function bezier_surface_display ( node_file_name, rectangle_file_name )

%*****************************************************************************80
%
%% bezier_surface_display() displays the faces of a shape defined by a Bezier surface file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Usage:
%
%    bezier_surface_display ( 'node_file_name', 'rectangle_file_name' )
%
%  Input:
%
%    character NODE_FILE_NAME, the name of the node file.
%
%    character RECTANGLE_FILE_NAME, the name of the rectangle file.
%
  timestamp ( );

  fprintf ( 1, '\n' );
  fprintf ( 1, 'BEZIER_SURFACE_DISPLAY\n' );
  fprintf ( 1, '  MATLAB version\n' );
  fprintf ( 1, '  Reads the nodes and rectangles defining\n' );
  fprintf ( 1, '  a Bezier surface and displays the object\n' );
  fprintf ( 1, '  as a MATLAB shape.\n' );
%
%  If at least one command line argument, it's the node file name.
%
  if ( nargin < 1 )

    fprintf ( 1, '\n' );
    fprintf ( 1, 'BEZIER_SURFACE_DISPLAY:\n' );
    node_file_name = input ( 'Enter the name of the node file:' );

  end
%
%  If at least two command line arguments, it's the node file name.
%
  if ( nargin < 2 )

    fprintf ( 1, '\n' );
    fprintf ( 1, 'BEZIER_SURFACE_DISPLAY:\n' );
    rectangle_file_name = input ( 'Enter the name of the rectangle file:' );

  end
%
%  Read the nodes.
%
  [ node_num, node_xyz ] = bezier_surface_node_file_read ( node_file_name );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Number of nodes = %d\n', node_num );
%
%  Read the rectangles.
%
  [ rectangle_num, rectangle_node ] = bezier_surface_rectangle_file_read ( ...
    rectangle_file_name );

  fprintf ( 1, '  Number of rectangles = %d\n', rectangle_num );
%
%  Display the crude image as a collection of rectangular patches involving only
%  the corner nodes.
%
  corners = [1,4,16,13];

  face_matrix = rectangle_node(corners,1:rectangle_num)';

  handle = patch ( 'Vertices', node_xyz', 'Faces', face_matrix );
  
  set ( handle, 'FaceColor', [0.5, 0.6, 0.8], 'EdgeColor', 'Black' );

  axis equal; 
  grid ( 'on' );

  xlabel ( '--X Axis--' )
  ylabel ( '--Y Axis--' )
  zlabel ( '--Z Axis--' )
%
%  The TITLE function will interpret underscores in the title.
%  We need to unescape such escape sequences!
%
  title_string = s_escape_tex ( rectangle_file_name );
  title ( title_string )
%
%  Terminate.
%
  fprintf ( 1, '\n' );
  fprintf ( 1, 'BEZIER_SURFACE_DISPLAY:\n' );
  fprintf ( 1, '  Normal end of execution.\n' );
  fprintf ( 1, '\n' );
  timestamp ( );

  return
end
function [ node_num, node_xyz ] = bezier_surface_node_file_read ( ...
  node_file_name )

%*****************************************************************************80
%
%% bezier_surface_node_file_read() reads node information from a Bezier surface node file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    11 June 2006
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Edward Angel,
%    Interactive Computer Graphics, 
%    a Top-Down Approach with OpenGL,
%    Addison-Wesley, 2000.
%
%  Input:
%
%    string NODE_FILE_NAME, the name of the node file.
%
%  Output:
%
%    integer NODE_NUM, the number of nodes defined.
%
%    real NODE_XYZ(3,NODE_NUM), the coordinates of nodes.
%
  [ dim_num, node_num ] = r8mat_header_read ( node_file_name );

  node_xyz = r8mat_data_read ( node_file_name, dim_num, node_num );

  return
end
function [ rectangle_num, rectangle_node ] = ...
  bezier_surface_rectangle_file_read ( rectangle_file_name )

%*****************************************************************************80
%
%% bezier_surface_rectangle_file_read() reads rectangles from a Bezier surface rectangle file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    11 June 2006
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Edward Angel,
%    Interactive Computer Graphics, 
%    a Top-Down Approach with OpenGL,
%    Addison-Wesley, 2000.
%
%  Input:
%
%    string RECTANGLE_FILE_NAME, the name of the rectangle file.
%
%  Output:
%
%    integer RECTANGLE_NUM, the number of rectangles defined.
%
%    real RECTANGLE_NODE(4,RECTANGLE_NUM), the nodes making up each rectangle.
%
  [ dim_num, rectangle_num ] = i4mat_header_read ( rectangle_file_name );

  rectangle_node = i4mat_data_read ( rectangle_file_name, ...
    dim_num, rectangle_num );

  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:
%
%    21 February 2004
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string INPUT_FILE_NAME, the name of the file.
%
%  Output:
%
%    integer COLUMN_NUM, the number of columns in the file.
%

%
%  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 ) 
    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:
%
%    31 December 2006
%
%  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 table = i4mat_data_read ( input_filename, m, n )

%*****************************************************************************80
%
%% i4mat_data_read() reads data from an I4MAT file.
%
%  Discussion:
%
%    An I4MAT is an array of I4'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 in the data.
%
%  Output:
%
%    integer TABLE(M,N), the point coordinates.
%

%
%  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!' );
  end

  table = zeros ( m, n );

  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.
%
%  Discussion:
%
%    An I4MAT is an array of I4'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, '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 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 s2 = s_escape_tex ( s1 )

%*****************************************************************************80
%
%% s_escape_tex() de-escapes TeX escape sequences.
%
%  Discussion:
%
%    In particular, every occurrence of the characters '\', '_',
%    '^', '{' and '}' will be replaced by '\\', '\_', '\^',
%    '\{' and '\}'.  A TeX interpreter, on seeing these character
%    strings, is then likely to return the original characters.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    19 January 2007
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string S1, the string to be de-escaped.
%
%  Output:
%
%    string S2, a copy of the string, modified to avoid TeX escapes.
%
  s1_length = length ( s1 );

  s1_pos = 0;
  s2_pos = 0;
  s2 = [];

  while ( s1_pos < s1_length )

    s1_pos = s1_pos + 1;

    if ( s1(s1_pos) == '\' || ...
         s1(s1_pos) == '_' || ...
         s1(s1_pos) == '^' || ...
         s1(s1_pos) == '{' || ...
         s1(s1_pos) == '}' )
      s2_pos = s2_pos + 1;
      s2 = strcat ( s2, '\' );
    end

    s2_pos = s2_pos + 1;
    s2 = strcat ( s2, s1(s1_pos) );

  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 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 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.
%
  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 )
      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
 
