function polygon_triangulate_test ( )

%*****************************************************************************80
%
%% polygon_triangulate_test() tests polygon_triangulate().
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    26 February 2019
%
%  Author:
%
%    John Burkardt
%
  addpath ( '../polygon_triangulate' );

  timestamp ( );
  fprintf ( 1, '\n' );
  fprintf ( 1, 'polygon_triangulate_test():\n' );
  fprintf ( 1, '  MATLAB/Octave version %s\n', version ( ) );
  fprintf ( 1, '  Test polygon_triangulate().\n' );

  polygon_triangulate_test01 ( );

  polygon_triangulate_test02 ( 'comb' );
  polygon_triangulate_test02 ( 'hand' );
  polygon_triangulate_test02 ( 'i18' );

  polygon_triangulate_test03 ( 'comb' );
  polygon_triangulate_test03 ( 'hand' );
  polygon_triangulate_test03 ( 'i18' );
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'polygon_triangulate_test():\n' );
  fprintf ( 1, '  Normal end of execution.\n' );
  fprintf ( 1, '\n' );
  timestamp ( );

  rmpath ( '../polygon_triangulate' );

  return
end
function polygon_triangulate_test01 ( )

%*****************************************************************************80
%
%% polygon_triangulate_test01() tests the "comb_10" polygon.
%
%  Discussion:
%
%    There are N-3 triangles in the triangulation.
%
%    For the first N-2 triangles, the first edge listed is always an
%    internal diagonal.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    03 May 2014
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'polygon_triangulate_test01():\n' );
  fprintf ( 1, '  Triangulate the comb_10() polygon.\n' );

  x = [ ...
    8; ...
    7; ...
    6; ...
    5; ...
    4; ...
    3; ...
    2; ...
    1; ...
    0; ...
    4];

  y = [ ...
    0; ...
   10; ...
    0; ...
   10; ...
    0; ...
   10; ...
    0; ...
   10; ...
    0; ...
   -2 ];

  n = 10;

  triangles = polygon_triangulate ( n, x, y );

  i4mat_transpose_print ( 3, n - 2, triangles, '  Triangles' );

  return
end
function polygon_triangulate_test02 ( prefix )

%*****************************************************************************80
%
%% polygon_triangulate_test02() triangulates a polygon described in a file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    04 May 2014
%
%  Author:
%
%    John Burkardt.
%

%
%  Create filenames.
%
  node_filename = strcat ( prefix, '_nodes.txt' );
  element_filename = strcat ( prefix, '_elements.txt' );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'polygon_triangulate_test02():\n' );
  fprintf ( 1, '  Read polygon coordinates in "%s"\n', node_filename );
%
%  Read the node coordinates.
%
  [ ~, n ] = r8mat_header_read ( node_filename );

  xy = r8mat_data_read ( node_filename, 2, n );
%
%  Get the triangulation.
%
  triangle_num = n - 2;
  triangles = polygon_triangulate ( n, xy(1,:), xy(2,:) );
%
%  Write the triangulation to a file.
%
  i4mat_write ( element_filename, 3, triangle_num, triangles );

  fprintf ( 1, '  Write triangulation to "%s"\n', element_filename );

  return
end
function polygon_triangulate_test03 ( prefix )

%*****************************************************************************80
%
%% polygon_triangulate_test03() plots a triangulation.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    23 October 2015
%
%  Author:
%
%    John Burkardt.
%

%
%  Create filenames.
%
  node_filename = strcat ( prefix, '_nodes.txt' );
  plot1_filename = strcat ( prefix, '.png' );
  plot2_filename = strcat ( prefix, '_triangulation.png' );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'polygon_triangulate_test03():\n' );
  fprintf ( 1, '  Read polygon coordinates in "%s"\n', node_filename );
%
%  Read the node coordinates.
%
  [ ~, n ] = r8mat_header_read ( node_filename );

  xy = r8mat_data_read ( node_filename, 2, n );
%
%  Plot the polygon.
%
  figure ( 1 );
  clf ( );
  grid ( 'on' );
  hold ( 'on' );

