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

calculusintegralintegrationMATLABpolyareatrapz

Hi!
I would like to calculate the area under the curve (in direction to Z axis – see the attachment file), which is formed of discrete values on the edge of a closed curve. I have an idea, but it is a quite arduous method (using 'trapz' function), does anyone have any other suggestions?
Thanks in advance!

Best Answer

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:
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