[coordinates,elements3,dirichlet]=refinement_uniform(coordinates,elements3,dirichlet)

function [coordinates,elements3,dirichlet]=refinement_uniform(coordinates,elements3,dirichlet) 
%function: [coordinates,elements3,dirichlet]=refinement_uniform(coordinates,elements3,dirichlet) 
%requires: getEdges, symetrizeMatrix  
%uniform refinement of a 2D triangulation 

%uniform refinement   
[element2edges, edge2nodes]=getEdges(elements3);    
nodes2edge=sparse(edge2nodes(:,1),edge2nodes(:,2),1:size(edge2nodes,1),size(coordinates,1),size(coordinates,1));
nodes2edge=symetrizeMatrix(nodes2edge); 
    
%elements on of uniformly refined mesh
elements3_internal=element2edges+size(coordinates,1);
elements3_refin1= [elements3(:,1) elements3_internal(:,3) elements3_internal(:,2)];
elements3_refin2= [elements3(:,2) elements3_internal(:,1) elements3_internal(:,3)];
elements3_refin3= [elements3(:,3) elements3_internal(:,2) elements3_internal(:,1)];    
elements3=[elements3_internal; elements3_refin1; elements3_refin2; elements3_refin3];  

%dirichlet edges of uniformly refined mesh
dirichlet_edges=diag(nodes2edge(dirichlet(:,1),dirichlet(:,2)));
dirichlet=[dirichlet(:,1) dirichlet_edges+size(coordinates,1); dirichlet_edges+size(coordinates,1) dirichlet(:,2)];

%coordinates of uniformly refined mesh
coordinates_internal=(coordinates(edge2nodes(:,1),:)+coordinates(edge2nodes(:,2),:))/2;
coordinates=[coordinates; coordinates_internal];