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I want to find inflections point for point data input?

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i have input points
x=[0 1 2 3 4 5 6 7 8 9 10]
y=[5.0000 6.0000 8.0000 9.0000 8.5000 8.0000 7.0000 6.5000 7.0000 8.0000 10.0000]
x1=0:0.001:10;
y1=interp1(x,y,x1,'spline');
plot(x1,y1);
i want to find inflection points on that curve?
explain with full code please.

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Accepted Answer

Guillaume
Guillaume on 15 Jun 2018
The inflections points are when the sign of the difference of your y changes. So, whichever way you obtain your y points (as is or using linear or spline interpolation), the indices of the inflection points are:
inflection_idx = find(diff(sign(diff(y)))) + 1; %+1 to compensate for the index shift caused by the double diff
Note that linear interpolation won't change the location of the inflection points, it'll still be at y=9 and y=6.5, and even with spline interpolation it's not going to change much.

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Vishal Rajpurohit
Vishal Rajpurohit on 16 Jun 2018
sir, your code show the maxima or minima points.
Possibly inflection points are those points where curvature of curve changes sign.
Guillaume
Guillaume on 18 Jun 2018
Yes, not sure what I was thinking, it's the 2nd derivative, so a double diff:
inflection_idx = find(diff(sign(diff(diff(y1))))) + 1;
It may be more accurate to use gradient instead of diff to calculate the 2nd derivate:
inflection_idx = find(diff(sign(gradient(gradient(y1)))));

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