function triangulation_q2l ( prefix )

%*****************************************************************************80
%
%% MAIN is the main program for TRIANGULATION_Q2L.
%
%  Discussion:
%
%    TRIANGULATION_Q2L makes a linear triangulation from a quadratic one.
%
%    A quadratic triangulation is assumed to consist of 6-node triangles,
%    as in the following:
%
%    11-12-13-14-15
%     |\    |\    |
%     | \   | \   |
%     6  7  8  9 10
%     |   \ |   \ |
%     |    \|    \|
%     1--2--3--4--5
%
%    This routine rearranges information so as to define the 3-node
%    triangulation:
%
%    11-12-13-14-15
%     |\ |\ |\ |\ |
%     | \| \| \| \|
%     6--7--8--9-10
%     |\ |\ |\ |\ |
%     | \| \| \| \|
%     1--2--3--4--5
%
%  Usage:
%
%    triangulation_q2l ( 'prefix' )
%
%    where 'prefix' is the common filename prefix:
%
%    * 'prefix'_nodes.txt contains the node coordinates (not needed by this program),
%    * 'prefix'_elements.txt contains the element definitions.
%    * 'prefix'_q2l_elements.txt will contain the linearized element definitions.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    04 October 2009
%
%  Author:
%
%    John Burkardt
%
  timestamp ( );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'TRIANGULATION_Q2L\n' );
  fprintf ( 1, '  MATLAB version\n' );
  fprintf ( 1, '  Read a "quadratic" triangulation and\n' );
  fprintf ( 1, '  write out a "linear" triangulation.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read a triangulation dataset of TRIANGLE_NUM1\n' );
  fprintf ( 1, '  triangles using 6 nodes.\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Create a 3 node triangulation by breaking\n' );
  fprintf ( 1, '  every 6 node triangle into 4 smaller ones.\n' );
  fprintf ( 1, '  Write the new linear triangulation to a file.\n' );
%
%  Get the number of command line arguments.
%
  if ( nargin < 1 )

    fprintf ( 1, '\n' );
    fprintf ( 1, 'TRIANGULATION_Q2L:\n' );
    prefix = input ( ...
      '  Please enter the common filename prefix.' );

  end
%
%  Create the filenames.
%
  element_filename = strcat ( prefix, '_elements.txt' );
  element_q2l_filename = strcat ( prefix, '_q2l_elements.txt' );
%
%  Read the data.
%
  [ triangle_order1, triangle_num1 ] = i4mat_header_read ( ...
    element_filename );

  if ( triangle_order1 ~= 6 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'TRIANGULATION_Q2L - Fatal error!\n' );
    fprintf ( 1, '  Data is not for a 6-node triangulation.\n' );
    error ( 'TRIANGULATION_Q2L - Fatal error!' );
  end

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the header of ""%s".\n', element_filename );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  Triangle order = %d\n', triangle_order1 );
  fprintf ( 1, '  Number of triangles TRIANGLE_NUM1  = %d\n', triangle_num1 );

  triangle_node1(1:triangle_order1,1:triangle_num1) = i4mat_data_read ( ...
    element_filename, triangle_order1, triangle_num1 );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Read the data in ""%s".\n', element_filename );

  i4mat_transpose_print_some ( triangle_order1, triangle_num1, triangle_node1, ...
    1, 1, 6, 10, '  6 by 10 portion TRIANGLE_NODE1:' );
%
%  Set the number of linear triangles:
%
  triangle_num2 = 4 * triangle_num1;
  triangle_order2 = 3;
%
%  Convert the data.
%
  triangle_node2 = triangulation_order6_to_order3 ( triangle_num1, ...
    triangle_node1 );

  i4mat_transpose_print ( triangle_order2, triangle_num2, ...
    triangle_node2, '  TRIANGLE_NODE2' );
%
%  Write out the node and triangle data for the quadratic mesh
%
  i4mat_write ( element_q2l_filename, triangle_order2, ...
    triangle_num2, triangle_node2 );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Wrote the linearized data to ""%s".\n', element_q2l_filename );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'TRIANGULATION_Q2L\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

  fprintf ( 1, '\n' );
  timestamp ( );

  return
end
function c = ch_cap ( c )

