Start with a mirror, to see how this lining up and curling up plays out.

If you took out the paths near the end of the mirror, it wouldn't make so much difference, as the arrows contributed by the triplets of waypoints from those regions tend to curl up. But ignoring the contributions from nearer the centre does make a difference, so a rough and ready rule is that you'll only need to consider paths where the angle of incidence = the angle of reflection, which is comfortingly familiar.