function  beam_C1_L2_defl (i_p) 
% Copyright 2004, J.E. Akin.  All rights reserved.
%  ------------------------------------------------------
%  Matlab graph of i_p-th component value of 1 eigenvector, 
%  at mesh node locations 
%  ------------------------------------------------------

% 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_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

  clear fid_1 fid_5 
  if ( nargin == 0 )
    i_p = 1 ; 
  end % if

%    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 > 1 )
    %b error ('This is not a 1D mesh')
    fprintf ('Not 1D: will use x-coordinate only \n')
  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)

  ng = 1 ; % number of generalized dof
% ==================== 4 files ====================
  file_1 = ['node_results'];
  filename_1 = [file_1, '.tmp'];
  fid_1= fopen(filename_1, 'r') ;

%    load the file array for this result
  Result_1 = fscanf (fid_1, '%g  \n', [inf]) ;
  NP = size (Result_1, 1) ;
  if ( NP == 0 )
    error ('Error missing file ', file_1, '.tmp')
  end % if error
  if ( NP ~= np )
    fprintf ('Read %g nodal dof  \n', NP)
    ng = NP / np ;
    fprintf ('with %g per node \n', ng )
  end % if
  max_p = ng ; 
  if ( i_p > max_p ) 
    error ('i_p > available data')
  end % if error
  Result_1 = reshape (Result_1, ng, np) ;
  Result_1 = Result_1' ;

% ==================== end 4 files ====================
  H (2)       = 0. ;
  HC1 (4)     = 0. ;
  DHC1 (4)     = 0. ;
  x (np)      = 0.       ;       % pre-allocate array x
  
  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

  y_1  = Result_1(:, 1) ; % nodal disp
  R1x  = max(y_1) ; R1n  = min(y_1);
  dy_1 = Result_1(:, 2) ; % nodal slope
  R2x  = max(dy_1) ; R2n  = min(dy_1);
  [norm, at] = max ( abs (y_1) );
  if ( norm == 0 )
    error ('Null displacement, nothing to plot')
  end % if
  %b norm = y_1 (at) ;
  %b y_1 = y_1 / norm ;
  %b dy_1 = dy_1 / norm ;
  if ( i_p == 1 )
    y = y_1 ;
  else
    y = dy_1 ;
  end % if

%    Initialize plots
  xmax = max (x)      ; xmin = min (x) ;
  y_1X = max (y)    ; y_1N = min (y) ;

  ymax = max (y_1X) ;                       
  ymin = min (y_1N) ;                       
      ymax = ymax + abs (ymax)/10. ;
      ymin = ymin - abs (ymin)/10. ;
  if ( ymin == ymax )
    disp(ymin)
    error('All values are the above constant')
  end % if
%b ymax=1.0
%b ymin=-2
  clf                               % clear graphics
  %b axis ([xmin, xmax, ymin, ymax])   % set axes
  hold on                           % hold image for plots
  xlabel ('X')                      % add label 

%    Loop over all elements
  el_min = ymin ; el_max = ymax ;
  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
      A = abs( t_x(2) - t_x(1)) ; % element length
      t_y  = y_1 (t_nodes) ;         % y at those nodes, only
      t_dy  = dy_1 (t_nodes) ;         % dy at those nodes, only
      D (1:2:4) = t_y ;
      D (2:2:4) = t_dy ;

%      Loop over local points on the cubic 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,+1    1------------2
        H (1) = 0.5*(1 - X) ;
        H (2) = 0.5*(1 + X) ;
        x_el (k) = H * t_x ;  % true X value
        HC1(1) = (2 - 3*X + X^3)/4;        
        HC1(2) = (1 - X - X^2 + X^3)*A/8;
        HC1(3) = (2 + 3*X - X^3)/4;    
        HC1(4) = (-1 - X + X^2 + X^3)*A/8;
        y_el (k) = HC1 * D' ;  % tXue y value
        DHC1(1) = (-3 + 3*X*X) * 0.5 / A;
        DHC1(2) = (-1 - 2*X + 3*X*X) * 0.25 ;
        DHC1(3) = ( 3 - 3*X*X) * 0.5d0 / A;
        DHC1(4) = (-1 + 2*X + 3*X*X) * 0.25;
        dy_el (k) = DHC1 * D' ;  % true y value
      end % for k

      format short
      plot (x, y, 'ko') % nodal value symbols
      if ( i_p == 1 )
        plot (x_el, y_el)   % interpolated values
        max_el = max (y_el) ;
        min_el = min (y_el) ;
      elseif ( i_p == 2 )
        plot (x_el, dy_el)   % interpolated values
        max_el = max (dy_el) ;
        min_el = min (dy_el) ;
      end % if
      if ( max_el > el_max )
        el_max = max_el ;
      end % if
      if ( min_el < el_min )
        el_min = min_el ;
      end % if
    end % if has non-zero nodes
  end % for all elements
  %b if ( el_max > ymax )
    fprintf ('Max interior value was %g \n', el_max)
    ymax = el_max ;
  %b end % if
  %b if ( el_min < ymin )
    ymin = el_min ;
    fprintf ('Min interior value was %g \n', el_min)
  %b end % if
  axis ([xmin, xmax, ymin, ymax])   % set axes

  if ( i_p == 1 )
    ylabel (['Beam Displacement (nodal max = ', ...
              num2str(R1x), ', min = ', num2str(R1n), ')'])
    title(['Displacement: ', int2str(nt),' Elements, ', ...
           int2str(np), ' Nodes, (', int2str(nod_per_el), ...
           ' per Element)'])
  elseif ( i_p == 2 )
    ylabel (['Beam Slope  (nodal max = ', ...
              num2str(R2x), ', min = ', num2str(R2n), ')'])
    title(['Slope: ', int2str(nt),' Elements, ', ...
           int2str(np), ' Nodes, (', int2str(nod_per_el), ...
           ' per Element)'])
  end % if
  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'] ;
  end % if
  fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
  hold off 
% end of beam_C1_L2_defl