function vran = direction_uniform_3d ( )
%*****************************************************************************80
%
%% direction_uniform_3d() picks a random direction vector in 3D.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 12 January 2021
%
% Author:
%
% John Burkardt
%
% Output:
%
% real VRAN(3), the random direction vector, with unit norm.
%
dim_num = 3;
%
% Pick a uniformly random VDOT, which must be between -1 and 1.
% This represents the dot product of the random vector with the Z unit vector.
%
% Note: this works because the surface area of the sphere between
% Z and Z + dZ is independent of Z. So choosing Z uniformly chooses
% a patch of area uniformly.
%
vdot = - 1.0 + 2.0 * rand ( 1, 1 );
phi = acos ( vdot );
%
% Pick a uniformly random rotation between 0 and 2 Pi around the
% axis of the Z vector.
%
theta = 2.0 * pi * rand ( 1, 1 );
vran(1) = cos ( theta ) * sin ( phi );
vran(2) = sin ( theta ) * sin ( phi );
vran(3) = cos ( phi );
return
end