function [elems2edges, edges2nodes]=get_edges(elems2nodes)
%function: [element2edges, edge2nodes]=get_edges(elems2nodes)
%requires: deleterepeatedrows
%generates edges of (triangular) triangulation defined in elems2nodes
%elems2nodes is matrix, whose rows contain numbers of its element nodes 
%element2edges returns edges numbers of each triangular element
%edge2nodes returns two node numbers of each edge
%example in 2D: [element2edges, edge2nodes]=get_edges([1 2 3; 2 4 3])
%example in 3D: [element2edges, edge2nodes]=get_edges([1 2 3 4; 1 2 3 5; 1 2 4 6])
 % Liu minghong 20221026   
%2D case
if (size(elems2nodes,2)==3)
    %extracts sets of edges 
    edges1=elems2nodes(:,[2 3]);
    edges2=elems2nodes(:,[3 1]);
    edges3=elems2nodes(:,[1 2]);

    %as sets of their nodes (vertices)
    vertices=zeros(size(elems2nodes,1)*3,2);
    vertices(1:3:end,:)=edges1;
    vertices(2:3:end,:)=edges2;
    vertices(3:3:end,:)=edges3;

    %repeated sets of nodes (joint edges) are eliminated 
    [edges2nodes,elems2edges]=deleterepeatedrows(vertices);
    elems2edges=reshape(elems2edges,3,size(elems2nodes,1))';
end

%3D case
if (size(elems2nodes,2)==4)
    %extracts sets of edges 
    edges1=elems2nodes(:,[1 2]);
    edges2=elems2nodes(:,[1 3]);
    edges3=elems2nodes(:,[1 4]);
    edges4=elems2nodes(:,[2 3]);     
%     edges5=elems2nodes(:,[3 4]);
%     edges6=elems2nodes(:,[4 2]);
       % Liu minghong 20221026 
    edges5=elems2nodes(:,[4 2]);
    edges6=elems2nodes(:,[3 4]);
        
    %as sets of their nodes (vertices)
    vertices=zeros(size(elems2nodes,1)*6,2);
    vertices(1:6:end,:)=edges1;
    vertices(2:6:end,:)=edges2;
    vertices(3:6:end,:)=edges3;
    vertices(4:6:end,:)=edges4;
    vertices(5:6:end,:)=edges5;
    vertices(6:6:end,:)=edges6;
    
    %repeated sets of nodes (joint edges) are eliminated 
    [edges2nodes,elems2edges]=deleterepeatedrows(vertices);
    elems2edges=reshape(elems2edges,6,size(elems2nodes,1))';
    % *** 20221026
    edges2nodes=sort(edges2nodes,2);
    
end


function [matrix,I]=deleterepeatedrows(matrix)
%function: [element2edges, edge2nodes]=edge_numbering(elements)
%requires: deleterepeatedrows
%generates edges of (triangular) triangulation defined in elements
%elements is matrix, whose rows contain numbers of its element nodes 
%element2edges returns edges numbers of each triangular element
%edge2nodes returns two node numbers of each edge
%example: [element2edges, edge2nodes]=edge_numbering([1 2 3; 2 4 3])


%fast and short way suggested by John D'Ericco working in both 2D and 3D
matrixs=sort(matrix,2);
[dummy,J,I] = unique(matrixs,'rows');
%I=reshape(I,size(matrixs,2),size(I,1)/size(matrixs,2));
matrix=matrix(J,:);