function p = circle_nonuniform ( n )

%% CIRCLE_NONUNIFORM returns sample points from a circle.
%
%  Discussion:
%
%    This routine returns N points sampled nonuniformly at random
%    from within the unit circle.
%
%  Modified:
%
%    20 May 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer N, the number of points to generate.
%
%    Output, real P(2,N), the sample points.
%

%
%  Step 1: Generate N points in the unit circle.
%  (Generate N normally distributed points.
%   Normalize them (now they lie on the circumference).
%   Assign a radius.)
%
  p(1:2,1:n) = randn(2,n);

  p_norm(1:n) = sqrt ( dot ( p, p, 1 ) );

  r(1:n) = rand(1,n);

  for i = 1 : 2
    p(i,1:n) = sqrt ( sqrt ( r(1:n) ) ) .* p(i,1:n) ./ p_norm(1:n);
  end