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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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.

Accepted Answer

Bruno Luong
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')
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);
axis equal

More Answers (1)

Image Analyst
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?





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