After playing a little with Excel.

http://www.mediafire.com/file/w9va4mud8rv0ex1/Lissajous 03.xls

 

I think you should add phase shift and amplitude to the equation. Also, why are there two different inputs for frequency of each channel, each one with different and misleading name, when one is enough?

 

To avoid being misled by the names you could call them Horace and Susanne or just "coarse" and "fine".

I do not know if I should add phase and amplitude... but certainly I could.

Thanks for taking the time to comment.