meshremap.m

function newval = meshremap(fromval, elemid, elembary, toelem, nodeto)
%
% newval=meshremap(fromval,elemid,elembary,toelem,nodeto)
%
% Redistribute nodal values from the source mesh to the target mesh so that
% the sum of each property on each mesh is the same
%
% 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 target mesh element that encloses the nodes of
%            the source mesh nodes; a vector of length of src mesh node
%            count; elemid and elembary can be generated by calling
%
%           [elemid,elembary]=tsearchn(node_target, elem_target, node_src);
%
%           note that the mapping here is inverse to that in meshinterp()
%
%    elembary: the bary-centric coordinates of each source mesh nodes
%            within the target mesh elements, sum of each row is 1, expect
%            3 or 4 columns (or can be N-D)
%    toelem: the element list of the target mesh
%    nodeto: the total number of target mesh nodes
%
%
% 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); % src mesh
%    [n2,f2,e2]=meshabox([0 0 0],[10 20 5],2); % target mesh
%    [id, ww]=tsearchn(n2,e2,n1);              % project src to target mesh
%    value_src=n1(:,[2 3 1]);             % create dummy values at src mesh
%    newval=meshremap(value_src,id,ww,e2,size(n2,1)); % map to target
%
% -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
%

if (size(fromval, 1) == 1)
    fromval = fromval(:);
end

if (size(fromval, 2) == length(elemid))
    fromval = fromval.';
end

newval = zeros(nodeto, size(fromval, 2));

idx = ~isnan(elemid);
fromval = fromval(idx, :);
elembary = elembary(idx, :);
idx = elemid(idx);

nodeval = repmat(fromval, [1, 1, size(elembary, 2)]) .* repmat(permute(elembary, [1, 3, 2]), [1, size(fromval, 2), 1]);

for i = 1:size(elembary, 2)
    [ix, iy] = meshgrid(toelem(idx, i), 1:size(fromval, 2));
    nval = nodeval(:, :, i).';
    newval = newval + accumarray([ix(:), iy(:)], nval(:), size(newval));
end