function [V,E,C,bdry_cells]=vertex_edges_cells(center_positions,DPLAY)
%[V,E,C,bdry_cells]=vertex_edges_cells(center_positions);
%P - Output of function centers_list.m
%V - Two column list of positions of vertices comprising cellular network
%E - Two column list of vertices that form the interior edges of the
%cellular network.
%C - Cell array, indicating vertrices bounding individual cells, listed to
%correspond to the Numeric label in 'P'
%bdry_cells - Labels of cells in 'C' (and 'P'), that have vertices at the
%boundaries. Edges of these cells are not reliable physical
%representations.
%
%Display results if DPLAY='ON';
%
%For bugs, comments, etc. please contact Kapil Krishan :
%kkrishan@uci.edu
%www.physics.uci.edu/~foams
%version: I


%Using the x,y coordinates of each cell center to extract the Voronoi
%diagram vertices, and cell centers
x=center_positions(:,1);y=center_positions(:,2);
[V,C] = voronoin([x y]);

%'bdry_cells' indicates the cells whose vertices lie outside the boundary
bdry_vtxs=unique([find(V(:,1)>max(x));find(V(:,1)<min(x));...
    find(V(:,2)>max(y));find(V(:,2)<min(y))]);
bdry_cells=[];
for cell_no=1:size(C,1)
    cell_vtxs=C{cell_no};
    if prod(size(intersect(cell_vtxs,bdry_vtxs)))>0
        bdry_cells=[bdry_cells;cell_no];
    end
end

ct=0;%counter
for ic=setdiff([1:size(C,1)],bdry_cells')%'ic' enumerates interior cells
    ct=ct+1;
    C_interior{ct}=C{ic};
end
C_interior=C_interior';%'C_interior' is a cell array comprising only of interior cells

E=[0 0];%dummy initialization, gotten rid off in 5 lines.
for ic=1:size(C_interior,1)
    vtxs=C_interior{ic};%Vertices of the 'ic'th interior cell
    E=[E;setdiff(sort([vtxs;[vtxs(2:end) vtxs(1)]])',E,'rows')];%unique list of edges of cells thus far.
end
E(1,:)=[];%complete list of non-boundary edges.

%DISPLAY RESULTS ONLY
%All the following lines display the primary results of the program. They may
%be commented out.

if strcmp(DPLAY,'ON')==1
    hold on;
    for ic=1:size(E,1)
        line([V(E(ic,1),1) V(E(ic,2),1)],[V(E(ic,1),2) V(E(ic,2),2)],'color',[0 0 0]);
        title('Voronoi construction')
    end;drawnow;
end