function  smooth_result (i_p)
% Copyright 2000 J.E. Akin. All rights reserved.
% plot finite element result as a surface for 1 <= i_p<= n_g_fre
% convert any type of mesh to a structured square mesh

% x,y   ==  nodal coordinates of the FEA
% f     ==  nodal solution of the FEA
% X,Y   ==  nodal coordinates of the structured square mesh
% F     ==  interpolated solution for the structured square mesh
% NX    ==  number of nodes in x-direction for structured mesh 
% NY    ==  number of nodes in y-direction for structured mesh

% clear
if ( nargin == 0 )
  i_p = 0 ;
end % if no arguments

load msh_bc_xyz.tmp;
pre_p = 1;
np = size (msh_bc_xyz, 1);
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

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 )
  error ('i_p > available data')
end % if error

% NX, NY = 31 are default values, these can be altered by user
NX = 31; NY = 31;

x = msh_bc_xyz (:, 2); y = msh_bc_xyz (:, 3);
 
if ( i_p >= 1 )
  f = node_results(:, i_p) ;
else % i_p = 0, get root mean sq
  for k = 1:np
    f (k) = sqrt ( sum (node_results (k, 1:max_p).^2)) ;
  end % for k
end % if get RMS value

%    Cite max, min values
[V_X, L_X] = max (f) ;
[V_N, L_N] = min (f) ;
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)

xlin = linspace (min(x), max(x), NX);
ylin = linspace (min(y), max(y), NY);
[X, Y] = meshgrid (xlin, ylin);
F = griddata (x, y, f, X, Y, 'cubic');

clf
% mesh  (X, Y, F)
% haxes=gca
haxes=mesh  (X, Y, F)
% set(haxes,'xcolor','k');
% set(haxes,'ycolor','k');
hold on
if ( i_p >= 1 )
  zlabel (['Component ', int2str(i_p), ' (max = ', ...
  num2str(V_X), ', min = ', num2str(V_N), ')'])
 %title(['Matlab Smoothed FEA Solution Component\_', int2str(i_p)]);
  title(['Matlab Smoothed FEA Solution Component\_', ...
         int2str(i_p),': at ', int2str(np),' Nodes']);
else % i_p = 0, get root mean sq
  zlabel (['RMS Value (max = ', ...
  num2str(V_X), ', min = ', num2str(V_N), ')'])
  title(['Matlab Smoothed FEA RMS Solution Value at ', ...
         int2str(np),' Nodes'])
  %title(['Matlab Smoothed FEA RMS Solution Value'])
end % if get RMS value
% xlabel ('X'); ylabel (['Y: ', int2str(np),' Nodes'])
xlabel ('X'); ylabel ('Y');

% label max min points 
  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]) ;
%       -depsc -tiff            % for an eps version
  % print ('-dpsc', ['smooth_result_', int2str(i_p)])
  % print ('-dps', ['smooth_result_', int2str(i_p)])
  hold off
  % v_text = ['Created smooth_result_', int2str(i_p), '.ps'] ;
  % fprintf (1,'%s', v_text) ; fprintf (1, ' \n' )
% end of smooth_result