# Count the number of intersections between any two curves

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SATHYA PRIYA SUGUMAR on 11 Nov 2019
Edited: Matt J on 11 Nov 2019
Hi all,
I have two curves and I need to find and count the number of times they intersect. Is there any matlab function to do so?

Dimitris Kalogiros on 11 Nov 2019
Do you have an analytical function for each of these curves or you have just two arrays containing samples of these curves at some time instances ?
SATHYA PRIYA SUGUMAR on 11 Nov 2019
I have two analytical functions.

Matt J on 11 Nov 2019
Edited: Matt J on 11 Nov 2019
The only general way (i.e., for arbitrary curves) is using the Symbolic Math Toolbox,
solve(curve1==curve2)

Dimitris Kalogiros on 11 Nov 2019
Edited: Dimitris Kalogiros on 11 Nov 2019
If you have two functions y=f(t) and y=g(t) you can find their intersections by solving the equation f(t)=g(t). But such a thing (maybe) should be an impossible task.
So, here you are a more general approach
clearvars;
clc;
syms t f(t) g(t)
%define functions
f(t)=(t^2)+3*sin(2*pi*t)-2
g(t)=exp((1/2)*t)
%plot the functions
fplot(f(t)); hold on;
fplot(g(t));
%refine plot
grid on;
legend('f', 'g');
ax = gca;
ax.YAxisLocation='origin';
ax.XAxisLocation='origin';
%determine intersections
downLimit=-5; upperLimit=5; %area of searching
dt=0.1; % accuracy step (it should be small enough)
rootCounter=0;
h(t)=f(t)-g(t);
for t=downLimit:dt:upperLimit
if h(t)==0 %f(t)=g(t)
rootCounter=rootCounter+1;
elseif h(t)*h(t+dt)<0 % f(to)=g(to), t<to<t+dt
rootCounter=rootCounter+1;
end
end
fprintf('found %d roots', rootCounter);

#### 1 Comment

Dimitris Kalogiros on 11 Nov 2019
.... and here you are what you get, when you run this code 