MATLAB: How to find area enclosed by a closed curve

MATLAB

I have a set of (x,y) coordinates that, when connected, create an ellipse-like shape on my plot. How can I find the area enclosed within my curve?

Best Answer

One option is to use the "polyarea" function,

https://www.mathworks.com/help/matlab/ref/polyarea.html

where each point is interpreted as a vertex on a polygon. A straight line connects each point, but if you include enough points, your shape will begin to approximate a curve, and your area calculation will be more accurate.

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MATLAB: How to calculate integral along the boundary of closed curve

Provided than (x,y) points are very dense you can approximate the area you ask, good enough:

clear; clc;
% generation of input data
t=0:0.01:2*pi-0.01;
x=4*cos(t); 
y=2*sin(t);
z=sqrt(abs(x))+y.^2+exp(0.6*x);
stem3(x,y,z,'-b'); hold on;
plot3(x,y,0*z,'-k.'); hold on;
plot3(x,y,z,'r*');
xlabel('x'); ylabel('y'); zlabel('z');
% calculation of area (approximately)
A=0;
for n=1:length(x)-1
    A= A+ sqrt( (x(n+1)-x(n))^2 + (y(n+1)-y(n))^2 ) * (z(n)+z(n+1))/2 ;
end
fprintf('Area is %f \n', A)

If you run this script, you will receive something like this:

MATLAB: Can we find the area of curve(i have all data points) with no function

Try with the trapz function

https://fr.mathworks.com/help/matlab/ref/trapz.html

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Related Solutions

MATLAB: How to calculate integral along the boundary of closed curve

MATLAB: Can we find the area of curve(i have all data points) with no function

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