How can you get equations from the complicated graphs by using Matlab?

Hello,

I need equations from the graphs below

The one way I did is to pick several points from these graphs by hand and then, put those points into data in Matlab, and use "Basic fitting" and finally obtained equations. However, It is not perfectly fitting and took me long time. Is there any way to get well fitting equations conveniently?

Thank you

Answer 1

[John D'Errico]

No. There is NO simple equation that will represent those curves, or any general curve you wish to draw. In fact, there are infinitely many functions that will reproduce the data, almost all of which will be garbage in between the points.

Your best bet, if you simply want something that will interpolate the curve is to use a spline. However, a spline can never then be converted to be seen as a simple function, not an easy to write or read function.

If you have a model of the process, then it may SOMETIMES be possible to estimate coefficients of the model that will approximate the curve. But you NEED a model that has the appropriate shape. It is best if the model is derived from physical principles for the process that generated the data.

Just because you have some points does not mean there is a simple function that will represent them well.

[Walter Roberson]

The spline might also have no relationship to the actual function. But it will tend to look pleasing.