Hi, generatin random points inside a cuboid problem

Hi, I need to generate a total I of points inside a specific cuboid(a*b*c) and plot it then after havings these points and their coordinations generate a sphere for each point.I already did a script but unfortunately, it gives me a cube results :

clc
close all
a=10; % mm 
b=10; % mm 
depth=0.3; %mm
i= 1145916; %total number of pores and thus of points inside the parallelepiped
v=i*[];
Vt=a*b*depth; %volume expression mm^3
s = 10; 
n = bsxfun(@plus,0,s.*rand(i,3));
r=normrnd(0.005,0.001,[1 i]); %mu=0,005 mm ==>5µm
x=n(:,1);
y=n(:,2);
z=n(:,3);
scatter3(x,y,z,r,'fill')
for k=1:i   
 v(k)=(4*pi*(r(k)^3))/3; 
end
figure
plot(v)

Best regards

[KSSV]

You want random points inside sphere?

[fatima-zahra achbah]

no, I want random points inside my cuboid and then draw a sphere on each point

Answer 1

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/327990-generate-random-coordinates-inside-a-convex-polytope#answer_257270 for a discussion about "fair" point generation within a convex polytope.

n = bsxfun(@plus,0,s.*rand(i,3));

The bsxfun to add 0 is not doing anything useful there. You might as well have

n = s .* rand(i,3);

However, the reason you get a cube is that you are not weighting the coordinates according to the size of their dimension. I would suggest,

n = rand(i, 3) * diag([a, b, depth]);   %* rather than .* is deliberate

Or if you are using R2016b or later, you could use

n = rand(i, 3) .* [a, b, depth] ;    %needs R2016b or later.

The bsxfun equivalent would be

n = bsxfun(@times, [a, b, depth], rand(i,3) );

In my R2017b system, the time required for bsxfun(@times, data, s) and data .* s are pretty much indistinguishable, and the time for data * diag(s) is about 50% more.

[fatima-zahra achbah]

Oh my god, it works, thank you so much, I truly appreciate your help