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Determine function from drawing of curve

Is there a specific approach or computer program which can determine the function of a curve in the form ‘f(x)=...’ from the drawing of the curve on the cartesian plane/ next to the x and y axis?

Thank you!
You can decompose the function into some complete set I suppose, like a Fourier series, you will always get an f(x) but whether you will be able to write it with a finite amount of ink is another question.
Unless you know something that the function is close to so you can use least squares or something you won't be able to get it into anything nice.
(edited 4 years ago)
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Medikj
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(edited 4 years ago)
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mqb2766
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Original post by Medikj
Say this is the curve:
Attachment not found


I divided the curve in three sections, the first being from x=0 to x=A, the second from x=A to x=B and the third from x=B to x=where the graph intercepts the x-axis.
It quite easy to find the line equation for the first and third section, as they are lines, I just need to find the coordinates of two points each and that’s it. However, how do I find the equation for the second section, the one that goes from x=A to x=B?
I tried by translating and transforming the parabola y=x^2 but I can’t seem to find how to do that, is there a program which can do that?

If you wanted to fit a quadratic to it, putting it a normal form like
y = a(x - c)^2 + d
Might be easier where the stationary point occurs at (c,d) and a is (half) the curvature. Your middle curve is not symmetric though. So either you have some knowledge about how the curve is generated or fit some form of spline (piecewise polynomial) to it.
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Medikj
OP
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Original post by mqb2766
If you wanted to fit a quadratic to it, putting it a normal form like
y = a(x - c)^2 + d
Might be easier where the stationary point occurs at (c,d) and a is (half) the curvature. Your middle curve is not symmetric though. So either you have some knowledge about how the curve is generated or fit some form of spline (piecewise polynomial) to it.


Thank you!
I mean, you can approximate it. Lagrange polynomials would allow you to approximate the function.

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