faceneighbors

 facenb=faceneighbors(t,opt)

 to find 4 face-neighboring elements of a tetrahedron

 author: Qianqian Fang, <q.fang at neu.edu>

 input:
     t: tetrahedron element list, 4 columns of integers
     opt: if opt='surface', return boundary triangle list 
          (should be the same as the face output from v2m)
          if opt='rowmajor', same as 'surface', except the 
          order of the triangles are in the row-major order
%
          otherwise, return the element list for each element:
          each row contains 4 numbers, representing the element
          indices sharing triangular faces [1 2 3],[1 2 4],[1 3 4]
          and [2 3 4] in order, where 1~4 is the node local index.
          if the index is 0, indicating the face has no neighbor
          (i.e. a boundary face)

 output:
     facenb: see opt

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

0001 function facenb=faceneighbors(t,opt)
0002 %
0003 % facenb=faceneighbors(t,opt)
0004 %
0005 % to find 4 face-neighboring elements of a tetrahedron
0006 %
0007 % author: Qianqian Fang, <q.fang at neu.edu>
0008 %
0009 % input:
0010 %     t: tetrahedron element list, 4 columns of integers
0011 %     opt: if opt='surface', return boundary triangle list
0012 %          (should be the same as the face output from v2m)
0013 %          if opt='rowmajor', same as 'surface', except the
0014 %          order of the triangles are in the row-major order
0015 %%
0016 %          otherwise, return the element list for each element:
0017 %          each row contains 4 numbers, representing the element
0018 %          indices sharing triangular faces [1 2 3],[1 2 4],[1 3 4]
0019 %          and [2 3 4] in order, where 1~4 is the node local index.
0020 %          if the index is 0, indicating the face has no neighbor
0021 %          (i.e. a boundary face)
0022 %
0023 % output:
0024 %     facenb: see opt
0025 %
0026 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0027 %
0028 
0029 faces=[t(:,[1,2,3]);
0030        t(:,[1,2,4]);
0031        t(:,[1,3,4]);
0032        t(:,[2,3,4])];
0033 
0034 faces=sort(faces,2);
0035 [foo,ix,jx]=unique(faces,'rows');
0036 if(isoctavemesh)
0037         u=unique(jx);
0038         qx=u(hist(jx,u)==2);
0039 else
0040         vec=histc(jx,1:max(jx));
0041         qx=find(vec==2);
0042 end
0043 
0044 nn=max(t(:));
0045 ne=size(t,1);
0046 facenb=zeros(size(t));
0047 
0048 % now I need to find all repeatitive elements
0049 % that share a face, to do this, unique('first')
0050 % will give me the 1st element, and 'last' will
0051 % give me the second. There will be no more than 2
0052 
0053 % doing this is 60 times faster than doing find(jx==qx(i))
0054 % inside a loop
0055 
0056 if(isoctavemesh || datenum(version('-date'))>datenum('January 27 2006')) % compare to matlab 7.2
0057     [ujx,ii]=unique(jx,'first');
0058     [ujx,ii2]=unique(jx,'last');
0059 else
0060     ujx=unique(jx);
0061     [t1,ii2]=ismember(ujx,jx);
0062     [t1,ii]=ismember(ujx,flipwd(jx(:)));
0063     ii=length(jx)-ii+1;
0064 end
0065 
0066 % iddup is the list of all pairs that share a common face
0067 
0068 iddup=[ii(qx) ii2(qx)];
0069 faceid=ceil(iddup/ne);
0070 eid=mod(iddup,ne);
0071 eid(eid==0)=ne;
0072 
0073 % now rearrange this list into an element format
0074 
0075 for i=1:length(qx)
0076     facenb(eid(i,1),faceid(i,1))=eid(i,2);
0077     facenb(eid(i,2),faceid(i,2))=eid(i,1);
0078 end
0079 
0080 % facenb may contain 0s, that just means the corresponding
0081 % face is a boundary face and has no neighbor.
0082 
0083 % if the second option is 'surface', I am going to find
0084 % and return surface patches only
0085 
0086 if(nargin==2)
0087   if(strcmp(opt,'surface'))
0088     facenb=faces(find(facenb==0),:);
0089   elseif(strcmp(opt,'rowmajor'))
0090     index=[1:length(faces)];
0091     index=(reshape(index,[],4))';
0092     faces=faces(index(:),:);
0093     facenb=faces(find(facenb'==0),:);
0094   else
0095         error(['supplied option "' opt '" is not supported.']);
0096   end
0097 end