Nice! 
The lens model looks pretty close
In this paper http://www.cs.columbia.edu/techreports/cucs-004-01.pdf they use a reflecting surface of Sr (t)=(z(t) , g(t)) not sure if that is just a random shape they selected or some sort of ideal.

The lens model looks pretty close
In this paper http://www.cs.columbia.edu/techreports/cucs-004-01.pdf they use a reflecting surface of Sr (t)=(z(t) , g(t)) not sure if that is just a random shape they selected or some sort of ideal.
Comment