Finding inflection point on a x,y plot

Hi, how can i find the inflection point of the plot in the circled area. See attached image. The plot is based on x,y coordinates rather than a function.

Thanks

[John D'Errico]

There are actually THREE inflection points on that plot.

[Image Analyst]

Do you mean the x location where the "flat-ish" part in the black oval goes from concave down to concave up? Just curious, since this could be imprecise and happen anywhere over a wide range of x, why do you want this location?

[Image Analyst]

Do you mean the x location where the "flat-ish" part in the black oval goes from concave down to concave up? Just curious, since this could be imprecise and happen anywhere over a wide range of x, why do you want this location?

[jchris14]

well yes. But is there a way to find the exact points from either the plot or the x,y data?

Answer 1

[Adam Barber]

Do you have an analytic (symbolic) representation of the function? Or just numerical data?

If you have an analytic representation, you can just differentiate it twice to find the inflection point. You can also do this numerically with gradient or diff, then find where it is zero (or approximately zero) to find the inflection point.

[jchris14]

I understand the function differentiation to get the inflection point. However i only have numerical data.. sigh.

[Matt J]

Then you should do a curve fit to the data, and use analytical differentiation on the resulting fit.

[jchris14]

already thought about that but what fit fits that crazy plot?

[Matt J]

Maybe a smoothing spline,

http://www.mathworks.com/help/curvefit/csaps.html