function  result_C1_L3_graph (i_p)
% Copyright 2000 J.E. Akin. All rights reserved.
% under construction: requires analytic exact solution
%  ------------------------------------------------------
%  Matlab graph of i_p-th component value at mesh nodes
%  for a mesh of 3 node quintic Hermite line elements
%   i_p = 1 is solution, = 2 is solution slope
%  ------------------------------------------------------

% c_x    = x 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

% UNDER_CONSTRUCTION
  if ( nargin == 0 )
    i_p = 1 ; 
  end % if no arguments
  format short

%    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 coordinates \n', np)
  ns = size (msh_bc_xyz,2) - pre_p ;   % space dimension
  if ( ns ~= 1)
    error ('This is not a 1D mesh')
  end % if not 1D 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)
  if ( nod_per_el ~= 3 )
    error ('This is not a mesh of 3 node line elements')
  end % if 

  load node_results.tmp
  nr = size (node_results, 1);
  if ( nr == 0 )
    error ('Error missing file node_results.tmp')
  end % if error
  max_p = size (node_results, 2) ; % number of columns
  fprintf ('Read %g nodal solution values \n', nr)
  fprintf ('     with %g components each \n', max_p)
  if ( i_p > max_p ) 
    fprintf ('Data requested for component i_p = %g \n', i_p)
    error ('i_p > available data')
  end % if error

  H (3)       = 0. ;
  HC1 (6)     = 0. ;
  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
  t_dy (nod_per_el) = 0 ;        % Optional pre-allocation
  c_x (nod_per_el) = 0 ;        % Optional pre-allocation
  c_y (nod_per_el) = 0 ;        % Optional pre-allocation

%                set constants
  loop = [1:nod_per_el] ; % default to sequential order

  % msh_bc_xyz has: pre_p items then: x, y
  x = msh_bc_xyz (1:np, (pre_p+1)) ; % extract x column
  xmax = max (x)      ; xmin = min (x) ;

  y  = node_results(:, 1) ;
  dy = node_results(:, 2) ;

%    Cite max, min values
  if ( i_p == 1 ) % deflection values
    [V_X, L_X] = max (y) ;
    [V_N, L_N] = min (y) ;
  else
    [V_X, L_X] = max (dy) ;
    [V_N, L_N] = min (dy) ;
  end % if defl or slope
  fprintf ('Max value is %g at node %g \n', V_X, L_X)
  fprintf ('Min value is %g at node %g \n', V_N, L_N)
  null (1:np) = V_N ;

%    Initialize plots
   if ( i_p == 1 )
     maxy = max (y)      ; miny = min (y) ;
   end % if
   if ( i_p == 2 )
     maxy = max (dy)      ; miny = min (dy) ;
   end % if

% finalize axes
   ymax = maxy;
   ymin = miny;
   diff = abs(ymax-ymin) ;
   ymax = ymax + abs (diff)/10. ;
   ymin = ymin - abs (diff)/10. ;
   max_all = ymax ;
   min_all = ymin ;

   clf                               % clear graphics
   hold on                           % hold image for plots
   xlabel (['X, Node at 45 deg (', int2str(nod_per_el), ...
            ' per element), Element at 90 deg'])
   title(['Qunitic C1 FEA Component\_', int2str(i_p),' from:  ', ...
          int2str(nt),' Elements, ', int2str(np),' Nodes'])     

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

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

%      Skip point elements, if any
    if ( all (t_nodes) ) % then valid line

%      Extract element coordinates & values
      t_x  = x (t_nodes) ;         % x at those nodes, only
      %b if ( t_x(2) ~= (t_x(1)+t_x(3))/2 )
        %b fprintf ('Bad Jaconian element %g \n', it)
      %b end % if non-constant Jacobian
      t_y  = y (t_nodes) ;         % y at those nodes, only
      t_dy  = dy (t_nodes) ;         % dy at those nodes, only
      D (1:2:6) = t_y ;
      D (2:2:6) = t_dy ;
      if ( i_p == 1 )
        plot (t_x, t_y, 'ko')        % plot nodal value symbols
      else
        plot (t_x, t_dy, 'ko')        % plot nodal value symbols
      end % if

