Projecting curves onto a cylinder

Hello,

I have encountered an unexpected outcome while using the project curve component. The attached definition shows a cylinder, divided to give straight diagonals connecting top to bottom.  These were then projected onto the outer surface of the cylinder. The vectors giving the direction of the projection all seem to be heading in the correct direction. The problem is that instead of the expected single projection of each curve onto the surface, there is a second projection opposite to this. I was hoping for some clarification on why this is happening with the hope of a simple solution. Further complexity comes when the number of curve divisions change. Things are a bit chaotic with 2 or 3 divisions but when 4 is reached, now all even numbered divisions give the same result. I hope this is not too confusing an explanation for what I hope to be a simple misunderstanding of how a component work. I know this is a strange definition since I am only sending the first part of a longer effort to make a cylindrical sawtooth.  I actually succeeded but the process was not pretty nor was it able to be usefully parametric due to the extra projections on the surface. 

thanks in advance.

robin