_E25-Diamond IAnswer
    25-Diamond I
    November 5, 2020

    I added spline interpolation to give you an idea what it looks like and why I suggested to stay with linear interpolation.

    You could change "cspline" to "lspline" for a less oscillating curve, but I guess that there is no benefit in using spline interpolation.

    Werner_E_0-1604607928584.png

    Remark: You talked about "polynomial fit" and even though I called my function (wrongly) "fit" it is NOT a fit but rather an interpolation, no matter if linear or spline. A polynomial fit could be obtained using polyfit, but the resulting curve normally would not run through a single single one of the 15 given data points (unless you chose a polynomial of order 14) but will be a good overall fit. Here an example to fit the data with a simple quadratic parabola:

    Werner_E_0-1604611372660.png

     

    One additional remark: Luckily the x values were the same for both data sets (vx=vx65). If the data would have been sampled at different x values, an additional step would have been necessary.

     

     

    Modified P6 worksheet attached

     

      D
      DGR_Carter1-VisitorAuthor
      1-Visitor
      November 5, 2020

      Hello Werner,

       

      That is really great and exactly what I was looking for. I also worked this in Excel and did the linear interpolation between the two points individually to generate a new curve, but was not sure how to do this in MathCAD. 

       

      Thanks very much for your help!

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