function fem_basis_t6_display ( node_file, element_file )

%% FEM_BASIS_T6_DISPLAY displays a finite element T6 basis.
%
%  Discussion:
%
%    This program reads a data file defining a set of nodes, and a
%    data file defining the triangulation of those nodes using 6 node triangles.
%
%    It is assumed that the 6 node triangles have straight sides, that is,
%    that each midside node lies on the line segment connecting the
%    corresponding vertices.
%
%    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_t6_display ( 'node_file.txt', 'element_file.txt' )
%
%  Modified:
%
%    13 August 2006
%
%  Author:
%
%    John Burkardt
%
  timestamp;
  fprintf ( 1, '\n' );
  fprintf ( 1, 'FEM_BASIS_T6_DISPLAY:\n' );
  fprintf ( 1, '  MATLAB version\n' );
  fprintf ( 1, '  Display a basis function associated with a finite element grid.\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,\n' );
  fprintf ( 1, '  and the program displays a surface plot of that basis function.\n' );
%
%  Read the data.
%
  p = load ( node_file )';
  [ dim_num, node_num ] = size ( p );

  t = load ( element_file )';
  [ triangle_order, triangle_num ] = size ( t );

  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 1 to %d.\n', node_num );
  fprintf ( 1, '\n' );
  
  node_index = input ( 'Enter the index of a node: ' );
%
%  Clear the graphics page.
%
  clf
  
  fprintf ( 1, '\n' );
  
  for triangle = 1 : triangle_num

    pt(1,1:6) = p(1,t(1:6,triangle)); 
    pt(2,1:6) = p(2,t(1:6,triangle));

    local = 0;
    for j = 1 : 6
      if ( t(j,triangle) == node_index )
        local = j;
        fprintf ( 1, '  Node %d occurs as local node %d in element %d.\n', ...
          node_index, j, triangle );
      end 
    end

    if ( local == 0 )

      x = zeros(2,2);
      y = zeros(2,2);
      z = zeros(2,2);
      x(1,1) = pt(1,1);
      y(1,1) = pt(2,1);
      x(2,1) = pt(1,1);
      y(2,1) = pt(2,1);
      x(1,2) = pt(1,2);
      y(1,2) = pt(2,2);
      x(2,2) = pt(1,3);
      y(2,2) = pt(2,3);

    else

      for i = 0 : 10
%
%  To use surface, we need to define a logical rectangular grid of points.
%  But our region is a triangle, so the easiest thing to do is to identify
%  two corners of the grid.  
%  We try to do this in such a way that the same thing happens in each
%  element, and the resulting grid looks less haphazard.
%
        if ( local == 1 | local == 5 )
          xlo = ( ( 10 - i ) * pt(1,1) + i * pt(1,2) ) / 10;
          ylo = ( ( 10 - i ) * pt(2,1) + i * pt(2,2) ) / 10;
          xhi = ( ( 10 - i ) * pt(1,1) + i * pt(1,3) ) / 10;
          yhi = ( ( 10 - i ) * pt(2,1) + i * pt(2,3) ) / 10;
        elseif ( local == 2 | local == 6 )
          xlo = ( ( 10 - i ) * pt(1,2) + i * pt(1,1) ) / 10;
          ylo = ( ( 10 - i ) * pt(2,2) + i * pt(2,1) ) / 10;
          xhi = ( ( 10 - i ) * pt(1,2) + i * pt(1,3) ) / 10;
          yhi = ( ( 10 - i ) * pt(2,2) + i * pt(2,3) ) / 10;
        elseif ( local == 3 | local == 4 )
          xlo = ( ( 10 - i ) * pt(1,3) + i * pt(1,2) ) / 10;
          ylo = ( ( 10 - i ) * pt(2,3) + i * pt(2,2) ) / 10;
          xhi = ( ( 10 - i ) * pt(1,3) + i * pt(1,1) ) / 10;
          yhi = ( ( 10 - i ) * pt(2,3) + i * pt(2,1) ) / 10;
        end 

        for j = 0 : 10

          pp(1) = ( ( 10 - j ) * xlo + j * xhi ) / 10;
          pp(2) = ( ( 10 - j ) * ylo + j * yhi ) / 10;
          
          zz = basis_11_t6 ( pt, local, pp );

          x(i+1,j+1) = pp(1);
          y(i+1,j+1) = pp(2);
          z(i+1,j+1) = zz;

        end
      end

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

  end

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

  title_string = s_escape_tex ( element_file );
  title ( title_string )

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

  fprintf ( 1, '\n' );
  fprintf ( 1, 'FEM_BASIS_T6_DISPLAY:\n' );
  fprintf ( 1, '  Normal end of execution.\n' );

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