% given N points and a triangulation of these points
% draw the inscribed circles 
function plot_central_regions2(x,y,tri,radii)
   N=size(tri,1);
   for n=1:N
       % compute the vetices
       a=x(tri(n,1))+i*y(tri(n,1));
       b=x(tri(n,2))+i*y(tri(n,2));
       c=x(tri(n,3))+i*y(tri(n,3));

       % draw circular arc connecting tangent points
       plot_prop_arc(a,b,c,radii(n,1));
       plot_prop_arc(b,a,c,radii(n,2));
       plot_prop_arc(c,a,b,radii(n,3));

       % fill in region between these arcs
       plot_prop_arc_fill(a,b,c,radii(n,1),radii(n,2),radii(n,3));

       % draw the  central half-disks
       if 0==0
          z1=a+radii(n,1)*(b-a)/abs(b-a);
          z2=b+radii(n,2)*(a-b)/abs(b-a);
          z=(z1+z2)/2;
          arc1=z+abs((z2-z1)/2)*sign(imag(log((c-a)/(b-a))))*...
              ((b-a)/abs(b-a))*exp(pi*i*[0:.02:1]);
          plot(real(arc1),imag(arc1),'b');

          z1=b+radii(n,2)*(c-b)/abs(c-b);
          z2=c+radii(n,3)*(b-c)/abs(c-b);
          z=(z1+z2)/2;
          arc2=z+abs((z2-z1)/2)*sign(imag(log((a-b)/(c-b))))*...
              ((c-b)/abs(c-b))*exp(pi*i*[0:.02:1]);
          plot(real(arc2),imag(arc2),'b');

          z1=c+radii(n,3)*(a-c)/abs(a-c);
          z2=a+radii(n,1)*(c-a)/abs(a-c);
          z=(z1+z2)/2;
          arc3=z+abs((z2-z1)/2)*sign(imag(log((b-c)/(a-c))))*...
              ((a-c)/abs(a-c))*exp(pi*i*[0:.02:1]);
          plot(real(arc3),imag(arc3),'b');
       end % if 

   end % for n
return
