function  exact_3d_graph (i_p)
% Copyright 2000, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab line plot of i_p-th component value, in z-direction,
%  on top of line mesh (e.g. truss) at z=0. Mesh is black, 
%  component is red.  If i_p = 0, show RMS value.
%  ------------------------------------------------------

% c_x    = x coordinates of nod_per_el line element
% c_y    = y coordinates of nod_per_el line element
% msh_typ_nodes   = connectivity list for elements, nt x nod_per_el
% loop   = corners for nod_per_el line element
% 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

  fprintf ('Begin component value 3D graph: \n')
  if ( nargin == 0 )
    i_p = 0 ;
  end % if no arguments

%    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  
  fprintf ('Read %g mesh coordinate pairs \n', np)
  ns = size (msh_bc_xyz,2) - pre_p ;   % space dimension
  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 
  nod_per_el = size (msh_typ_nodes,2) - pre_e -1 ; % nodes per elem
  fprintf ('Read %g elements connections \n', nt)

  load exact_node_solution.tmp
  nrr = size (exact_node_solution, 1);
  max_pp = size (exact_node_solution, 2) ; % number of columns
  if ( nrr == 0 )
    error ('Error missing file exact_node_solution.tmp')
  end % if error
  fprintf ('Read %g exact nodal value sets \n', nrr)
  fprintf ('     with %g components each \n', max_pp)
 
  if ( i_p > max_pp ) 
    error ('i_p > available data')
  end % if error

  x (np)      = 0.       ;       % pre-allocate array x
  y (np)      = 0.       ;       % pre-allocate array y
  z (np)      = 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
  c_x (nod_per_el + 1) = 0 ;    % Optional pre-allocation
  c_y (nod_per_el + 1) = 0 ;    % Optional pre-allocation
  c_z (nod_per_el + 1) = 0 ;    % Optional pre-allocation

%                set constants
  [loop] = get_El_Loop (nod_per_el) ;
  %b fprintf ('Begin element plots:')


  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column
  y = msh_bc_xyz (1:np, (pre_p+2)) ; % extract y column 

  if ( i_p >= 1 )
    z = exact_node_solution(:, i_p) ;
  else % i_p = 0, get root mean sq
    for k = 1:np
      z (k) = sqrt ( sum (exact_node_solution (k, 1:max_pp).^2)) ;
    end % for k
  end % if get RMS value

%    Cite max, min values
  [V_X, L_X] = max (z(1:np)) ;
  [V_N, L_N] = min (z(1:np)) ;
  fprintf ('Max component value is %g at node %g \n', V_X, L_X)
  fprintf ('Min component value is %g at node %g \n', V_N, L_N)
  z_t (1:nod_per_el+1) = V_N ;  % Fake z element coordinate
  null(1:np)           = V_N ;  % Fake z element coordinate
% node to value connect
  x2 (1:2) = V_N; y2 (1:2) = V_N; z2 (1:2) = V_N; 

%    Initialize plots
   xmax = max (x)  ; xmin = min (x) ;
   ymax = max (y)  ; ymin = min (y) ;
   zmax = V_X      ; zmin = V_N  ;
  if ( zmax == zmin )
    zmax = zmin + 1 ;
    if ( ymax == ymin )
      ymax = ymin + 1 ;
    end % if
  end % if planar or axial
   clf                               % clear graphics
   axis ([xmin, xmax, ymin, ymax, zmin, zmax])   % set axes

%    Get view azimuth and elevation
  [az, el] = view ;

   hold on                           % hold image for plots
   xlabel ('X, nodes at z=0, try view([0,1,0])')  % add label
   ylabel ('Y, nodes at z=0, try view([1,0,0])')  % add label
   if ( i_p >= 1 )
     title(['Exact Solution Component\_', int2str(i_p), ...
     ' at ', int2str(np),' Nodes (', int2str(nt),' Elements)'])
     %title(['Exact Solution Component\_', int2str(i_p), ...
            %' Evaluated at the Nodes'])
     zlabel (['Component ', int2str(i_p), ' (max = ', ...
     num2str(V_X), ', min = ', num2str(V_N), ')'])
   else % i_p = 0, get root mean sq
     title(['Exact Solution RMS Value', ...
     ' at ', int2str(np),' Nodes (', int2str(nt),' Elements)'])
     %title(['Exact Solution RMS Value Evaluated at the Nodes'])
     zlabel (['RMS Value (max = ', ...
     num2str(V_X), ', min = ', num2str(V_N), ')'])
   end % if get RMS value

%    Loop over all elements
  for it = 1:nt  ;

%      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
    t_z  = z (t_nodes) ;         % z at those nodes, only

%      Plot this element
    c_x  = t_x (loop) ;       % x for nod_per_el line element
    c_y  = t_y (loop) ;       % y for nod_per_el line element
    c_z  = t_z (loop) ;
    plot3 (c_x, c_y, z_t, 'g-')   % plot mesh lines
    plot3 (c_x, c_y, c_z, 'k-')   % plot result lines
  end % for over all elements
  plot3(c_x, c_y, c_z, 'k-'), grid  % add grid to last one
 
%   Mark node points
  plot3 (x, y, null,'k*')
  plot3 (x, y, z,   'r*')

%    label max min points 
  % plot3 (x(L_X), y(L_X), V_X, 'kx')
  % plot3 (x(L_N), y(L_N), V_N, 'ko')
  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]) ;

%     Label node numbers at value location
  for i = 1:np
    x2 (1:2) = x(i) ; y2 (1:2) = y(i) ;
    z2 (1) = V_N    ; z2(2) = z(i) ;
    plot3 (x2, y2, z2, 'r--')      % connector

%    p_text = sprintf ('  %g', i);  % offset # from pt
%    text (x(i), y(i), z(i), p_text)
  end % for nodes

%       -depsc -tiff            % for an eps version
  %bprint ('-dpsc', ['exact_', int2str(i_p), '_3d_graph'])
  hold off
  %bv_text = ['Created exact_', int2str(i_p), '_3d_graph.ps'] ;
  %bfprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of exact_3d_graph