%*****************************************************************************80
%
%% CH_CAP capitalizes a single character.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 November 2003
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, character C, the character to capitalize.
%
%    Output, character C, the capitalized character.
%
  if ( 'a' <= c & c <= 'z' )
    c = c + 'A' - 'a';
  end

  return
end
function truefalse = ch_eqi ( c1, c2 )

%*****************************************************************************80
%
%% CH_EQI is a case insensitive comparison of two characters for equality.
%
%  Example:
%
%    CH_EQI ( 'A', 'a' ) is TRUE.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    28 July 2000
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, character C1, C2, the characters to compare.
%
%    Output, logical TRUEFALSE, is TRUE (1) if the characters are equal.
%
  FALSE = 0;
  TRUE = 1;

  if ( ch_cap ( c1 ) == ch_cap ( c2 ) )
    truefalse = TRUE;
  else
    truefalse = FALSE;
  end

  return
end
function digit = ch_to_digit ( c )

%*****************************************************************************80
%
%% CH_TO_DIGIT returns the integer value of a base 10 digit.
%
%  Example:
%
%     C   DIGIT
%    ---  -----
%    '0'    0
%    '1'    1
%    ...  ...
%    '9'    9
%    ' '    0
%    'X'   -1
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 November 2003
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, character C, the decimal digit, '0' through '9' or blank
%    are legal.
%
%    Output, integer DIGIT, the corresponding integer value.  If C was
%    'illegal', then DIGIT is -1.
%
  if ( '0' <= c & c <= '9' )

    digit = c - '0';

  elseif ( c == ' ' )

    digit = 0;

  else

    digit = -1;

  end

  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 GNU LGPL license. 
%
%  Modified:
%
%    21 February 2004
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    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!' );
    column_num = -1;
    return;
  end
%
%  Read one line, but skip blank lines and comment lines.
%  Use FGETL so we drop the newline character!
%
  got_one = FALSE;

  while ( 1 )

    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 [ i, j ] = file_name_ext_get ( file_name )

%*****************************************************************************80
%
%% FILE_NAME_EXT_GET determines the "extension" of a file name.
%
%  Discussion:
%
%    The "extension" of a filename is the string of characters
%    that appears after the LAST period in the name.  A file
%    with no period, or with a period as the last character
%    in the name, has a "null" extension.
%
%    Blanks are unusual in filenames.  This routine ignores all
%    trailing blanks, but will treat initial or internal blanks
%    as regular characters acceptable in a file name.
%
%    If no period occurs in FILE_NAME, then
%      I = J = -1;
%    Otherwise,
%      I is the position of the LAST period in FILE_NAME, and J is the
%      position of the last nonblank character following the period.
%
%  Example:
%
%    FILE_NAME   I  J
%
%    bob.for     4  7
%    N.B.C.D     6  7
%    Naomi.      6  6
%    Arthur     -1 -1
%    .com        1  1
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 February 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string FILE_NAME, a file name to be examined.
%
%    Output, integer I, J, the indices of the first and last characters
%    in the file extension.
%
  i = s_index_last_c ( file_name, '.' )

  if ( i == -1 )

    j = -1;

  else

    j = s_len_trim ( file_name );

  end

  return
end
function file_name_new = file_name_ext_swap ( file_name, ext )

%*****************************************************************************80
%
%% FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
%
%  Discussion:
%
%    The "extension" of a filename is the string of characters
%    that appears after the LAST period in the name.  A file
%    with no period, or with a period as the last character
%    in the name, has a "null" extension.
%
%  Example:
%
%          Input           Output
%    ================     =============
%    FILE_NAME    EXT     FILE_NAME_NEW
%    
%    bob.for      obj     bob.obj
%    bob.bob.bob  txt     bob.bob.txt
%    bob          yak     bob.yak
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    15 August 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, character FILE_NAME(*), a file name.
%    On output, the extension of the file has been changed.
%
%    Input, character EXT(*), the extension to be used on the output
%    copy of FILE_NAME, replacing the current extension if any.
%
%    Output, character FILE_NAME_NEW(*), a copy of the input file name,
%    with the new extension.
%
  file_name_len = length ( file_name );

  ext_len = length ( ext );

  period = file_name_len + 1;

  for i = file_name_len : -1 : 1
    if ( file_name(i:i) == '.' )
      period = i;
      break
    end
  end

  file_name_new(1:period-1) = file_name(1:period-1);
  file_name_new(period) = '.';
  file_name_new(period+1:period+ext_len) = ext(1:ext_len);

