I want to find inflections point for point data input?

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.

Answer 1

[Guillaume]

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.

[Vishal Rajpurohit]

sir, i have edited the question. Can u please explain with full code? It will be helpful. thank you

[Guillaume]

It's still the same code I've written, except you replace y by y1. But as I said, interpolating doesn't really change the location of your inflection points.

[Vishal Rajpurohit]

When I replace y by y1. it shows like this

where square show(4,8) and there are two curve blue and red where blue curve created with the help of interp1(spline) and red curve with help of plot(x,y). what is the meaning of three values (77,3039,...)?

[Guillaume]

what is the meaning of three values

They're the indices of your inflection points. The x coordinate of these points is thus

x1(inflection_idx)

and the y coordinate

y1(inflection_idx)

[Vishal Rajpurohit]

sir, your code show the maxima or minima points.

Possibly inflection points are those points where curvature of curve changes sign.

[Guillaume]

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)))));

[Vishal Rajpurohit]

thank you sir,