function [ p, t ] = cvt_square_uniform ( n, sample_num, delaunay_display )

%*****************************************************************************80
%
%% CVT_SQUARE_UNIFORM demonstrates how a CVT can be computed and displayed in MATLAB.
%
%  Discussion:
%
%    This simple example carries out an iterative CVT calculation in the 
%    unit square, with a uniform density.  The initial placement of the
%    generators is random.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 May 2006
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Qiang Du, Vance Faber, Max Gunzburger,
%    Centroidal Voronoi Tessellations: Applications and Algorithms,
%    SIAM Review, 
%    Volume 41, 1999, pages 637-676.
%
%  Parameters:
%
%    Input, integer N, the number of generators.
%
%    Input, integer SAMPLE_NUM, the number of sample points.
%
%    Input, logical DELAUNAY_DISPLAY, is TRUE (nonzero) if the Delaunay
%    triangulation is to be displayed.
%
%    Output, real P(N,2), the location of the generators.
%
%    Output, integer T(NT,3), information defining the Delaunay
%    triangulation of the generators.  NT is the number of triangles,
%    which varies depending on the arrangement of the generators.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'CVT_SQUARE_UNIFORM:\n' );
  fprintf ( 1, '  A simple demonstration of a CVT computation\n' );
  fprintf ( 1, '  (Centroidal Voronoi Tessellation)\n' );
  fprintf ( 1, '  in a square, with a uniform density.\n' );
  
  if ( nargin < 1 )
    n = 100;
    fprintf ( 1, '\n' );
    fprintf ( 1, 'CVT_SQUARE_UNIFORM - Note:\n' );
    fprintf ( 1, '  No value of N was supplied.\n' );
    fprintf ( 1, '  N is the number of generators.\n' );
    fprintf ( 1, '  A default value N = %d will be used.\n', n );
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, '  User specified number of generators = %d\n',  n );
  end

  if ( nargin < 2 )
    sample_num = 1000 * n;
    fprintf ( 1, '\n' );
    fprintf ( 1, 'CVT_SQUARE_UNIFORM - Note:\n' );
    fprintf ( 1, '  No value of SAMPLE_NUM was supplied.\n' );
    fprintf ( 1, '  SAMPLE_NUM is the number of sample points.\n' );
    fprintf ( 1, '  A default value SAMPLE_NUM = %d will be used.\n', ...
      sample_num );
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, '  User specified number of sample points = %d\n', ...
      sample_num );
  end

  if ( nargin < 3 )
    delaunay_display = 0;
    fprintf ( 1, '\n' );
    fprintf ( 1, 'CVT_SQUARE_UNIFORM - Note:\n' );
    fprintf ( 1, '  No value of DELAUNAY_DISPLAY was supplied.\n' );
    fprintf ( 1, '  DELAUNAY_DISPLAY is TRUE (nonzero) if the\n' );
    fprintf ( 1, '  Delaunay triangulation is also to be displayed.\n' );
    fprintf ( 1, '  A default value DELAUNAY_DISPLAY = %d will be used.\n', ...
      delaunay_display );
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, '  User specified DELAUNAY_DISPLAY = %d\n', ...
      delaunay_display );
  end
%
%  This switch is set to 1 (TRUE) if the ACCUMARRAY command is available.
%  That speeds up the calculation a lot.  If you don't have the ACCUMARRAY
%  command, just set this to 0.
% 
  fprintf ( 1, '\n' );
  fprintf ( 1, 'CVT_SQUARE_UNIFORM:\n' );
  fprintf ( 1, '  MATLAB''s ACCUMARRAY command can be used for faster\n' );
  fprintf ( 1, '  computation.  This command is not available in\n' );
  fprintf ( 1, '  some versions of MATLAB.  If ACCUMARRAY is available,\n' );
  fprintf ( 1, '  simply make sure that the ACCUMARAY_AVAILABLE variable\n' );
  fprintf ( 1, '  is set to 1!\n' );
  
  accumarray_available = 1;

  if ( accumarray_available )
    fprintf ( 1, '\n' );
    fprintf ( 1, '  The ACCUMARRAY command will be used.\n' );
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, '  The ACCUMARRAY command will NOT be used.\n' );
  end
%
%  Clear the figure screen, if already open.
%
  clf
%
%  Randomize the initial locations of the generators in the unit square.
%  If another region is used, then this initialization should be changed.
%
  p = rand ( n, 2 );
  plot ( p(:,1), p(:,2), 'b.' );
  axis ( [ 0.0, 1.0, 0.0, 1.0 ] )
  line ( [ 0.0, 1.0, 1.0, 0.0, 0.0 ], [ 0.0, 0.0, 1.0, 1.0, 0.0 ], ...
    'Color', 'r', 'LineWidth', 2 );
  title_string = sprintf ( 'Initial Generators' );
  title ( title_string );
  axis equal
  drawnow