  plot ( xy(1,1:n), xy(2,1:n), 'k.', 'MarkerSize', 25 );

  for i = 1 : n

    ip1 = mod ( i, n ) + 1;
 
    line ( [ xy(1,i), xy(1,ip1) ], ...
           [ xy(2,i), xy(2,ip1) ], ...
           'LineWidth', 3, 'Color', 'b' );

  end

  xlabel ( '<-- X -->', 'Fontsize', 16 );
  ylabel ( '<-- Y -->', 'Fontsize', 16 );
  title ( prefix, 'Fontsize', 24 );
  axis ( 'equal' );

  hold ( 'off' );

  print ( '-dpng', plot1_filename );
  fprintf ( 1, '  Graphics saved as "%s"\n', plot1_filename );
%
%  Get the triangulation.
%
  triangle_num = n - 2;
  triangles = polygon_triangulate ( n, xy(1,:), xy(2,:) );
%
%  Plot the triangulation.
%
  figure ( 2 );
  clf ( );
  grid ( 'on' );
  hold ( 'on' );

  plot ( xy(1,1:n), xy(2,1:n), 'k.', 'MarkerSize', 25 );

  for i = 1 : n

    ip1 = mod ( i, n ) + 1;
 
    line ( [ xy(1,i), xy(1,ip1) ], ...
           [ xy(2,i), xy(2,ip1) ], ...
           'LineWidth', 3, 'Color', 'b' );

  end

  for i = 1 : n - 3
    i1 = triangles(1,i);
    i2 = triangles(2,i);
    line ( [ xy(1,i1), xy(1,i2) ], ...
           [ xy(2,i1), xy(2,i2) ], ...
           'LineWidth', 3, 'Color', 'r' );
  end

  xlabel ( '<-- X -->', 'Fontsize', 16 );
  ylabel ( '<-- Y -->', 'Fontsize', 16 );
  title ( prefix, 'Fontsize', 24 );
  axis ( 'equal' );

  hold ( 'off' );

  print ( '-dpng', plot2_filename );
  fprintf ( 1, '  Graphics saved as "%s"\n', plot2_filename );

  return
end
function column_num = file_column_count ( input_file_name )

%*****************************************************************************80
%
%% file_column_count() counts the columns in the first line of a file.
%
%  Discussion:
%
%    The file is assumed to be a simple text file.
%
%    Most lines of the file are presumed to consist of COLUMN_NUM words,
%    separated by spaces.  There may also be some blank lines, and some 
%    comment lines, which have a "#" in column 1.
%
%    The routine tries to find the first non-comment non-blank line and
%    counts the number of words in that line.
%
%    If all lines are blanks or comments, it goes back and tries to analyze
%    a comment line.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILE_NAME, the name of the file.
%
%  Output:
%
%    integer COLUMN_NUM, the number of columns in the file.
%
  FALSE = 0;
  TRUE = 1;
%
%  Open the file.
%
  input_unit = fopen ( input_file_name );

  if ( input_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'file_column_count(): Error!\n' );
    fprintf ( 1, '  Could not open the file "%s".\n', input_file_name );
    error ( 'file_column_count(): Error!' );
  end
%
%  Read one line, but skip blank lines and comment lines.
%  Use FGETL so we drop the newline character!
%
  got_one = FALSE;

  while ( true )

    line = fgetl ( input_unit );

    if ( line == -1 )
      break;
    end

    if ( s_len_trim ( line ) == 0 )

    elseif ( line(1) == '#' )

    else
      got_one = TRUE;
      break;
    end

  end

  fclose ( input_unit );

  if ( got_one == FALSE ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'file_column_count(): Warning!\n' );
    fprintf ( 1, '  The file does not seem to contain any data.\n' );
    column_num = -1;
    return
  end

  column_num = s_word_count ( line );

  return
end
function row_num = file_row_count ( input_file_name )

