Calculate the Root Mean Square Slope of a surface elevation matrix.

I have a surface elevation matrix with 1987 x 2353 points from a laser scanner. The spacing in the x and y direction is 0.0497 and 0.0415 respectively. I need to calculate the root mean surface slope(Sdq) of the surface which should be calculated from the following equation. I am an newbie in MATLAB and nee your help. A sample of the data matrix is attached here since the comlete file is so big I hope this data part will be okay. If you can write a short code to calculate the room mean slope given the formula I would appreciate. Thanks.

Answer 1

[Ashutosh]

Hello, I will assume that by A you mean the lateral area of the surface you are studying. Hopefully you are aware of general coding structures like a 'for' loop. If not, first please refer to this.

For convention, assume rows as the 'y' dimension and columns as the 'x' dimension. For integrals in MATLAB, you can calculate the value of the integrand for each individual element, and then sum them up using a for loop as below:

t = readtable("<ProvidePathToDataHereWithinQuotes>", "ReadRowNames",false,"ReadVariableNames",false);
t = table2array(t);     % reading the xlsx file and converting to a matrix

dx = 0.0497;
dy = 0.0415;
sum = 0;
for i=1:109         % iterate through y dimension
    for j=1:99      % iterate through x dimension
        dzy = (t(i+1,j)-t(i,j))/dy;     % dz/dy
        dzx = (t(i,j+1)-t(i,j))/dx;     % dz/dx
        s = (dzy^2 + dzx^2) * dx * dy;  % squaring dz/dy, dz/dx and multiplying with dx, dy
        sum = sum + s;
    end
end
Y = size(t,1)*dy;   
X = size(t,2)*dx;
A = X*Y;
rms_slope = sqrt(sum/A);

Hope this helps. In case something is not clear, let me know so you can get used to MATLAB faster.

[Benson]

Thank you!!

[Florin]

Check here below for the standard way to calculate dzy and dzx in the code provided above:

Root mean square slope (R∆q, P∆q, W∆q) | Surface Roughness Parameters | What is line roughness? | Solving the questions about profile and surface roughness measurements! Introduction to "Roughness" | KEYENCE International Belgium