Ray tracing (?) a shape from a plane to a curved surface

Hello board,

Glad to be a part of the community.

After searching the boards and online, I haven't been able to find exactly how to accomplish projecting through a shape located on a plane to a curved surface.  A sample of what I am trying to do is attached.  Ideally, I would like to know what the shape would be on the curved surface (revolve) if a light were shone through the splined extrude on the plane located a distance from it. Using project curves this could be accomplished (from what I gather) but only with paralell rays. I would like to see the angled rays and be able to adjust the extruded length of the shape in order to be able to adjust the corresponding shape on the surface. I hope this explanation is clear.

Any help would be greatly appreciated.

Thanks,

Trevor

SolidworksSurfacing