function newval=meshinterp(fromval,elemid,elembary,fromelem)
%
% newval=meshinterp(fromval,elemid,elembary,fromelem)
%
% Interpolate nodal values from the source mesh to the target mesh based on
% a linear interpolation
%
% author: Qianqian Fang (q.fang at neu.edu)
%
% input:
% fromval: values defined at the source mesh nodes, the row or column
% number must be the same as the source mesh node number, which
% is the same as the elemid length
% elemid: the IDs of the source mesh element that encloses the nodes of
% the target mesh nodes; a vector of length of target mesh node
% count; elemid and elembary can be generated by calling
%
% [elemid,elembary]=tsearchn(node_src, elem_src, node_target);
%
% note that the mapping here is inverse to that in meshremap()
%
% elembary: the bary-centric coordinates of each target mesh nodes
% within the source mesh elements, sum of each row is 1, expect
% 3 or 4 columns (or can be N-D)
% fromelem: the element list of the source mesh
%
%
% output:
% newval: a 2D array with rows equal to the target mesh nodes (nodeto),
% and columns equals to the value numbers defined at each source
% mesh node
% example:
%
% [n1,f1,e1]=meshabox([0 0 0],[10 20 5],1); % target mesh
% [n2,f2,e2]=meshabox([0 0 0],[10 20 5],2); % src mesh
% [id, ww]=tsearchn(n2,e2,n1); % project target to src mesh
% value_src=n2(:,[2 1 3]); % create dummy values at src mesh
% newval=meshinterp(value_src,id, ww, e2);
%
% -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
%
if(size(fromval,1)==1)
fromval=fromval(:);
end
idx=find(~isnan(elemid));
allval=reshape(fromval(fromelem(elemid(idx),:),:),length(idx),size(elembary,2),size(fromval,2));
tmp=cellfun(@(x) sum(elembary(idx,:).*x,2), num2cell(allval,[1 2]),'UniformOutput',false);
newval=size(length(elemid),size(fromval,2));
newval(idx,:)=squeeze(cat(3,tmp{:}));
