how to distribute users uniformly or non uniformly inside circle

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

Answer 1

[Image Analyst]

See the FAQ: http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_set_of_random_locations_within_a_circle.3F

[Ahmad Hani]

Thanks for this answer

Answer 2

[Jan]

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.