How to calculate the volume of object that has several 2D profiles (slices)

Dear All,

I would need help on how to calculate the volume of object that has several 2D profiles (slices). All 2D profiles has the same number of data.

Thank you

Aziz

Answer 1

[Ayush]

Hi,

Assuming that the slices are equally spaced and represent cross-sections of the object, you can approximate the volume by summing the areas of the slices and then multiplying by the distance between the slices. It is similar to what we do in calculus for finding the volume of solids of revolution. Suppose the slices are not equally spaced, for which you can make use of numerical integration of the slice areas along object length.

For better understanding, refer to an example below, assuming the slices are equally spaced:

% Example to calculate the volume of an object from 2D slices

% Define the areas of each slice (in square units). For example purposes, let's use arbitrary values.
% In a real scenario, you would calculate these areas based on your 2D profile data.
sliceAreas = [100, 150, 120, 130, 110]; % Example areas of slices

% Define the distance between each slice (in units). Assume it's constant for simplicity.
sliceDistance = 5; % Example distance between slices

% Calculate the volume using the trapezoidal rule for numerical integration.
% The trapezoidal rule is a good choice for approximating the integral when data points are evenly spaced.
volume = trapz(sliceAreas) * sliceDistance;

% Display the calculated volume
disp(['The approximate volume of the object is ', num2str(volume), ' cubic units.']);

In the above example, the "trapz" function has been used for numerical integration; for more information on it, refer to the below documentation:

https://www.mathworks.com/help/matlab/ref/trapz.html