Count the number of intersections between any two curves

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]

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]

I have two analytical functions.

Answer 1

[Matt J]

The only general way (i.e., for arbitrary curves) is using the Symbolic Math Toolbox,

solve(curve1==curve2)

Answer 2

[Dimitris Kalogiros]

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);

[Dimitris Kalogiros]

.... and here you are what you get, when you run this code