%      Plot the element number
      x_bar = sum (t_x' )/nod_per_el ;
      t_text = sprintf ('   (%g)', it);  % offset # from pt
      text (x_bar, V_N, t_text, 'Rotation', 90) % incline
      plot (x_bar, V_N, 'k+')

%     Loop over local points on the quadratic polynomial element
     n_poly = ceil ( 95 / nt) ;
     for k = 1: (n_poly + 1) % points in parametric space
%         get element parametric interpolation functions
        R     = (k - 1)/n_poly ;   % on 0 to 1
        X     = 2*R - 1 ;          % on -1 to 1
%       H = ELEMENT SHAPE FUNCTIONS
%       X = LOCAL COORDINATE OF POINT,    -1 TO +1
%       LOCAL NODE COORD. ARE -1,0,+1    1-----2-----3
        H (1) = 0.5*(X*X - X) ;
        H (2) = 1. - X*X ;
        H (3) = 0.5*(X*X + X) ;
        x_el (k) = H * t_x ;  % true x value

        A = abs(t_x(3) - t_x(1)) ;
        P = X ;
        P_2 = P * P   ; P_3 = P * P_2 ;
        P_4 = P * P_3 ; P_5 = P * P_4 ;
        HC1(1) = (4*P_2 - 5*P_3 - 2*P_4 + 3*P_5) * 0.25 ;
        HC1(2) = (P_2 - P_3 - P_4 + P_5) * 0.125 * A ;
        HC1(3) =  1 - 2*P_2 + P_4 ;
        HC1(4) = (P - 2*P_3 + P_5) * A * 0.5 ;
        HC1(5) = (4*P_2 + 5*P_3 - 2*P_4 - 3*P_5) * 0.25  ;
        HC1(6) = (-P_2 - P_3 + P_4 + P_5) * 0.125 * A ;
        y_el (k) = HC1 * D' ;  % true y value

        DHC1 (1) = (8*P - 15*P_2 - 8*P_3 + 15*P_4) * 0.5 / A ;
        DHC1 (2) = (2*P - 3*P_2 - 4*P_3 + 5*P_4) * 0.25 ;
        DHC1 (3) = (-4*P + 4*P_3) * 2 / A ;
        DHC1 (4) = (1 - 6*P_2 + 5*P_4) ;
        DHC1 (5) = (8*P + 15*P_2 - 8*P_3 - 15*P_4) * 0.5 / A ;
        DHC1 (6) = (-2*P - 3*P_2 + 4*P_3 + 5*P_4) * 0.25 ;
        dy_el (k) = DHC1 * D' ;  % true y value
      end % for k

      if ( i_p == 1 )
        max_el = max(y_el) ;
        min_el = min(y_el) ;
        plot (x_el, y_el)
      else
        max_el = max(dy_el) ;
        min_el = min(dy_el) ;
        plot (x_el, dy_el)
      end % if

      if ( max_el > max_all ) 
        max_all = max_el ;
      end % if
      if ( min_el < min_all ) 
        min_all = min_el ;
      end % if
    end % if zero in connectivity
  end % for over all elements
  fprintf ('Scale ranges %g \n', min_all, max_all)
  ylabel (['DOF (',num2str(V_N), ' to ', num2str(V_X), ' )' ]) 

   axis ([xmin, xmax, min_all, max_all])   % set axes

% plot node points on axis
  for i = 1:np
    t_text = sprintf ('   %g', i);  % offset # from pt
    text (x(i), null(i), t_text, 'Rotation', 45) % incline
  end % for all
  plot (x, null, 'k*')
  grid
 
% label max min points 
  % plot (x(L_X), y(L_X), 'kx')
  % plot (x(L_N), y(L_N), 'ko')
  v_text = sprintf ('---min') ;
  text  (x(L_N), V_N, v_text) ;
  v_text = sprintf ('---max') ;
  text  (x(L_X), V_X, [v_text]) ;

%       -depsc -tiff            % for an eps version
  %b print ('-dpsc', ['true_L3_result_', int2str(i_p), '_graph'])
  hold off
  %b v_text = ['Created true_L3_result_', int2str(i_p), '_graph.ps'] ;
  %b fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of result_C1_L3_graph