function  qp_tau_value_plot (L1,L2,U1,U2)
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab plot 2-D FE numerical error in elements
%  ------------------------------------------------------
%bUNDER_CONSTRUCTION
% c_x    = x coordinates of nod_per_el line polygon
% c_y    = y coordinates of nod_per_el line polygon
% inc_e  = increment in element %-error on plot, if > 0
  inc_e  = 1 ;
% inc_p  = increment in node numbers on plot, if > 0
% msh_typ_nodes   = connectivity list for elements, nt x nod_per_el
% loop   = corners for nod_per_el line polygon
% lab_p  = 1, if node points are circled
  lab_p  = 0;
% nod_per_el = Nodes per element
% np     = Number of Points
% nt     = Number of elements
% pre_e  = Element items before connectivity list
  pre_e  = 0 ;
% pre_p  = Nodal items before coordinates
  pre_p = 1;
% msh_bc_xyz = Nodal coordinates (with preceeding data)
% t_x    = x coordinates of nod_per_el corners
% t_y    = y coordinates of nod_per_el corners
% xy     = Coordinates of points, np x 2

%    Read coordinate file and connectivity file
%    integer bc code, real xy pairs for np points (pre_p = 1)

%    Set control data: number of points
  load msh_bc_xyz.tmp ;  
  np = size (msh_bc_xyz,1) ;   % number of nodal points  
  ns = size (msh_bc_xyz,2) - pre_p ;   % dimension of space
  if ( np == 0 )
    error ('Error missing file msh_bc_xyz.tmp')
  end % if error
  fprintf ('\n Read %g mesh coordinate pairs \n', np)
  % fprintf ('       x        y \n')
  
%    Set control data: number elements & nodes per element
  load  msh_typ_nodes.tmp ; % nod_per_el nodes per element
  nt = size (msh_typ_nodes,1) ;  % number of elements in mesh 
  nod_per_el = size (msh_typ_nodes,2) - pre_e-1; % nodes per elem
  fprintf ('\n Read %g elements connections \n', nt)

  load el_qp_xyz_tau.tmp
  neqp = size (el_qp_xyz_tau,1) ;
  if ( neqp == 0 )
    error ('Error missing file el_qp_xyz_tau.tmp')
  end % if error
  fprintf ('\n Read %g qp tau values \n', neqp)
  nqp = neqp / nt ; % qp per elem

  [V_X, L_X] = max (el_qp_xyz_tau(:, 3))  ;
  [V_N, L_N] = min (el_qp_xyz_tau(:, 3)) ; ;
  V_XN = V_X - V_N + eps; % for color scale
  fprintf ('Max value is %g in element %g \n', V_X, L_X)
  fprintf ('Min value is %g in element %g \n', V_N, L_N)

  x (np)      = 0.       ;       % pre-allocate array x
  y (np)      = 0.       ;       % pre-allocate array y
  t_nodes (nod_per_el) = 0 ;    % Optional pre-allocation
  t_x (nod_per_el) = 0 ;        % Optional pre-allocation
  t_y (nod_per_el) = 0 ;        % Optional pre-allocation
  c_x (nod_per_el + 1) = 0 ;    % Optional pre-allocation
  c_y (nod_per_el + 1) = 0 ;    % Optional pre-allocation
  loop (nod_per_el + 1) = 0 ;   % Optional pre-allocation

%                set constants
  [loop] = get_El_Loop(nod_per_el) ;

  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column of xy
  if ( ns >= 2)
    y = msh_bc_xyz (1:np, (pre_p+2)) ; % extract y column of xy
  else
    y (1:np) = 0. ;
  end % if 1D
 
%    Initialize plots
  xmax = max (x)      ; xmin = min (x) ;
  ymax = max (y)      ; ymin = min (y) ;
  xdiff = xmax - xmin ; ydiff = ymax - ymin ;
  if ( ns == 1 )
  % if ( ydiff == 0.0 )
    % ydiff = 0.5 ; % allow for 1-D mesh (with y == 0)
    ydiff = xdiff/20 ; % allow for 1-D mesh (with y == 0)
  end % if no y coordinates
  xmax = xmax + xdiff/20; ymax = ymax + ydiff/20;
  xmin = xmin - xdiff/20; ymin = ymin - ydiff/20;
  clf                               % clear graphics
  axis ([xmin, xmax, ymin, ymax])   % set axes
  axis ('equal')                    % true shape style
  hold on                           % hold image for plots
  grid                              % add grid dots
  
  xlabel (['X: ', int2str(nt),' Elements'])
  ylabel (['Y: ', int2str(np),' Nodes'])
  title(['Tau normalized at quadrature points. (Max = ', ...
  num2str(V_X), ', min = ', num2str(V_N), ')'])
 
%      Plot input mesh points 
  if (lab_p == 1)                   % plot all points
    plot (x, y, 'b.')               % mark each node
  end % if show labels

%%    Show 20 nodes and 50 elements
%  inc_p = floor(np/20) ; inc_e = floor(nt/50) ;
%  if (inc_p == 0 ) 
%    inc_p = np - 1 ;
%  end % if inc_p
%  if (inc_e == 0 ) 
%    inc_e = nt - 1 ;
%  end % if inc_e
%%    Show all if a small mesh
%  if ( np <= 20 )
%    inc_p = 1 ;
%  end % if np
%  if ( nt <= 50 )
%    inc_e = 1 ;
%  end % if nt
inc_e=0; inc_p=0;
  if (inc_p > 0)                      % plot node numbers
    for i = 1:inc_p:np                % convert to string
      p_text = sprintf ('  %g4', i);   % offset # from pt
      text (x(i), y(i), p_text)       % plot pt number
    end % for all points
  end % if show labels
  disp (' ')

%    Loop over all elements
  for it = [L1:L2, U1:U2] ; %b lower and upper pair

%      Extract corner connectivity 
    t_nodes = msh_typ_nodes (it, (pre_e+2):(nod_per_el+pre_e+1)); 

%      Extract corner coordinates
    t_x  = x (t_nodes) ;         % x at those nodes, only
    t_y  = y (t_nodes) ;         % y at those nodes, only
    plot (t_x, t_y, 'ko')

%      Get the qp location and tau values
    kount = nqp*(it - 1) ;
    for k = 1:nqp
      kount=kount+1;
      x_bar = el_qp_xyz_tau (kount, 1) ;       
      y_bar = el_qp_xyz_tau (kount, 2) ;       
      tau   = el_qp_xyz_tau (kount, 3) ;       
      ratio = tau/V_X ;
      t_text = sprintf ('+  %5.4g', ratio) ;
      text (x_bar, y_bar, t_text, 'Rotation', 20)
    end % for qp points

%      Plot this polygon
    c_x  = t_x (loop) ;       % x for nod_per_el line polygon
    c_y  = t_y (loop) ;       % y for nod_per_el line polygon
    plot (c_x, c_y,'b-')           % plot nod_per_el lines in blue
  end % for over all elements

%%    Finish the plots with elem error estimate numbers
%  if (inc_e > 0)                     % plot elem number, inclined
%    for i = 1:inc_e:nt               % convert to string
%      v = 100. * el_qp_xyz_tau (i) ;  % el %-error value
%      t_text = sprintf ('%g', v);    % convert to text  
%      text (x_bar(i), y_bar(i), t_text, 'Rotation', 40) % incline
%    end % for all polygons
%  end % if show labels
%       -depsc -tiff            % for an eps version
  %bprint -dpsc qp_tau_value_plot
  hold off
%bfprintf ('Created file qp_tau_value_plot.ps \n')
% end of qp_tau_value_plot