function fem_basis_t3_display ( node_file, element_file )

%*****************************************************************************80
%
%% FEM_BASIS_T3_DISPLAY displays a finite element T3 basis.
%
%  Discussion:
%
%    This program reads a data file defining a set of nodes, and a
%    data file defining the triangulation of those nodes using 3 node triangles
%    (or 6 node triangles, as long as the vertices are listed first).
%
%    The program then asks the user interactively to select one of the
%    nodes.  It computes the basis function associated with that node
%    and displays it over the entire mesh.  Of course, the basis function
%    will only be nonzero over a small number of the elements, but it
%    is instructive to see the entire mesh.
%
%    The display is initially "flat", but by using the manipulator
%    on the graphics menu, the user can easily get some dramatic images
%    of the basis function.
%
%  Usage:
%
%    fem_basis_t3_display ( 'node_file.txt', 'element_file.txt' )
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    26 February 2009
%
%  Author:
%
%    John Burkardt
%
%  Parameters:
%
%    Input, string NODE_FILE, ELEMENT_FILE, the names of the files
%    containing the node and element information.
%
  timestamp ( );
  fprintf ( 1, '\n' );
  fprintf ( 1, 'FEM_BASIS_T3_DISPLAY:\n' );
  fprintf ( 1, '  MATLAB version\n' );
  fprintf ( 1, '  Display basis functions associated with \n' );
  fprintf ( 1, '  a finite element grid of linear triangles ("T3").\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  This program reads two files:\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  * node_file,     the node file,\n' );
  fprintf ( 1, '  * element_file,  the element file,\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  The user specifies a basis function by node index, and\n' );
  fprintf ( 1, '  the program displays a surface plot of that basis function.\n' );
  fprintf ( 1, '  (Use the 3D ROTATE option to see the full picture!\n' );
%
%  Read the data.
%
  node_xy = load ( node_file )';
  [ dim_num, node_num ] = size ( node_xy );

  element_node = load ( element_file )';
  [ element_order, element_num ] = size ( element_node );

  if ( element_order ~= 3 )
    fprintf ( 1, '\n' );
    fprintf ( 1, 'FEM_BASIS_T3_DISPLAY\n' );
    fprintf ( 1, '  This program requires that the elements have order 3.\n' );
    fprintf ( 1, '  Your elements have order %d\n', element_order );
    error ( 'FEM_BASIS_T3_DISPLAY - Fatal error!' );
  end

  x_min = min ( node_xy(1,:) );
  x_max = max ( node_xy(1,:) );
  y_min = min ( node_xy(2,:) );
  y_max = max ( node_xy(2,:) );
  z_min = 0.0;
  z_max = 1.0;

  node_min = min ( min ( element_node ) );
  node_max = max ( max ( element_node ) );

  fprintf ( 1, '\n' );
  fprintf ( 1, '  Every basis function is associated with a node.\n' );
  fprintf ( 1, '  To chooose a basis function, you specify a node.\n' );
  fprintf ( 1, '  Nodes range in value from %d to %d.\n', node_min, node_max );
  
  while ( 1 )

    fprintf ( 1, '\n' );
    prompt = sprintf ( 'Enter a node between %d and %d: ', node_min, node_max );
    node_index = input ( prompt );

    if ( node_index < node_min | node_max < node_index )
      break
    end
%
%  Clear the graphics page.
%
    clf
    
    fprintf ( 1, '\n' );
  
    for element = 1 : element_num
    
      local = 0;
      for j = 1 : element_order
        if ( element_node(j,element) == node_index )
          fprintf ( 1, '  Node %d occurs as local node %d in element %d.\n', ...
            node_index, j, element );
          local = j;
        end 
      end

      z(1:2,1:2) = 0.0;

      if ( local == 0 )

        x(1,1) = node_xy(1,element_node(1,element)); 
        y(1,1) = node_xy(2,element_node(1,element));
        x(2,1) = node_xy(1,element_node(1,element)); 
        y(2,1) = node_xy(2,element_node(1,element));
        x(1,2) = node_xy(1,element_node(2,element)); 
        y(1,2) = node_xy(2,element_node(2,element));
        x(2,2) = node_xy(1,element_node(3,element)); 
        y(2,2) = node_xy(2,element_node(3,element));

      else

        x(1,1) = node_xy(1,element_node(local,element)); 
        y(1,1) = node_xy(2,element_node(local,element));
        z(1,1) = 1.0;

        x(2,1) = node_xy(1,element_node(local,element)); 
        y(2,1) = node_xy(2,element_node(local,element));
        z(2,1) = 1.0;

        j = i4_wrap ( local + 1, 1, element_order );
        x(1,2) = node_xy(1,element_node(j,element)); 
        y(1,2) = node_xy(2,element_node(j,element));

        j = i4_wrap ( j + 1, 1, element_order );
        x(2,2) = node_xy(1,element_node(j,element)); 
        y(2,2) = node_xy(2,element_node(j,element));

      end
    
      caxis ( [ -0.4, 1.2 ] )
      surface ( x, y, z, 'FaceColor', 'interp' )

    end

    axis ( [ x_min, x_max, y_min, y_max, z_min, z_max ] );
    axis equal

    xlabel ( '--X axis--' );
    ylabel ( '--Y axis--' );
    zlabel ( '--Z axis--' );

    title_string = sprintf ( 'T3 basis function for node %d', node_index );
    title ( title_string );

    fprintf ( 1, '\n' );
    fprintf ( 1, 'Press return...\n' );
    pause

  end

  fprintf ( 1, '\n' );
  fprintf ( 1, 'FEM_BASIS_T3_DISPLAY:\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

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

  return
end