%%  Example 2. Spiral tube.   Compare with the previous equation!
   %
   %   its equation is  r = <(2 +sin v)*cos u, (2+sinv) sin u, u + cos v>
 du = pi/48;  
 dv = pi/48;
 
 [u,v] = meshgrid(0:du:2*pi, 0:du:2*pi); 
   X = (2 + sin(v)).*cos(u);
   Y = (2 + sin(v)).*sin(u);
   Z = u + cos(v);
          surf(X,Y,Z,'FaceColor',[0.8 1 0.8]);        % surface plotting
  
  % now plot the traces
      u0 = pi;
  
   x = (2 + sin(v)).*cos(u0);
   y = (2 + sin(v)).*sin(u0);
   z = u0 + cos(v);
   
     hold on
     plot3(x,y,z,...
                'r','LineWidth',3);
    
     v0 = pi;         
     u1 = (0:du:2*pi)';
   x = (2 + sin(v0)).*cos(u1);
   y = (2 + sin(v0)).*sin(u1);
   z = u1 + cos(v0);
   
     plot3(x,y,z,...
                'b','LineWidth',3);      
   hold off