- if we move by r * -(v dot r) we will have a point on the wall (similar to the projection of the reflected point on the wall);
- if we do it again, we have the reflected point.
I guess I'm still kinda confused about this aspect of what you said. I'm happy to accept that this is true, but I'm confused as to why
this is true. Maybe this is more of a general question that requires some additional maths educatio on my part?