function  hidden_T3_flux_surface (i_p, row) %CL
%b function  hidden_T3_flux_surface (i_p)
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab hidden surface (discontinuous) plot of i_p-th 
%  flux component value in linear T3 elements
%  ------------------------------------------------------
 %? global az el   ? these are not changing with new view

% c_x    = x coordinates of nod_per_el line polygon
% c_y    = y coordinates of nod_per_el line polygon
% msh_typ_nodes   = connectivity list for elements, nt x nod_per_el
% loop   = corners for nod_per_el line polygon
% nod_per_el = Nodes per element
% np     = Number of Points
% nt     = Number of elements
% pre_e  = Element items before connectivity list
% pre_p  = Nodal items before coordinates
% pre_r  = Elem items before flux results %CL
% row    = row number where cord & connectivity start, 1 or 2 %CL
% 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

  pre_e  = 0 ;
  pre_p = 1;
  pre_r = 0 ; %CL
  %bfprintf ('Begin component value hidden carpet plots: \n')
  if ( nargin == 0 )
    i_p = 0 ; row = 1 ;
  elseif ( nargin == 1 ) %CL
    row = 1 ;
  elseif ( nargin == 2 ) %CL
    pre_e = 0 ; %CL
    % pre_r = 2 ; %CL
    %b row = 1 ; %CL
  end % if no arguments
  less = row - 1 ; %CL

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

%    Set control data: number of points
  np = size (msh_bc_xyz,1) ;   % number of nodal points  
  np = np - less ;   %CL
  % fprintf ('Read %g mesh coordinate pairs \n', np)
  ns = size (msh_bc_xyz,2) - pre_p ;   % space dimension
  pre_r = ns ; % coordinates of point are before flux
  if ( ns < 2 )
    error ('This is not a 2D mesh')
  end % if not 2D data
  
%    Set control data: number elements
  load  msh_typ_nodes.tmp ; % nod_per_el nodes per element
  nt = size (msh_typ_nodes,1) ;          % number of elements in mesh 
  nt = nt - less ; %CL
  nod_per_el = size (msh_typ_nodes,2) - pre_e -1 ; % nodes per elem
  % fprintf ('Read %g elements connections \n', nt)
  Col_1 = pre_e+2 ; %CL
  Col_2 = nod_per_el+pre_e+1 ; %CL

  load el_qp_xyz_fluxes.tmp
  nr = size (el_qp_xyz_fluxes, 1) ; % n_elem * n_qp
  if ( nr == 0 )
    error ('Error missing file el_qp_xyz_fluxes.tmp')
  end % if error
  nq = nr / nt; % quadrature pts per el, use only first
  max_p = size (el_qp_xyz_fluxes, 2) - pre_r ; % number of columns %CL
  fprintf ('Read %g element Gauss points \n', nq)
  if ( i_p > max_p ) 
    error ('i_p > available data')
  end % if error

  x (np)      = 0.       ;       % pre-allocate array x
  y (np)      = 0.       ;       % pre-allocate array y
  z (nt)      = 0.       ;       % pre-allocate array z
  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
  t_z (nod_per_el) = 0 ;        % Optional pre-allocation, all same
  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
  %b x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column
  x = msh_bc_xyz (row:(np+less), (pre_p+1)) ; % extract x  %CL
  %b y = msh_bc_xyz (1:np, (pre_p+2)) ; % extract y column 
  y = msh_bc_xyz (row:(np+less), (pre_p+2)) ; % extract y %CL

  if ( i_p >= 1 )
    for k = 1:nt;  % element loop
      kq = 1 + nq*(k-1); % single gauss point
      z (k) = el_qp_xyz_fluxes(kq, pre_r+i_p) ; %CL
    end % for
  else % i_p = 0, get root mean sq
    for k = 1:nt
      kq = 1 + nq*(k-1); % single gauss point
      z (k) = sqrt(sum(el_qp_xyz_fluxes (kq, pre_r+1:pre_r+max_p).^2));
    end % for k
  end % if get RMS value

%    Cite max, min values
  [V_X, L_X] = max (z) ;
  [V_N, L_N] = min (z) ;
  fprintf ('Max value is %g at element %g \n', V_X, L_X)
  fprintf ('Min value is %g at element %g \n', V_N, L_N)

%    Initialize plots
   xmax = max (x)      ; xmin = min (x) ;
   ymax = max (y)      ; ymin = min (y) ;
   zmax = max (z)      ; zmin = min (z) ;
   z_inc = abs(zmax - zmin)/1000 ;
% zmax=16
% zmin=0

   clf                               % clear graphics
   axis ([xmin, xmax, ymin, ymax, zmin, zmax])   % set axes
% view([52.5,30])

   hold on                           % hold image for plots
   xlabel ('X')                      % add label 
   ylabel ('Y')                      % add label
   if ( i_p >= 1 )
     zlabel (['Flux ', int2str(i_p), ' (max = ', ...
               num2str(V_X), ', min = ', num2str(V_N), ')'])
     title(['FEA T3 Flux Component\_', int2str(i_p),': ', ...
            int2str(nt),' Elements, ', int2str(np), ...   
            ' Nodes, (', int2str(nod_per_el), ' per Element)'])
   else % i_p = 0, get root mean sq
   % zlabel (['RMS Value (max = ', num2str(V_X), ...
   %          ', min = ', num2str(V_N), ')'])
     title(['FEA T3 Flux RMS Value: ', ...
            int2str(nt),' Elements, ', int2str(np), ...       
            ' Nodes, (', int2str(nod_per_el), ' per Element)'])
     zlabel ('RMS Flux Value')
   end % if get RMS value

%    Loop over all elements
  %b n1 = pre_e+2 ; n2 = nod_per_el+pre_e+1 ;
  inc_e = 0 ; % user control
  for it = 1:nt  ;

%      Extract corner connectivity 
    t_nodes = msh_typ_nodes ((it+less), Col_1:Col_2 ) ; %CL
    if ( all ( t_nodes > 0 ) ) %B

%      Extract corner coordinates
      t_x  = x (t_nodes) ;         % x at those nodes, only
      t_y  = y (t_nodes) ;         % y at those nodes, only
      t_z(1:nod_per_el) = z (it);  % constant at all el nodes

%      Get the centroid
      x_bar = sum (t_x' )/nod_per_el ;
      y_bar = sum (t_y' )/nod_per_el ;

%      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
      c_z  = t_z (loop) ;
      fill3 (c_x, c_y, c_z, 'y'  )           % plot nod_per_el lines

%      show element number
      if ( inc_e > 0 )
        t_text = sprintf ('%g', it);
        z_bar = z(it) + z_inc ;
        text (x_bar, y_bar, z_bar, t_text)
      end % if
    end % if all
  end % for over all elements, it
  grid
 
%% label max min points 
%  v_text = sprintf ('------min') ;
%  text  (x(L_N), y(L_N), V_N, v_text) ;
%  v_text = sprintf ('------max') ;
%  text  (x(L_X), y(L_X), V_X, [v_text]) ;   ;

% end % if show labels
%       -depsc -tiff            % for an eps version
% print ('-dpsc', ['hidden_T3_flux_', int2str(i_p), '_surface'])
  hold off
%  v_text = ['Created hidden_T3_flux_', int2str(i_p), '_surface.ps'] ;
% fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of hidden_T3_flux_surface