%% Helix

%%
% Here is a way to plot a helix on a cylinder.  
% It will use a parametric description of the cylinder.  The cylinder is a 
% right circular cylinder of radius 1 centered on the z-axis.  It is the
% set of all points of the form
%%
% 
% $$(\cos(U),\sin(U),V),\qquad 0 \le U \le 2\pi,\quad \mbox{--}\infty < V < \infty. $$
% 
% I'll limit the graph to 
%%
% 
% $$ 0 \le V \le 6\pi.$$
%
% I begin by making a 50x50 mesh of the points [U,V] I'll use in the graph.

u=linspace(0,2*pi,50); v=linspace(0,6*pi,50);
[U,V]=meshgrid(u,v);

%%
% To be able to get a thick curve for the helix, I use the *plot3*
% command. I plot the helix as a very thick curve and use the command 
% *surf* to plot the cylinder.   
% The command *colormap white* prevents shading of the cylinder. 

t=linspace(0,6*pi,300);
plot3(cos(t),sin(t),t,'LineWidth',3), hold on
title('Helix on a cylinder')
surf(cos(U),sin(U),V), colormap white, hold off