how to calculate volume of deviation point cloud from integral ?

Hello everyone. I want to find the volume using the formular as in the figure. I constructed the pavement texture point cloud. F(x,y) is the function of point cloud contain x,y,z coordinate so z = F(x,y). It represents the elevation point of pavement texture. F0 is the space plane (reference plane) with the same x,y coordinate. It differents only z coordinate. Therefore, How can I calucate the volume of different plane ? Thank you very much.

Answer 1

[Simran]

Hello @Lyhour Chhay,

To calculate the volume between the two surfaces, the “pavement texture”, which I see you have represented as a point cloud with a function “F(x,y)” and a “reference plane” represented as “(F_0)”, you can follow the following steps:

1.) Open your MATLAB and create a live script.

2.) Then define your function F(x,y).

3.) Define the plane height for which u want to calculate the volume for. For me, I took an example value of:

F0 = 5;

4.) Define the integrand as the difference: F0 – F(x,y).

5.) Then define the limits of your integration. I took these example values:

x1 = 0;
x2 = 10;
y1 = 0;
y2 = 5;

6.) Lastly, perform the double integration as follows:

volume = integral2(integrand, x1, x2, y1, y2);

For my example data, I got the following result:

You can refer to the following documentation for more help:

“integral2” - https://www.mathworks.com/help/releases/R2021a/matlab/ref/integral2.html