Going outside the box / wrapping the view around

[VoS]

Have a little problem of theory...
I have a game in which the user sees a top down view of their player
When the player reaches the end of the world they get moved to the other side of the world so they can never really fall off or reach an edge.

my problem is that when the user reaches the end of the world a big part of the game window is showing areas outside of the playing field, areas which i really want it to be rendering from the other side of the map so the user never really knows when they are at the edge. Im afraid im not that good at explaining so i tried drawing a picture of it..


The red part is the view outside the map area, the red area should really be showing what is in the green area, even though this is on the other side of the map.

So, has anyone dealt with it or how can I go about fixing it?
At the moment im kind of stumped as to how i could do it at all.

I mean i could check every entity in my entity list and see if they are within the view on the other side but that seems terribly inefficient.

Thanks for the help / ideas..