How to determine concavity point?

I have a bunch of data that when plotted look similar to this:

I want to know how I can use MATLAB to determine the corner or vertex or sometimes called concavity point (there are two in this plot that I have, one in the red data and one in the blue data)?

Answer 1

[John D'Errico]

You give no data, so I'll need to make some up for an example.

x = linspace(-30,30,500);
y = cumsum((atan(x - 10)/2 + 1));
plot(x,y)
grid on

So a simple enough curve. Can we locate the point where there is a change? As long as the stride between points is constant, then a tool like findchangepts might help.

ipt = findchangepts(y,'Stat','linear')

ipt = 331

[x(ipt),y(ipt)]

ans = 1×2

9.6794 88.9733

hold on
plot(x(ipt),y(ipt),'ro')