function zs=f(t,z)
global child_path_flag;
if(child_path_flag==1)
  [X,Xs,Y,Ys]=child1(t);
elseif(child_path_flag==2)
  [X,Xs,Y,Ys]=child2(t);
else
  [X,Xs,Y,Ys]=child3(t);
end
v=[Xs Ys]';
w=[X-z(1) Y-z(2)]';
w=w/norm(w);
zs=(v'*w)*w;