how to distribute users uniformly or non uniformly inside circle

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Ahmad Hani
Ahmad Hani 2018-3-21
编辑： Jan 2018-3-21
I have a circle with raduis R, how can I distribute users inside this circle in a uniform distribution and after that how can I find the xy coordination of each user inside the circle. thanks

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Image Analyst
Image Analyst 2018-3-21

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Jan
Jan 2018-3-21
编辑：Jan 2018-3-21
To get 100 points ("users") inside a circle with radius R with a cheap rejection method
R = 19;
want = 100;
have = 0;
pos = zeros(want, 2);
R2 = R^2;
while have < want
% A random point in [-R, R], 2D:
point = (2 * rand(1, 2) - 1) * R;
% Accept point if inside the circle:
if point(1)^2 + point(2)^2 <= R2
have = have + 1;
pos(have, :) = point;
end
end
A constructive method:
R = 19;
want = 100;
r = sqrt(rand(want, 1)) * R;
alpha = rand(want, 1) * (2 * pi);
pos = [r .* cos(alpha), r .* sin(alpha)];
This is almost correct. The only problem is that rand replies values in the open interval (0,1), but alpha should live on the half open interval [0,1) including the 0. But even then the value 0.0 will occur with the probability of 2^-52 only, such the the difference is tiny.

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