  string = input ( 'RETURN, or Q to quit: ', 's' );

  if ( string == 'q' | string == 'Q' )
    return
  end

  it = 0;
  
  while ( 1 )
%
%  Compute the Delaunay triangle information T for the current nodes.
%
    t = delaunay ( p(:,1), p(:,2) );
%
%  Display the Delaunay triangulation, if requested.
%
    if ( delaunay_display )
      subplot ( 1, 2, 2 )
      trimesh ( t, p(:,1), p(:,2), zeros(n,1), 'EdgeColor', 'b' )
      hold on
      plot ( p(:,1), p(:,2), 'b.' );
      axis ( [ -0.0, 1.0, -0.0, 1.0 ] )
      line ( [ 0.0, 1.0, 1.0, 0.0, 0.0 ], [ 0.0, 0.0, 1.0, 1.0, 0.0 ], ...
        'Color', 'r', 'LineWidth', 2 );
      title_string = sprintf ( 'Delaunay, step %d', it );
      title ( title_string );
      axis equal
      view ( 2 )
      hold off
    end
%
%  Display the CVT generators, and the associated Voronoi diagram.
%
    if ( delaunay_display )
      subplot ( 1, 2, 1 )
    end
    
    voronoi ( p(:,1), p(:,2), t );
    axis ( [ -0.0, 1.0, -0.0, 1.0 ] )
    line ( [ 0.0, 1.0, 1.0, 0.0, 0.0 ], [ 0.0, 0.0, 1.0, 1.0, 0.0 ], ...
      'Color', 'r', 'LineWidth', 2 );
    title_string = sprintf ( 'Voronoi, step %d', it );
    title ( title_string );
    axis equal
    axis tight
    drawnow
%
%  Generate sample points.  
%
%  These sample points implicitly define the geometry of the region.  
%  If the region is not a unit square, then the range of the sample 
%  data must be changed.
%
%  The data is sampled uniformly.  If a nonuniform density is desired,
%  then the sampling must be done in a biased way.
%    
    xs = rand ( sample_num, 1 );
    ys = rand ( sample_num, 1 );
%
%  For each sample point, find K, the index of the nearest generator.
%  We do this efficiently by using the Delaunay information with
%  Matlab's DSEARCH command, rather than a brute force nearest neighbor
%  computation.
%  
    k(1:sample_num,1) = dsearch ( p(:,1), p(:,2), t, xs, ys );
%
%  The centroid of the Voronoi region associated with each generator
%  is approximated by the average of the sample points it was closest to.
%
    if ( accumarray_available )

      count(1:n) = accumarray ( k, ones(sample_num,1) );
      centroid(1,1:n) = accumarray ( k, xs );
      centroid(2,1:n) = accumarray ( k, ys );

    else

      count(1:n) = 0;
      centroid(1,1:n) = 0.0;
      centroid(2,1:n) = 0.0;

      for i = 1 : sample_num
        j = k(i);
        count(j) = count(j) + 1;
        centroid(1,j) = centroid(1,j) + xs(i);
        centroid(2,j) = centroid(2,j) + ys(i);
      end

    end
%
%  Replace the generators by the centroids.
%
    p(1:n,1) = ( centroid(1,1:n) ./ count(1:n) )';
    p(1:n,2) = ( centroid(2,1:n) ./ count(1:n) )';

    string = input ( 'RETURN, or Q to quit: ', 's' );

    if ( string == 'q' | string == 'Q' )
      break
    end

    it = it + 1;
    
  end

  fprintf ( 1, '\n' );
  fprintf ( 1, 'CVT_SQUARE_UNIFORM:\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

  return
end
function p = square_uniform ( n )

%*****************************************************************************80
%
%% SQUARE_UNIFORM returns sample points from the unit square.
%
%  Discussion:
%
%    This routine returns N points sampled uniformly at random
%    from within the unit square.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    24 May 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer N, the number of points to generate.
%
%    Output, real P(N,2), the sample points.
%
  p(1:n,1:2) = rand(n,2);

  return
end