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
