function  C1_L3_beam_plots (i_p)  % ==========================
% Copyright 2008 J.E. Akin. All rights reserved.
%  ------------------------------------------------------
%  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 deflection, = 2 is slope
%   = 3 is curvature (moment), = 4 is curvature rate (shear)
%  ------------------------------------------------------

% c_x    = x coordinates of nod_per_el line element
% msh_typ_nodes = connectivity list , 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

  if ( nargin == 0 )
    i_p = 1 ; 
  end % if no arguments
  Pts_wide = 2 ; % draw fat lines
  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  
  %b 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
  %b 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
  %b fprintf ('Read %g nodal solution values \n', nr)
  %b fprintf ('     with %g components each \n', max_p)
  if ( i_p > 4 ) 
    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. ; DHC1 (6)     = 0. ;
  D2HC1 (6)   = 0. ; D3HC1 (6)    = 0. ;
  D4HC1 (6)   = 0. ;
  x (np)      = 0.       ;      % pre-allocate array x
  y (np)      = 0.       ;      % pre-allocate array y
  dy (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) ;
  if ( any (y) == 0 )
    fprintf ('All values are zero. Plot skipped. \n')
    return
  end % if null solution

   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'])

%    Are properties needed ?
  if ( i_p > 2 )
    load msh_properties.tmp
    n_mats = size (msh_properties, 2) ;
    n_vals = size (msh_properties, 1) ;
  else
    n_mats = 0;
    n_vals = 0;
    EI = 1 ;
  end % if

%    Loop over all elements
  max_all = -1e9  ; min_all = 1e9  ;
  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
      if ( t_x(2) ~= (t_x(1) + t_x(3))/2 )
        fprintf ('WARNING: fixed bad mid-point in element %g \n', it)
        t_x(2) = (t_x(1) + t_x(3))/2 ;
      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
      end % if

%      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 ;

%       select result of interest, r_el
        if ( i_p == 1 ) % deflection
          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 ;
          r_el (k) = HC1 * D' ;  % true y value
  
        elseif ( i_p == 2 ) % slope      
          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 ;
          r_el (k) = DHC1 * D' ;  % true y' value

        elseif ( i_p == 3 ) % curvature or moment
          D2HC1 (1) = (8 - 30*P - 24*P_2 + 60*P_3) /A/ A ;
          D2HC1 (2) = (2 - 6*P - 12*P_2 + 20*P_3) * 0.5/A ;
          D2HC1 (3) = (-4 + 12*P_2) * 4 / A / A ;
          D2HC1 (4) = (-12*P + 20*P_3)*2 / A ;
          D2HC1 (5) = (8 + 30*P - 24*P_2 - 60*P_3) / A /A;
          D2HC1 (6) = (-2 - 6*P + 12*P_2 + 20*P_3) * 0.5 / A ;
          r_el (k) = D2HC1 * D' ;  % true y'' value

        elseif ( i_p == 4 ) % curvature rate or shear force
          D3HC1 (1) = (-30 - 48*P + 180*P_2) * 2 /A/A/ A ;
          D3HC1 (2) = (-6 - 24*P + 60*P_2) /A /A;
          D3HC1 (3) = (24*P) * 8 / A / A/A ;
          D3HC1 (4) = (-12 + 60*P_2)*4 / A/A ;
          D3HC1 (5) = (30 - 48*P - 180*P_2) * 2 / A /A/A;
          D3HC1 (6) = (-6 + 24*P + 60*P_2) / A/A ;
          r_el (k) = D3HC1 * D' ;  % true y''' value
        end % if plot type

      end % for k plot points
      if ( n_vals > 1 )
        EI = msh_properties(it,1)*msh_properties(it,2)  ;
        r_el = r_el* EI ;
      elseif ( n_vals == 1 )
        EI = msh_properties( 1,1)*msh_properties( 1,2)  ;
        r_el = r_el* EI ;
      end % if

%    elem max, min values
      [V_X, L_X] = max (r_el)  ;
      [V_N, L_N] = min (r_el);
       if ( V_X > max_all )
         max_all = V_X ;
       end
       if ( V_N < min_all )
         min_all = V_N ;
       end
       plot (x_el, r_el, 'b-', 'LineWidth',Pts_wide)
    end % if zero in connectivity

% Plot the element number
    x_bar = sum (t_x' )/nod_per_el ;
    y_bar = mean (r_el) ;
    t_text = sprintf ('   (%g)', it);  % offset # from pt
    text (x_bar, y_bar, t_text) % incline

  end % for over all elements

  null (1:np) = 0.5*(V_N + V_X) ;
  if ( V_N <= 0 & V_X >= 0 )
    null (1:np) = 0. ;
  end % if
% finalize axes
   ymax = max_all ; ymin = min_all ;
   diff = abs(ymax-ymin) ;
   ymax = ymax + abs (diff)/10. ;
   ymin = ymin - abs (diff)/10. ;
   axis ([xmin, xmax, ymin, ymax])   % set axes

   if ( i_p == 1 )
     title(['Qunitic Beam Deflection from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])     
     ylabel (['Deflection: max=', num2str(max_all), ...
               ', min=', num2str(min_all)])
     fprintf ('Max deflection value is %g \n', max_all)
     fprintf ('Min deflection value is %g \n', min_all)
   elseif ( i_p == 2 )
     title(['Qunitic Beam Slope from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])     
     ylabel (['Slope: max=', num2str(max_all), ...
               ', min=', num2str(min_all)])       
     fprintf ('Max slope value is %g \n', max_all)
     fprintf ('Min slope value is %g \n', min_all)
   elseif ( i_p == 3 )
     title(['Qunitic Beam Moment from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])     
     ylabel (['Moment: max=', num2str(max_all), ...
               ', min=', num2str(min_all)])   
     fprintf ('Max moment value is %g \n', max_all)
     fprintf ('Min moment value is %g \n', min_all)
   elseif ( i_p == 4 )
     title(['Qunitic Beam Shear from:  ', ...
            int2str(nt),' Elements, ', int2str(np),' Nodes'])     
     ylabel (['Transverse Shear: max=', num2str(max_all), ...
               ', min=', num2str(min_all)])   
     fprintf ('Max shear value is %g \n', max_all)
     fprintf ('Min shear value is %g \n', min_all)
   end % if

% 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
 
%       Create plot copies for report use 
  if ( i_p == 1 )
    print ('-dpng', ['Beam_deflections'])
    v_text = ['Created Beam_deflections.png'] ;
  elseif ( i_p == 2 )
    print ('-dpng', ['Beam_slope'])
    v_text = ['Created Beam_slope.png'] ;
  elseif ( i_p == 3 )
    print ('-dpng', ['Beam_moments'])
    v_text = ['Created Beam_moments.png'] ;
  elseif ( i_p == 4 )
    print ('-dpng', ['Beam_shears'])
    v_text = ['Created Beam_shears.png'] ;
  end % if
  fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
  hold off
% end of C1_L3_beam_plots  % ==========================