Helix on a cylinder

Helix on a cylinder

I want to plot geodesics on a cylinder. These are straight lines, circles
or helices. I can plot the first two, but I don't know how to draw the
helices.
To be precise, I would like to know how to draw an helix on this cylinder
(passing thru two points A and B, but the location of the points is not
relevant), using TikZ exclusively (maybe with pgfplots, but without using
pstricks):
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}
\node [cylinder,rotate=90,draw,aspect=2,minimum width=2cm,minimum
height=3.5cm](C){};
\draw[fill] (-0.5,-0.5) circle [radius=0.045]node[below]{$A$};
\draw[fill] (0.5,0.75) circle [radius=0.045]node[below]{$B$};
\end{tikzpicture}
\end{document}