function  true_L3_plot (x, y)      
%  ------------------------------------------------------
%  graph of value in 3 node quadratic line elements
%  ------------------------------------------------------
% n_p, n_e = Number of points and elements
% x, y   = Mesh coordinate and data values
% e_x, e_y   = coordinates & data values at 3 element nodes
% x_el, y_el = interpolated parametric values

% control data: number of nodes, elements & curve segments
 n_p=size(x, 1) ; n_e=(n_p-1)/2  ; 
 n_poly = 8 ;
 %b n_poly = 75/n_e
 %b n_poly = ceil (n_poly) ; 
 rows(3)=0 ; e_x(3)=0 ; e_y(3)=0 ; H(3)=0 ; % pre-allocation

%    Loop over all elements
  for it = 1:n_e  ;
    
%      Extract nodal coordinates & values. Plot nodes.
    rows = [1, 2, 3] + (it - 1)*2 ;   % get connectivity 
    e_x  = x (rows) ; e_y  = y (rows) ;
    plot (e_x, e_y, 'ko')             % nodal symbols
    e_text = sprintf ('   (%g)', it); % offset # from pt
    text (e_x(2), e_y(2), e_text)     % Plot element number

%     Loop over local points on the quadratic element
    for k = 1: (n_poly + 1) % points in parametric space
%     get parametric interpolation functions
      X    = 2*(k - 1)/n_poly - 1 ;   % on -1 to 1
      H(1) = 0.5*(X*X - X) ; H(2) = 1. - X*X ;
      H(3) = 0.5*(X*X + X) ;
      x_el (k) = H * e_x ; y_el (k) = H * e_y ; % true value
    end % for k parametric points in element
    plot (x_el, y_el) % parametric curve through 3 nodes

  end % for it over all elements
% end of true_L3_plot