# How to generate uniformly distributed points inside the volume of frustrum with base radius R and tip radius r and with a height of h.

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anuradha verma on 12 Nov 2022
Commented: anuradha verma on 12 Nov 2022
I want to generate points inside the volume of a frustrum which is at a certain height h1 from (0,0,0) and the axis of frustrum is parallel to z-axis.

Bruno Luong on 12 Nov 2022
Edited: Bruno Luong on 12 Nov 2022
Here we go
r = 1;
R = 2; % must be > r
h = 3;
if R <= r
error('Non valid parameter')
end
Zmin = r*h/(R-r); % Position where the frustrum starts
Zmax = R*h/(R-r); % Position where the frustrum ends
N = 1e4; % Number of point
zr = (Zmin/Zmax).^3;
z = (zr + (1-zr)*rand(1,N)).^(1/3);
rho = R*sqrt(rand(1,N)).*z;
theta = (2*pi)*rand(1,N);
x = rho.*cos(theta);
y = rho.*sin(theta);
z = Zmax*(1-z);
scatter3(x,y,z,'.');
axis equal
anuradha verma on 12 Nov 2022
Thank you so much sir for your help. Iam highly oblighed.

Image Analyst on 12 Nov 2022
OK, but do you have a question? I'm sure you used
n = 10000; % Whatever. It's the number of points
x = 2*R*rand(n, 1)
y = 2*R*rand(n, 1);
z = h1 * rand(n, 1);
to generate uniformly distributed points in the rectangular volume. And then you probably threw out points outside the frustrum (truncated cone) volume by looking at each point's radius and the radius of the frustrum at that z level. But what is your question? Is this homework, or is there a real world use case for this?
anuradha verma on 12 Nov 2022
sir it is a real world case i am considering aerial user in the region where the users are inside a frustrum.

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