Checking for screen boundary

[IndyUK]

Hi All,
I'm a bit stumpped with how to check if my pixel plot routine hits the screen boundary.

A quick bit of background on what I'm doing. At present I am learning how to plot and move a pixel directly using the screen RAM. This part is all working - I use the arrow keys and the pixel moves around as expected. However, what I cannot work out is how to check if I go beyond the visible screen boundary in any of the 4 directions. I just cannot seem to find any logic that helps. I've examined all sorts of register conditions but still cannot find a reliable state which I can check for. I already know of one solution and that is to keep tabs on the screen position based on the pixel movement and check for the x/y max but, I want to see if there's a more faster/effecient way of doing the same.
Thanks in advance.