Calculating the Volume between two 3D surfaces/meshes

I have two sets of data for the same surface, each with X, Y and Z coordinates. One data set for before and one for after the surface undergoes deformation. I am trying to calculate the volume between the two surfaces to quantify the change. My code is as follows:

clear,clc,close all

Table = readtable ('Final Data','Sheet','Analysis Data', 'ReadRowNames', true,'PreserveVariableNames', true);

%Sample Before

xs1 = Table ('X-P1B',:);

ys1 = Table ('Y-P1B',:);

zs1 = Table ('Z-P1B',:);

xn1 = table2array(xs1);

yn1 = table2array(ys1);

zn1 = table2array(zs1);

X1 = linspace(min(xn1),max(xn1),250);

Y1 = linspace(min(yn1),max(yn1),250);

[xq1,yq1] = meshgrid(X1,Y1);

zq1 = griddata(xn1,yn1,zn1,xq1,yq1,'natural');

%Volume Calculation

dxn1 = (max(xn1)-min(xn1))/250;

dyn1 = (max(yn1)-min(yn1))/250;

volB= dxn1*dyn1*sum(zq1(~isnan(zq1)));

%volk = trapz(Y1,trapz(X1,zq1(~isnan(zq1)),2)); Does not work.

plot3(xn1,yn1,zn1,'mo')

hold on

mesh(xq1,yq1,zq1)

xlabel('x')

ylabel('y')

%Sample After

xs2 = Table ('X-P1A',:);

ys2 = Table ('Y-P1A',:);

zs2 = Table ('Z-P1A',:);

xn2 = table2array(xs2);

yn2 = table2array(ys2);

zn2 = table2array(zs2);

X2 = linspace(min(xn2),max(xn2),250);

Y2 = linspace(min(yn2),max(yn2),250);

[xq2,yq2] = meshgrid(X2,Y2);

zq2 = griddata(xn2,yn2,zn2,xq2,yq2,'natural');

%Volume Calculation

dxn2 = (max(xn2)-min(xn2))/250;

dyn2 = (max(yn2)-min(yn2))/250;

volA= dxn2*dyn2*sum(zq2(~isnan(zq2)));

%volk = trapz(Y2,trapz(X2,zq2(~isnan(zq2)),2)); Does not work.

plot3(xn2,yn2,zn2,'mo')

hold on

mesh(xq2,yq2,zq2)

xlabel('x')

ylabel('y')

The first method I have used to calculate volume, returs a value. However, I am unsure of which reference plane has been used to calculate the volume. I assume it would be the plane formed by min(yn1) (or min(yn2) in the second case) and the meshgrid. Is it possible to define a common reference plane for both the Before and After Surfaces, so that simply the difference between the two can give me the desired result.

I've tried using trapz but that returns "Point spacing must be a scalar specifying uniform spacing or a vector of x-coordinates for each data point."

Thanks.

Answer 1

[KSSV]

You can use trapz.

https://in.mathworks.com/matlabcentral/answers/142739-how-can-i-know-the-volume-behind-a-surface

[Keith Hay]

I tried using trapz as:

volk = trapz(Y1,trapz(X1,zq1(~isnan(zq1)),2));

It returns the error "Point spacing must be a scalar specifying uniform spacing or a vector of x-coordinates for each data point.". The same happens when I try the method you linked.

[KSSV]

When you consider only numbers and remove nans the grid and data dimension changes.