Calculate volume below a 3D points

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sarah Abdellahi
sarah Abdellahi 2019-6-27
回答： darova 2019-6-28
I have a set of x,y,z numbers and would like to calculate the volume beneath the surface that passes through them. The data(T) is attached. x=T(:,1), y=T(:,2), z=T(:,3).
Can you please help me.
I use the followig code:
x=T(:,1);
y=T(:,2);
z=T(:,3);
plot3(x,y,z,'.')
interpZ = @(xi,yi) griddata(x,y,z,xi,yi) %set up interpolation
vol = quad2d(interpZ,min(x),max(x),min(y),max(y)) %volume should be close to 1
I get a Nan and " Non-finite result. The integration was unsuccessful. Singularity likely."

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采纳的回答

darova
darova 2019-6-28
Which volume do you want to calculate? Values of surface are below and above also
img.png Untitle1d.png
I tried rough method: values of Z in each node multiply dx*dy and sum
img1.png
But the result is not close to 1 ( )

更多回答（1 个）

infinity
infinity 2019-6-27
Hello,
There is a problem with the interpolation function which is not good to give us a smooth fuction. If you plot the "interpZ" function with the data of x and y like this
plot3(x,y,interpZ(x,y))
you will see the function of Z now is not single value function anymore.
To solve your problem, you need to find a nother way to approximate the data. Or, you may refer other methods that use numerical approximate directly on your data, for example,
https://it.mathworks.com/help/matlab/ref/trapz.html
https://it.mathworks.com/matlabcentral/answers/299064-double-numerical-integration-of-an-experimental-data-no-function

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