%*****************************************************************************80
%
%% file_row_count() counts the number of row records in a file.
%
%  Discussion:
%
%    Each input line is a "RECORD".
%
%    The records are divided into three groups:
%    
%    * BLANK LINES (nothing but blanks)
%    * COMMENT LINES (begin with a '#')
%    * DATA RECORDS (anything else)
%
%    The value returned by the function is the number of data records.
%
%    By the way, if the MATLAB routine FGETS is used, instead of
%    FGETL, then the variable LINE will include line termination 
%    characters, which means that a blank line would not actually
%    have zero characters.
%
%  Licensing:
%
%    This code is distributed under the MIT license. 
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILE_NAME, the name of the input file.
%
%  Output:
%
%    integer ROW_NUM, the number of rows found. 
%
  input_unit = fopen ( input_file_name );

  if ( input_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'FILE_ROW_COUNT - Error!\n' );
    fprintf ( 1, '  Could not open the file "%s".\n', input_file_name );
    error ( 'FILE_ROW_COUNT - Error!' );
  end

  blank_num = 0;
  comment_num = 0;
  row_num = 0;
  
  record_num = 0;

  while ( true )

    line = fgetl ( input_unit );

    if ( line == -1 )
      break;
    end

    record_num = record_num + 1;
    record_length = s_len_trim ( line );
    
    if ( record_length <= 0 )
      blank_num = blank_num + 1;
    elseif ( line(1) == '#' )
      comment_num = comment_num + 1;
    else
      row_num = row_num + 1;
    end

  end

  fclose ( input_unit );

  return
end
function i4mat_transpose_print ( m, n, a, title )

%*****************************************************************************80
%
%% i4mat_transpose_print() prints an I4MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 September 2009
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns.
%
%    integer A(M,N), an M by N matrix to be printed.
%
%    string TITLE, a title.
%
  i4mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

  return
end
function i4mat_transpose_print_some ( m, n, a, ilo, jlo, ihi, jhi, title )

%*****************************************************************************80
%
%% i4mat_transpose_print_some() prints some of an I4MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 September 2009
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer M, N, the number of rows and columns.
%
%    integer A(M,N), an M by N matrix to be printed.
%
%    integer ILO, JLO, the first row and column to print.
%
%    integer IHI, JHI, the last row and column to print.
%
%    string TITLE, a title.
%
  incx = 10;

  fprintf ( 1, '\n' );
  fprintf ( 1, '%s\n', title );

  if ( m <= 0 | n <= 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, '  (None)\n' );
    return
  end

  for i2lo = max ( ilo, 1 ) : incx : min ( ihi, m )

    i2hi = i2lo + incx - 1;
    i2hi = min ( i2hi, m );
    i2hi = min ( i2hi, ihi );

    inc = i2hi + 1 - i2lo;

    fprintf ( 1, '\n' );
    fprintf ( 1, '  Row: ' );
    for i = i2lo : i2hi
      fprintf ( 1, '%7d  ', i );
    end
    fprintf ( 1, '\n' );
    fprintf ( 1, '  Col\n' );
    fprintf ( 1, '\n' );

    j2lo = max ( jlo, 1 );
    j2hi = min ( jhi, n );

    for j = j2lo : j2hi

      fprintf ( 1, '%5d: ', j );
      for i2 = 1 : inc
        i = i2lo - 1 + i2;
        fprintf ( 1, '%7d  ', a(i,j) );
      end
      fprintf ( 1, '\n' );

    end

  end

  return
end
function i4mat_write ( output_filename, m, n, table )

%*****************************************************************************80
%
%% i4mat_write() writes an I4MAT file.
%
%  Discussion:
%
%    An I4MAT is an array of I4's.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    26 June 2010
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string OUTPUT_FILENAME, the output filename.
%
%    integer M, the spatial dimension.
%
%    integer N, the number of points.
%
%    integer TABLE(M,N), the points.
%

%
%  Open the file.
%
  output_unit = fopen ( output_filename, 'wt' );

  if ( output_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4MAT_WRITE - Error!\n' );
    fprintf ( 1, '  Could not open the output file.\n' );
    error ( 'I4MAT_WRITE - Error!' );
  end
%
%  Write the data.
%
  for j = 1 : n
    for i = 1 : m
      fprintf ( output_unit, '  %12d', round ( table(i,j) ) );
    end
    fprintf ( output_unit, '\n' );
  end
%
%  Close the file.
%
  fclose ( output_unit );

  return
end
function table = r8mat_data_read ( input_filename, m, n )

