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

%*****************************************************************************80
%
%% cvt_circle_nonuniform() computes a CVT in a circle with nonuniform weight.
%
%  Discussion:
%
%    This simple example carries out an iterative CVT calculation in a circle
%    with a nonuniform sampling density. 
%
%    This example has been modified to respond to MATLAB's undesired
%    changes in the Delaunay and Voronoi calculation procedures.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    06 June 2016
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Qiang Du, Vance Faber, Max Gunzburger,
%    Centroidal Voronoi Tessellations: Applications and Algorithms,
%    SIAM Review, 
%    Volume 41, 1999, pages 637-676.
%
%  Input:
%
%    integer N, the number of generators.
%
%    integer SAMPLE_NUM, the number of sample points.
%
%    logical DELAUNAY_DISPLAY, is TRUE (nonzero) if the Delaunay
%    triangulation is to be displayed.
%
%  Output:
%
%    real P(2,N), the location of the generators.
%
%    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_circle_nonuniform():\n' );
  fprintf ( 1, '  A simple demonstration of a CVT computation\n' );
  fprintf ( 1, '  (Centroidal Voronoi Tessellation)\n' );
  fprintf ( 1, '  in a circle, with a nonuniform density.\n' );
  
  if ( nargin < 1 )
    n = 100;
    fprintf ( 1, '\n' );
    fprintf ( 1, 'cvt_circle_nonuniform(): 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 = 10000 * n;
    fprintf ( 1, '\n' );
    fprintf ( 1, 'CVT_CIRCLE_NONUNIFORM - 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 = false;
    fprintf ( 1, '\n' );
    fprintf ( 1, 'CVT_CIRCLE_NONUNIFORM - 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_CIRCLE_NONUNIFORM:\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 = true;

  if ( accumarray_available )
    fprintf ( 1, '\n' );
    fprintf ( 1, '  CVT_CIRCLE_NONUNIFORM will use the ACCUMARRAY command.\n' );
  else
    fprintf ( 1, '\n' );
    fprintf ( 1, ...
      '  CVT_CIRCLE_NONUNIFORM will NOT use the ACCUMARRAY command.\n' );
  end
%
%  Clear the figure screen, if already open.
%
  clf ( );
%
%  Initialize the generators.
%
  p = circle_nonuniform ( n );
  
  for it = 0 : 50
%
%  Compute the Delaunay triangle information T for the current nodes.
%
    if ( true )
      t = delaunay ( p(:,1), p(:,2) );
    else
      t = DelaunayTri ( p(:,1), p(:,2) );
    end
%
%  Display the Delaunay triangulation, if requested.
%
    if ( delaunay_display )
      figure ( 1 );
      triplot ( t, p(:,1), p(:,2) );
      title_string = sprintf ( 'Delaunay, step %d', it );
      title ( title_string );
      axis ( 'equal' );
      view ( 2 );
    end
%
%  Display the CVT generators, and the associated Voronoi diagram.
%
    figure ( 2 );

    theta = 2.0 * pi * ( 0 : 50 ) / 50;
    x = cos ( theta );
    y = sin ( theta );

    if ( false )
      voronoi ( p(:,1), p(:,2), t );
    else
      voronoi ( p(:,1), p(:,2) );
    end

    hold ( 'on' );
    line ( x, y );
    title_string = sprintf ( 'Nonuniform Density on a Circle, CVT step %d', it );
    title ( title_string );
    axis ( 'equal' );
    drawnow ( );
    hold ( 'off' );
%
%  Generate sample points.  
%  
    ps = circle_nonuniform ( sample_num );
%
%  For each sample point, find K, the index of the nearest generator.
%  We do this efficiently by using the Delaunay information with
%  Matlab's DSEARCHN command, rather than a brute force nearest neighbor
%  computation.
%
    if ( true )
      k = dsearchn ( p, t, ps );
    else
      k = nearestNeighbor ( t, ps(:,1), ps(:,2) );
    end
%
%  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,1) = accumarray ( k, ones(sample_num,1) );
      centroid(1:n,1) = accumarray ( k, ps(:,1) );
      centroid(1:n,2) = accumarray ( k, ps(:,2) );

    else

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

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

    end
%
%  Replace the generators by the centroids.
%
    p(1:n,1) = centroid(1:n,1) ./ count(1:n,1);
    p(1:n,2) = centroid(1:n,2) ./ count(1:n,1);
    
  end
%
%  Save the graphics.
%
  figure ( 1 );
  filename = 'delaunay.png';
  print ( '-dpng', filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Graphics saved as "%s"\n', filename );

  figure ( 2 );
  filename = 'voronoi.png';
  print ( '-dpng', filename );
  fprintf ( 1, '  Graphics saved as "%s"\n', filename );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'cvt_circle_nonuniform():\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

  return
end
function p = circle_nonuniform ( n )

%*****************************************************************************80
%
%% circle_nonuniform() returns sample points from a circle.
%
%  Discussion:
%
%    This routine returns N points sampled nonuniformly at random
%    from within the unit circle.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    06 June 2016
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer N, the number of points to generate.
%
%  Output:
%
%    real P(N,2), the sample points.
%
% rng ( 'shuffle' );
%
%  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 = randn ( n, 2 );

  p_norm(1:n,1) = sqrt ( dot ( p, p, 2 ) );

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

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

  return
end
 
