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I am currently working on a computer science project where I have to evaluate charts. The charts are simple lines in a $x$ - $y$ coordinate-system, given by CSV files. The flatter the curve, the better for me. Now I am looking for an indicator for the "flatness" of this curves.

My first idea was to calculate the first derivative of the function and then calculate the average between two points. If this value is near $0$, then the function is pretty flat.

Is that a good idea? Is there any better solution?

Kazark
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Thomas Uhrig
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    How about curvature? – J. M. ain't a mathematician Sep 16 '11 at 16:31

  • "The charts are simple lines in a x - y coordinate-system".... are those charts lines or curves? If lines, then slope is simple to compute.

     –  Mar 08 '12 at 18:11
  • By "flatness" do you mean "horizontal-ness" or "un-curved-ness"? If the former, then the average slope at the point isn't a bad choice, assuming slowly varying data. But consider three points in sequence that form a letter "V" --- is the bottom of the "V" flat?. If the latter, then consider curvature. – John Hughes Apr 03 '18 at 13:03
  • Take the 1st and the last points (sorted by $x$). Compute the linear function $f(x)=ax+b$ thought those 2 points. For the remaining points, compute the standard deviation between $(x_i, y_i)$ and $(x_i, f(x_i))$. If it's 0, then the points are on the line. This should be a good enough indicator of flatness. – rtybase Apr 03 '18 at 17:33

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