edgeneighbors

 edgenb=edgeneighbors(t,opt)

 to find neighboring triangular elements in a triangule surface

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

 input:
     t: a triangular surface element list, 3 columns of integers
     opt: if opt='general', return the edge neighbors for a general
          triangular surface: each edge can be shared by more than 2
          triangles; if ignored, we assume all triangles are shared by no
          more than 2 triangles.

 output:
     edgenb: if opt is not supplied, edgenb is a size(t,1) by 3 array with
     each element being the triangle ID of the edge neighbor of that
     triangle. For each row, the order of the neighbors is listed as those
     sharing edges [1 2], [2 3] and [3 1] between the triangle nodes.

     when opt='general', edgenb is a cell array with a length of size(t).
     each member of the cell array is a list of edge neighbors (the order 
     is not defined).

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

0001 function edgenb=edgeneighbors(t,opt)
0002 %
0003 % edgenb=edgeneighbors(t,opt)
0004 %
0005 % to find neighboring triangular elements in a triangule surface
0006 %
0007 % author: Qianqian Fang, <q.fang at neu.edu>
0008 %
0009 % input:
0010 %     t: a triangular surface element list, 3 columns of integers
0011 %     opt: if opt='general', return the edge neighbors for a general
0012 %          triangular surface: each edge can be shared by more than 2
0013 %          triangles; if ignored, we assume all triangles are shared by no
0014 %          more than 2 triangles.
0015 %
0016 % output:
0017 %     edgenb: if opt is not supplied, edgenb is a size(t,1) by 3 array with
0018 %     each element being the triangle ID of the edge neighbor of that
0019 %     triangle. For each row, the order of the neighbors is listed as those
0020 %     sharing edges [1 2], [2 3] and [3 1] between the triangle nodes.
0021 %
0022 %     when opt='general', edgenb is a cell array with a length of size(t).
0023 %     each member of the cell array is a list of edge neighbors (the order
0024 %     is not defined).
0025 %
0026 % -- this function is part of iso2mesh toolbox (http://iso2mesh.sf.net)
0027 %
0028 
0029 edges=[t(:,[1,2]);
0030        t(:,[2,3]);
0031        t(:,[3 1])];
0032 edges=sort(edges,2);
0033 [foo,ix,jx]=unique(edges,'rows');
0034 
0035 if(nargin==2)
0036   if(strcmp(opt,'general'))
0037         ne=size(t,1);
0038         edgenb=cell(ne,1);
0039         for i=1:ne
0040             % this is very slow, need to be optimized
0041             nb=unique(mod([find(jx==jx(i) | jx==jx(i+ne) | jx==jx(i+2*ne))]',ne),'first');
0042             nb(nb==0)=ne;
0043             edgenb{i}=nb(nb~=i);
0044         end
0045         return;
0046   else
0047         error(['supplied option "' opt '" is not supported.']);
0048   end
0049 end
0050 
0051 if(isoctavemesh)
0052         u=unique(jx);
0053         qx=u(hist(jx,u)==2);
0054 else
0055         vec=histc(jx,1:max(jx));
0056         qx=find(vec==2);
0057 end
0058 
0059 nn=max(t(:));
0060 ne=size(t,1);
0061 edgenb=zeros(size(t));
0062 
0063 % now I need to find all repeatitive elements
0064 % that share a face, to do this, unique('first')
0065 % will give me the 1st element, and 'last' will
0066 % give me the second. There will be no more than 2
0067 
0068 % doing this is 60 times faster than doing find(jx==qx(i))
0069 % inside a loop
0070 
0071 [ujx,ii]=unique(jx,'first');
0072 [ujx,ii2]=unique(jx,'last');
0073 
0074 % iddup is the list of all pairs that share a common face
0075 
0076 iddup=[ii(qx) ii2(qx)];
0077 faceid=ceil(iddup/ne);
0078 eid=mod(iddup,ne);
0079 eid(eid==0)=ne;
0080 
0081 % now rearrange this list into an element format
0082 
0083 for i=1:length(qx)
0084     edgenb(eid(i,1),faceid(i,1))=eid(i,2);
0085     edgenb(eid(i,2),faceid(i,2))=eid(i,1);
0086 end
0087 
0088 % edgenb may contain 0s, that just means the corresponding
0089 % face is a boundary face and has no neighbor.
0090 
0091 % if the second option is 'surface', I am going to find
0092 % and return surface patches only
0093 
0094