Beam direction algorithm

Question

Suppose we are given with a system of mirrors. We also have a beam emitter and a beam receiver. Then we must find the direction in which the emitter should emit so that the beam reaches the receiver along the shortest path. How can this be effectively implemented?

An image is just a sketch, for example.

Answer 1

A simplified algorithm for a rectangular grid will work by calculating the virtual position of the receiver in the next grid - just as if you were playing a pool and wanted to make a stunning shot at the bank.

     +---------+----------+---------+----------+
     | O                  |                    |
     |===>                |                <===|
     |     Real           |    Virtual copy    |
     |                    |                    |
     A---------+----------+---------+----------a

O A, "a". () , . - / a (n), .