Calculate volume below a 3D points

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."

Answer 1

[darova]

Which volume do you want to calculate? Values of surface are below and above also

I tried rough method: values of Z in each node multiply dx*dy and sum

But the result is not close to 1 ( )

Answer 2

[infinity]

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