meshquality

 quality=meshquality(node,elem)

 compute the Joe-Liu mesh quality measure of an N-D mesh (N<=3)

 author: Qianqian Fang, <q.fang at neu.edu>
 date: 2011/02/26

 input:
    node:  node coordinates of the mesh (nn x 3)
    elem:  element table of an N-D mesh (ne x (N+1))

 output:
    quality: a vector of the same length as size(elem,1), with 
           each element being the Joe-Liu mesh quality metric (0-1) of 
           the corresponding element. A value close to 1 represents
           higher mesh quality (1 means equilateral tetrahedron); 
           a value close to 0 means nearly degenerated element.

 reference:
    A. Liu, B. Joe, Relationship between tetrahedron shape measures, 
                    BIT 34 (2) (1994) 268-287.

 -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)

0001 function quality=meshquality(node,elem,maxnode)
0002 %
0003 % quality=meshquality(node,elem)
0004 %
0005 % compute the Joe-Liu mesh quality measure of an N-D mesh (N<=3)
0006 %
0007 % author: Qianqian Fang, <q.fang at neu.edu>
0008 % date: 2011/02/26
0009 %
0010 % input:
0011 %    node:  node coordinates of the mesh (nn x 3)
0012 %    elem:  element table of an N-D mesh (ne x (N+1))
0013 %
0014 % output:
0015 %    quality: a vector of the same length as size(elem,1), with
0016 %           each element being the Joe-Liu mesh quality metric (0-1) of
0017 %           the corresponding element. A value close to 1 represents
0018 %           higher mesh quality (1 means equilateral tetrahedron);
0019 %           a value close to 0 means nearly degenerated element.
0020 %
0021 % reference:
0022 %    A. Liu, B. Joe, Relationship between tetrahedron shape measures,
0023 %                    BIT 34 (2) (1994) 268-287.
0024 %
0025 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0026 %
0027 
0028 if(nargin<3)
0029     maxnode=4;
0030 end
0031 if(size(elem,2)>maxnode)
0032     elem=elem(:,1:maxnode);
0033 end
0034 enum=size(elem,1);
0035 vol=elemvolume(node,elem);
0036 edges=meshedge(elem);
0037 ed=node(edges(:,1),:)-node(edges(:,2),:);
0038 ed=sum((ed.*ed)');
0039 ed=sum(reshape(ed,[enum length(ed)/enum])')';
0040 dim=size(elem,2)-1;
0041 
0042 coeff=10/9; % for tetrahedral
0043 if(dim==2)
0044     coeff=1;
0045 end
0046 quality=coeff*dim*2^(2*(1-1./dim))*3^((dim-1)/2)*vol.^(2/dim)./ed;
0047 maxquality=max(quality);
0048 if(maxquality>1)
0049     quality=quality./maxquality;
0050 end