AppleTV Air Mirroring: does the signal go through the WIFI router? A general question about how AirMirroring works, because I've some freezing problems and I would like to know if connecting my Apple TV to the rough by ehternet cable could help.

N.B. I'm not watching online streamed movies, but just using Apple TV for Air Mirroring. The videos are stored on my macbook Air hard disk.

How does Air Mirroring works: is the streaming going from 
macbook ---> Apple TV, or
macbook ---> WIFI Modem ---> Apple TV ?

If the second is true, connecting Apple TV to WIFI Modem could help.. even if the content is not online streaming... ?
Two different AirPlay devices exist:


AirPlay transmitters (such as iPhone/iPad/iPod/iTunes)
AirPlay receivers (Apple TV, AirPort Express and audio system with built-in AirPlay)


Apple TV will connect to your WiFi modem to get Internet access.

It will also connect to your computer (without modem) for Airplay/mirroring.

It could also connect true the AirPort Express modem if you have it set up for that. Check what settings do you have in this article.