How to create a surface with random spheres protruding?

I'm trying to generate a surface with randomly placed spheres protruding from it.

• Spheres can overlap.
• Sphere diameters should be randomized on a normal distrubution. (e.g. using normrnd, or something similar)
• Sphere height relative to surface should also be randomized on a normal distrubution.

I have this code currently which exhibits what I'm looking for except for the shapes being gaussian functions as opposed to spheres.

Thanks in advance!

close all   % closes open graphs
clear all   % clears out prev variables from workspace
clc         % clears console / cmd window
rng default % keeps RNG seed constant

M = zeros(100,100);                         % initial matrix
gritDensity = 0.002;                        % grit per area
N = size(M,1) .* size(M,2) .* gritDensity;  % number of grit
sigma = 4;                                  % stdev (width) of Gaussian function
maxHeight = 10;                             % maximum height

[x,y] = meshgrid(1:size(M,1),1:size(M,2)); % creates grid

for k = 1:N
    % random location of grit
    xc = randi(size(M,1));  % picks random location on x axis between 0 and max value
    yc = randi(size(M,2));  % picks random location on y axis between 0 and max value
    
    % Gaussian function
    exponent = ((x-xc).^2 + (y-yc).^2)./... % numerator
                    (2*sigma^2);            % denominator
    
    amplitude = rand()*maxHeight;           % picks random grit height from maxHeight value
    
    % add Gauss to the matrix M
   M = max(M, amplitude*exp(-exponent));
end

surf(M)
axis equal
shading faceted

Answer 1

[Bruno Luong]

Is this you want?

x = linspace(0,1);
y = linspace(0,1);
[X,Y] = meshgrid(x,y);
Z = zeros(size(X));
N = 30;
for k=1:N
    xc = min(x)+rand()*(max(x)-min(x));
    yc = min(y)+rand()*(max(y)-min(y));
    r = 0.1*rand(); % adapt to random law you want, eg r = 0.03*randn();
    s = r^2-((X-xc).^2+(Y-yc).^2);
    b = s>=0;
    Z(b) = max(Z(b),sqrt(s(b)));
end
surf(x,y,Z);
axis equal
shading faceted

[Ayan Siddiq]

Yes, thank you!