Count the number of intersections between any two curves

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SATHYA PRIYA SUGUMAR
编辑： Matt J 2019-11-11
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?
  2 个评论
Dimitris Kalogiros
Dimitris Kalogiros 2019-11-11
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 ?

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回答（2 个）

Matt J
Matt J 2019-11-11
编辑：Matt J 2019-11-11
The only general way (i.e., for arbitrary curves) is using the Symbolic Math Toolbox,
solve(curve1==curve2)
Dimitris Kalogiros
Dimitris Kalogiros 2019-11-11
编辑：Dimitris Kalogiros 2019-11-11
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);

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