%   this is a demo for cylindrical coordinates
% 
 
o = [0,0,0];   % origin will be shifted otherwise we won't see the arrows inside our ellipsoid

 arrow3(o, [1,0,0],'yellow');
 arrow3(o, [0,1,0],'yellow');
 arrow3(o, [0,0,1],'magenta');    % this plots the i,j,k, vectors
 
 zmin = 0;
 zmax = 4;       % plotting window
 
 
 % in fact, even to plot the cylinder, we need to use these  
 dtheta = pi/48;  
 r = 2;
 t = 0:dtheta:2*pi;
 
 [theta,Z] = meshgrid(t, zmin:0.2:zmax); 
   X = r*cos(theta);
   Y = r*sin(theta);
   Z = X*0 + theta;
          surf(X,Y,Z,'FaceColor',[0.8 1 0.8]);        % surface plotting
 
     % now plot the 3d spiral
   
     t = 0:0.2:8;
     theta = t;
     
   x = r*cos(theta);
   y = r*sin(theta);
   z = t/2; 
   
     hold on
     plot3(x,y,z,...
                'LineWidth',2);
     hold off