function x = sphere01_sample_3d_2 ( )
%*****************************************************************************80
%
%% sphere01_sample_3d_2() is a BAD method for sampling the unit sphere in 3D.
%
% Discussion:
%
% The unit sphere in 3D satisfies:
%
% X * X + Y * Y + Z * Z = 1
%
% Points on the unit sphere have coordinates ( PHI, THETA ) where
% PHI varies from 0 to PI, and THETA from 0 to 2 PI, so that:
%
% x = cos ( theta ) * sin ( phi )
% y = sin ( theta ) * sin ( phi )
% z = cos ( phi )
%
% This routine implements a sampling of the sphere that simply
% picks PHI and THETA uniformly at random from their ranges.
% This is a uniform sampling on the cylinder, but it is NOT
% a uniform sampling on the sphere. I implement it here just
% so I can run some tests against the code in SPHERE_UNIT_SAMPLE_3D.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 06 February 2005
%
% Author:
%
% John Burkardt
%
% Output:
%
% real X(3), the sample point.
%
phi = pi * rand ( 1, 1 );
theta = 2.0 * pi * rand ( 1, 1 );
x(1) = cos ( theta ) * sin ( phi );
x(2) = sin ( theta ) * sin ( phi );
x(3) = cos ( phi );
return
end