  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 GNU LGPL license. 
%
%  Modified:
%
%    31 December 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    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!' );
    row_num = -1;
    return;
  end

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

  while ( 1 )

    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 value = i4_modp ( i, j )

%*****************************************************************************80
%
%% I4_MODP returns the nonnegative remainder of I4 division.
%
%  Discussion:
%
%    If
%      NREM = I4_MODP ( I, J )
%      NMULT = ( I - NREM ) / J
%    then
%      I = J * NMULT + NREM
%    where NREM is always nonnegative.
%
%    The MOD function computes a result with the same sign as the
%    quantity being divided.  Thus, suppose you had an angle A,
%    and you wanted to ensure that it was between 0 and 360.
%    Then mod(A,360) would do, if A was positive, but if A
%    was negative, your result would be between -360 and 0.
%
%    On the other hand, I4_MODP(A,360) is between 0 and 360, always.
%
%  Example:
%
%        I     J     MOD  I4_MODP    Factorization
%
%      107    50       7       7    107 =  2 *  50 + 7
%      107   -50       7       7    107 = -2 * -50 + 7
%     -107    50      -7      43   -107 = -3 *  50 + 43
%     -107   -50      -7      43   -107 =  3 * -50 + 43
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    02 March 1999
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer I, the number to be divided.
%
%    Input, integer J, the number that divides I.
%
%    Output, integer VALUE, the nonnegative remainder when I is
%    divided by J.
%
  if ( j == 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4_MODP - Fatal error!\n' );
    fprintf ( 1, '  Illegal divisor J = %d\n', j );
    error ( 'I4_MODP - Fatal error!' );
  end

  value = mod ( i, j );

  if ( value < 0 )
    value = value + abs ( j );
  end

  return
end
function value = i4_wrap ( ival, ilo, ihi )

%*****************************************************************************80
%
%% I4_WRAP forces an integer to lie between given limits by wrapping.
%
%  Example:
%
%    ILO = 4, IHI = 8
%
%    I   Value
%
%    -2     8
%    -1     4
%     0     5
%     1     6
%     2     7
%     3     8
%     4     4
%     5     5
%     6     6
%     7     7
%     8     8
%     9     4
%    10     5
%    11     6
%    12     7
%    13     8
%    14     4
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    02 October 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer IVAL, an integer value.
%
%    Input, integer ILO, IHI, the desired bounds for the integer value.
%
%    Output, integer I4_WRAP, a "wrapped" version of IVAL.
%
  jlo = min ( ilo, ihi );
  jhi = max ( ilo, ihi );

  wide = jhi - jlo + 1;

  if ( wide == 1 )
    value = jlo;
  else
    value = jlo + i4_modp ( ival - jlo, wide );
  end

  return
end
function table = i4mat_data_read ( input_filename, m, n )

%*****************************************************************************80
%
%% I4MAT_DATA_READ reads data from an I4MAT file.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    27 January 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILENAME, the name of the input file.
%
%    Input, integer M, N, the number of rows and columns in the data.
%
%    Output, integer TABLE(M,N), the point coordinates.
%
  table = [];
%
%  Build up the format string for reading M real numbers.
%
  string = ' ';

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

  input_unit = fopen ( input_filename );

  if ( input_unit < 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4MAT_DATA_READ - Error!\n' );
    fprintf ( 1, '  Could not open the input file.\n' );
    error ( 'I4MAT_DATA_READ - Error!' );
    return;
  end

  i = 0;

  while ( i < n )

    line = fgets ( input_unit );

    if ( line == -1 )
      fprintf ( 1, '\n' );
      fprintf ( 1, 'I4MAT_DATA_READ - Error!\n' );
      fprintf ( 1, '  End of input while reading data.\n' );
      error ( 'I4MAT_DATA_READ - Error!' );
    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 ] = i4mat_header_read ( input_filename )

%*****************************************************************************80
%
%% I4MAT_HEADER_READ reads the header from an I4MAT file.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 October 2004
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string INPUT_FILENAME, the name of the input file.
%
%    Output, integer M, the spatial dimension.
%
%    Output, integer N, the number of points.
%
  m = file_column_count ( input_filename );

  if ( m <= 0 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'I4MAT_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, 'I4MAT_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 i4mat_transpose_print ( m, n, a, title )

