tri2pts.m

function [uxy,tn,a12,a13] = tri2pts( p, t, u, tn, a12, a13 )
% TRI2PTS - interpolate a scalar field defined on a triangular grid at some
% points not necessarily on a grid.
%
% Usage: [uxy,tn,a12,a13] = tri2pts( p, t, u, x, y )
%        uxy = tri2pts( p, t, u, tn, a12, a13 )
%
% Arguments and functioning are similar to tri2grid except that x and y
% need not define a grid.  x and y should be matrices of the same size.
%
% p and t should define a triangular grid as generated by initmesh, pdetool,
% etc. u is a scalar field defined on that grid.  u can also be a matrix
% with multiple columns, in which case, each column is a scalar field.
%
% If x is a vector, uxy will have interesting dimensions of PxN, where p
% is the length of x and N is the number of columns in u.  If x is a
% matrix, then uxy will have dimensions of P1xP2...xN, where Pi are the
% dimensions of x.
%
% Note that pdeintrp_arbitrary now basically depends on this function for
% interpolating scalars.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 	$Id: tri2pts.m 70 2007-02-22 02:24:34Z dmk $	
%
% Copyright (C) 2005 David M. Kaplan
% Licence: GPL (Gnu Public License)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Make a column vector if given a row vector.  Leave alone otherwise.
if prod(size(u)) == max(size(u))
  u = u(:);
end

if nargin == 5
  % Need to find enclosing triangles.
  x = tn;
  y = a12;

  [tn,a12,a13] = tsearch_arbitrary( p, t, x, y );
end

s = size(tn);
tn = tn(:);
a12 = a12(:);
a13 = a13(:);

ii = find( ~isnan(tn) );
uxy = repmat( NaN, [ length(tn), size(u,2) ] );

% Get interpolation.
oo = ones( 1, size(u,2) );
uxy(ii,:) = ( 1 - a12(ii,oo) - a13(ii,oo) ) .* u(t(1,tn(ii)),:) + ...
	  a12(ii,oo) .* u(t(2,tn(ii)),:) + ...
	  a13(ii,oo) .* u(t(3,tn(ii)),:);

% Reshape appropriately
ss = s;
if ss(end)==1, ss = ss(1:end-1); end
uxy = reshape( uxy, [ ss, size(u,2) ] );

if nargout > 1
  tn = reshape(tn,s);
  a12 = reshape(a12(:,1),s);
  a13 = reshape(a13(:,1),s);
else
  clear tn a12 13
end