QIX Logic?

I''ve been programming since 1987, and actually do it professionally now (although "game" programming is still primarily a hobby). I can plod through enough math and algebra to do what I need, but math has never been my strong suit. However, I''ve always wanted to write a QIX-like game (for those who don''t know, that''s an old arcade game where you draw lines up into the play area, filling in parts of the screen until the QIX (enemy) is bouncing around an area 25% or less). The reason I''ve never done this, however, is because I can''t seem to figure out how to determine the math involved in calculating which area to fill! Because the lines can be jagged and roaming, the player could in theory draw up and over, loop around the QIX and back. Basically, I have to figure out which area belongs to the QIX, and which area should be painted in for the player. I''m thinking about starting a QIX project, but I hate to do it the hard way (paint in the background, check to see if the QIX is in the painted area, and if so, undo and start painting elsewhere). Any advice? Mike Snyder Prowler Productions