function sol = ann(V,gb)  %gb = graph bounds 
ms = 20;   % this is the 'MarkerSize' for the crystals

     t= V(1);
     M=zeros(12,3);
     for i=1:13,
	     start = 3*(i-1) + 2;
	     M(i,1:3) = V(start:start+2);
     end

     p3 = M(:,1);
     p2 = M(:,2);
     p1 = M(:,3);

% Spline curve for annulus
B = [ ...
4 1 0 0 0 1
1 4 1 0 0 0
0 1 4 1 0 0
0 0 1 4 1 0
0 0 0 1 4 1
  1 0 0 0 1 4];

x = [p1(4) p1(5) p1(6) p1(7) p1(8) p1(9)]';
y = [p2(4) p2(5) p2(6) p2(7) p2(8) p2(9)]';
z = [p3(4) p3(5) p3(6) p3(7) p3(8) p3(9)]';

bx = 3*[x(2)-x(6) x(3)-x(1) x(4)-x(2) x(5)-x(3) x(6)-x(4) x(1)-x(5)]';
by = 3*[y(2)-y(6) y(3)-y(1) y(4)-y(2) y(5)-y(3) y(6)-y(4) y(1)-y(5)]';
bz = 3*[z(2)-z(6) z(3)-z(1) z(4)-z(2) z(5)-z(3) z(6)-z(4) z(1)-z(5)]';

invB = inv(B);
     
Dx = invB*(bx) ;
Dy = invB*(by);
Dz = invB*(bz);

     xmatrix = coeffmatrix(x,Dx);
     ymatrix = coeffmatrix(y,Dy);
     zmatrix = coeffmatrix(z,Dy);

for i=1:6
     xval(i,:) = xmatrix(i,:);
     yval(i,:) = ymatrix(i,:);
     zval(i,:) = zmatrix(i,:);
end
     
     t = 0:.1:1;
    
for i = 1:6
     fx(i,:) = polyval(xval(i,:),t);
     fy(i,:) = polyval(yval(i,:),t);
     fz(i,:) = polyval(zval(i,:),t);
end


% plot crystals and color appropriately
% plot connecting lines
% plot spline curve for annulus

subplot(1,2,1);
plot3(p1(1:2),p2(1:2),p3(1:2),'g.', ...         % pap crystals
      p1(3),p2(3),p3(3),'c.', ...               % alv crystal
      p1(4:9),p2(4:9),p3(4:9),'r.', ...      % annulus crystals
      p1(13),p2(13),p3(13),'c.', ...            % mid ant leaflet crystal
      p1(10),p2(10),p3(10),'b.', ...            % anterior leaf tip 
      p1(11),p2(11),p3(11),'g.', ...            % posterior leaf tip
      p1(12),p2(12),p3(12),'r.', ...            % apex crystal
      [p1(1) p1(2) p1(3) p1(1)], ...            % pap and alv lines
      [p2(1) p2(2) p2(3) p2(1)], ...
      [p3(1) p3(2) p3(3) p3(1)],'c-', ...
      [p1(10) p1(13) p1(7)], ...                % ant leaf lines
      [p2(10) p2(13) p2(7)], ...
      [p3(10) p3(13) p3(7)],'b-', ...
      [p1(11),p1(4)], ...                       % post leaf lines
      [p2(11),p2(4)], ...
      [p3(11),p3(4)],'g-', ...
      fx',fy',fz','r-', ...                     % annulus spline
      'MarkerSize',ms);
       grid on
       axis equal
       xlabel('x')
       ylabel('y')
       zlabel('z')
       title('13 crystals')
       axis(gb)

subplot(1,2,2);
plot(fx',fy','r-', ... 
     p1(4:9),p2(4:9),'r.','MarkerSize',ms);
grid on 
axis equal
xlabel('x')
ylabel('y')
title('annulus top view')
axis([gb(1) gb(2) gb(3) gb(4)])