How to calculate the volume of a 3D plot defined by a matrix

Hi everyone,

So basically, I am trying to calculate a volume. More precisely, I have a height field that is defined in every point of a 2D plane and nammed "h_real" in my code. This quantity is a 3D matrix because each height field is computed at every timestamp so for each time frame corresponds a given height field.

I would like to estimate the evolution of the volume associated to the height's progression during the considered time period (which is the length of the 3D matrix). I have tried this script but the result obtained is not accurate...

Could someone help me to find a new strategy to do so please ?

Thank you in advance

 for i = 1:length(h_real)
    
    volume(i) = sum(h_real(:,:,i),'all')*(scale^2)*(1e6);

    plot(volume)
    ylabel('Volume (ml)')
    xlabel('Number of images')
    title('Evolution du volume au cours du temps');
    
end

Answer 1

[Matt J]

It looks fine, though I would do it this way:

    volume=reshape( sum(h_real,[1,2]), 1,[])*(scale^2)*(1e6);
  
    
    plot(volume)
    ylabel('Volume (ml)')
    xlabel('Number of images')
    title('Evolution du volume au cours du temps');

[Wissem]

Thanks for sharing.

So you think that if this method doesn't give me a relevant result it's because there is something wrong with my initial data "h_real" ?

Don't you think that using the "sum" function is a little bit wrong in a certain way ?

Thank you again.

[Matt J]

So you think that if this method doesn't give me a relevant result it's because there is something wrong with my initial data "h_real" ?

Yes.

Don't you think that using the "sum" function is a little bit wrong in a certain way ?

Not if your data is smooth. You might be able to do a bit better with trapz().

 volume=reshape( trapz(trapz(h_real,1),2), 1,[])*(scale^2)*(1e6);

[Wissem]

Thank you for your answers : it helps me to reconsider again my initial experimental results.

Best regards.