%*****************************************************************************80
%
%% I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    31 January 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer M, N, the number of rows and columns.
%
%    Input, integer A(M,N), an M by N matrix to be printed.
%
%    Input, string TITLE, an optional 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 GNU LGPL license.
%
%  Modified:
%
%    21 June 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer M, N, the number of rows and columns.
%
%    Input, integer A(M,N), an M by N matrix to be printed.
%
%    Input, integer ILO, JLO, the first row and column to print.
%
%    Input, integer IHI, JHI, the last row and column to print.
%
%    Input, string TITLE, an optional title.
%
  incx = 10;

  if ( 0 < s_len_trim ( title ) )
    fprintf ( 1, '\n' );
    fprintf ( 1, '%s\n', title );
  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.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    09 August 2009
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string OUTPUT_FILENAME, the output filename.
%
%    Input, integer M, the spatial dimension.
%
%    Input, integer N, the number of points.
%
%    Input, integer TABLE(M,N), the points.
%
%    Input, logical HEADER, is TRUE if the header is to be included.
%

%
%  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!' );
    return;
  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 value = s_index_last_c ( s, c )

%*****************************************************************************80
%
%% S_INDEX_LAST_C finds the LAST occurrence of a given character.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    20 November 2004
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, character S(*), the string to be searched.
%
%    Input, character C, the character to search for.
%
%    Output, integer VALUE, the index in S where C occurs
%    last, or -1 if it does not occur.
%
  if ( c == ' ' )
    s_len = length ( s );
  else
    s_len = s_len_trim ( s );
  end

  for i = s_len : -1 : 1

    if ( s(i) == c )
      value = i;
      return
    end

  end

  value = -1;

  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 GNU LGPL license.
%
%  Modified:
%
%    14 June 2003
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string S, the string to be measured.
%
%    Output, integer LEN, 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 GNU LGPL license.
%
%  Modified:
%
%    30 January 2006
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    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 GNU LGPL license.
%
%  Modified:
%
%    14 February 2003
%
%  Author:
%
%    John Burkardt
%
  t = now;
  c = datevec ( t );
  s = datestr ( c, 0 );
  fprintf ( 1, '%s\n', s );

  return
end
function triangle_node2 = triangulation_order6_to_order3 ( triangle_num1, ...
  triangle_node1 )

%*****************************************************************************80
%
%% TRIANGULATION_ORDER6_TO_ORDER3 linearizes a quadratic triangulation.
%
%  Discussion:
%
%    A quadratic triangulation is assumed to consist of 6-node triangles,
%    as in the following:
%
%    11-12-13-14-15
%     |\    |\    |
%     | \   | \   |
%     6  7  8  9 10
%     |   \ |   \ |
%     |    \|    \|
%     1--2--3--4--5
%
%   This routine rearranges information so as to define the 3-node
%   triangulation:
%
%    11-12-13-14-15
%     |\ |\ |\ |\ |
%     | \| \| \| \|
%     6--7--8--9-10
%     |\ |\ |\ |\ |
%     | \| \| \| \|
%     1--2--3--4--5
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    24 March 2005
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, integer TRIANGLE_NUM1, the number of triangles in the quadratic
%    triangulation.
%
%    Input, integer TRIANGLE_NODE1(6,TRIANGLE_NUM1), the quadratic triangulation.
%
%    Output, integer TRIANGLE_NODE2(3,4*TRIANGLE_NUM1), the linear triangulation.
%
  tri2 = 0;

  for tri1 = 1 : triangle_num1

    n1 = triangle_node1(1,tri1);
    n2 = triangle_node1(2,tri1);
    n3 = triangle_node1(3,tri1);
    n4 = triangle_node1(4,tri1);
    n5 = triangle_node1(5,tri1);
    n6 = triangle_node1(6,tri1);

    tri2 = tri2 + 1;
    triangle_node2(1:3,tri2) = [ n1, n4, n6 ]';
    tri2 = tri2 + 1;
    triangle_node2(1:3,tri2) = [ n2, n5, n4 ]';
    tri2 = tri2 + 1;
    triangle_node2(1:3,tri2) = [ n3, n6, n5 ]';
    tri2 = tri2 + 1;
    triangle_node2(1:3,tri2) = [ n4, n5, n6 ]';

  end

  return
end