%*****************************************************************************80
%
%% r8mat_data_read() reads data from an R8MAT file.
%
%  Discussion:
%
%    An R8MAT is an array of R8's.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    08 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILENAME, the name of the input file.
%
%    integer M, N, the number of rows and columns of data.
%
%  Output:
%
%    real TABLE(M,N), the point coordinates.
%

%
%  Build up the format string for reading M real numbers.
%
  string = ' ';

  for i = 0 : m
    string = strcat ( string, ' %f' );
  end

  input_unit = fopen ( input_filename );

  if ( input_unit < 0 ) 
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_DATA_READ - Error!\n' );
    fprintf ( 1, '  Could not open the file.\n' );
    error ( 'R8MAT_DATA_READ - Error!' );
  end

  table = zeros(m,n);

  i = 0;

  while ( i < n )

    line = fgets ( input_unit );

    if ( line == -1 )
      break;
    end

    if ( line(1) == '#' )

    elseif ( s_len_trim ( line ) == 0 )
      
    else

      [ x, count ] = sscanf ( line, string );

      if ( count == m )
        i = i + 1;
        table(1:m,i) = x(1:m);
      end

    end

  end

  fclose ( input_unit );

  return
end
function [ m, n ] = r8mat_header_read ( input_filename )

%*****************************************************************************80
%
%% r8mat_header_read() reads the header from an R8MAT file.
%
%  Discussion:
%
%    An R8MAT is an array of R8's.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    22 October 2004
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILENAME, the name of the input file.
%
%  Output:
%
%    integer M, the spatial dimension.
%
%    integer N, the number of points.
%
  m = file_column_count ( input_filename );

  if ( m <= 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_HEADER_READ - Fatal error!\n' );
    fprintf ( 1, '  There was some kind of I/O problem while trying\n' );
    fprintf ( 1, '  to count the number of data columns in\n' );
    fprintf ( 1, '  the file %s.\n', input_filename );
  end

  n = file_row_count ( input_filename );

  if ( n <= 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'R8MAT_HEADER_READ - Fatal error!\n' );
    fprintf ( 1, '  There was some kind of I/O problem while trying\n' );
    fprintf ( 1, '  to count the number of data rows in\n' );
    fprintf ( 1, '  the file %s\n', input_filename );
  end

  return
end
function len = s_len_trim ( s )

%*****************************************************************************80
%
% S_LEN_TRIM returns the length of a character string to the last nonblank.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    14 June 2003
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string S, the string to be measured.
%
%  Output:
%
%    integer LENGTH, the length of the string up to the last nonblank.
%
  len = length ( s );

  while ( 0 < len )
    if ( s(len) ~= ' ' )
      return
    end
    len = len - 1;
  end

  return
end
function word_num = s_word_count ( s )

%*****************************************************************************80
%
%% s_word_count() counts the number of "words" in a string.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    30 January 2006
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string S, the string to be examined.
%
%  Output:
%
%    integer WORD_NUM, the number of "words" in the string.
%    Words are presumed to be separated by one or more blanks.
%
  FALSE = 0;
  TRUE = 1;

  word_num = 0;
  s_length = length ( s );

  if ( s_length <= 0 )
    return;
  end

  blank = TRUE;

  for i = 1 : s_length

    if ( s(i) == ' ' )
      blank = TRUE;
    elseif ( blank == TRUE )
      word_num = word_num + 1;
      blank = FALSE;
    end

  end

  return
end
function timestamp ( )

%*****************************************************************************80
%
%% timestamp() prints the current YMDHMS date as a timestamp.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    14 February 2003
%
%  Author:
%
%    John Burkardt
%
  t = now;
  c = datevec ( t );
  s = datestr ( c, 0 );
  fprintf ( 1, '%s\n', s );

  return
end
