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matlabcontourcontourf
Vignesh R
Vignesh R

Reputation: 53

Volume under a contour surface in matlab

I am using contourf to generate a contour plot for a 2 variable function.

My function is Z = f(x,y).

I generate x and y through meshgrid function in matlab and generate values for Z and then plot the contour using contour(x,y,z).

I want to be able to calculate the volume under this generated contour. Can anyone please help ?

Thanks in advance

Upvotes: 0

Views: 1268

Answers (1)

andrew
andrew

Reputation: 2469

couldn't you simply use a integral approximation like a riemann sum? Assuming uniform spacing for x and y something like this should work

delta_x = x(2) - x(1);
delta_y = y(2) - y(1);
vol = sum(Z(:)) * delta_x * delta_y;

This will not be the EXACT volume, but an approximation. Since you know your function you would get a more accurate answer by performing the integration of the function. But if you did not know the function you would use this method or any other numerical integration method.

From calculus we know that an actual integral is just a reimann sum where the width of each interval is infinitely small, so this should be a valid approximation

Upvotes: 1

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