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function [newnode, newelem] = barydualmesh(node, elem, flag)
%
% [newnode,newelem]=barydualmesh(node,elem)
%
% generate barycentric dual-mesh by connecting edge, face and elem centers
%
% author: Qianqian Fang, <q.fang at neu.edu>
%
% input:
% node: list of input mesh nodes
% elem: list of input mesh elements (each row are indices of nodes of each element)
% flag: if is 'cell', output newelem as cell arrays (each has 1x4 nodes)
%
% output:
% newnode: all new nodes in the barycentric dual-mesh (made of edge/face/elem centers)
% newelem: the indices of the face nodes for each original tet element
%
% example:
% [node,elem]=meshgrid6([0 60],[0 60],[0 60]);
% [newnode,newelem]=barydualmesh(node,elem,'cell');
% plotmesh(newnode,newelem);
% hold on; plotmesh(node,[],elem,'facecolor','none','edgecolor','b')
%
% -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
%
[enodes, eidx] = highordertet(node, elem); % compute edge-centers
[fnodes, fidx] = elemfacecenter(node, elem); % compute face-centers
c0 = meshcentroid(node, elem(:, 1:min(size(elem, 2), 4))); % compute elem-centers
% concatenated new nodes and their indices
newnode = [enodes; fnodes; c0];
newidx = [eidx, fidx + size(enodes, 1), (1:size(elem, 1))' + (size(enodes, 1) + size(fnodes, 1))];
newelem = [
1 8 11 7
2 7 11 9
3 9 11 8
4 7 11 10
5 8 11 10
6 9 11 10
];
newelem = newelem';
newelem = newidx(:, newelem(:));
newelem = reshape(newelem, [size(elem, 1) 4 6]);
newelem = permute(newelem, [1 3 2]);
newelem = reshape(newelem, [size(elem, 1) * 6 4]);
if (nargin > 2 && ischar(flag) && strcmp(flag, 'cell'))
newelem = num2cell(newelem, 2);
end
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