Calculate volume below a 3D points

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sarah Abdellahi
sarah Abdellahi el 27 de Jun. de 2019
Respondida: darova el 28 de Jun. de 2019
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."

Respuesta aceptada

darova
darova el 28 de Jun. de 2019
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 ( )

Más respuestas (1)

infinity
infinity el 27 de Jun. de 2019
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,

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