I'm trying to understand how to construct the reflection path of a ray from a curved surface. Here's the basic setup:
In a 2D space, assume a point S is the source of a ray and point R is the receiver. An arbitrary convex line is located in space and acts as a perfect reflector for incoming rays. How can I construct the reflection path (should it exist) between S and R?
If the reflector was a straight line, I'd would use the image-source-method and be done with it. If the reflector was a circle, I'd resort to something along the line discussed here.
But how can the problem be solved if the reflector is an arbitrary line? For simplicity we might assume that the curvature always remains positive, so the line is strictly convex. This would limit the number of possible solutions to exactly one.
Thanks for your input - any hint is greatly appreciated.