Chuck - You've re-piqued my intrest in Hector. A while back I thought he was wire driven, wire on spool - now I see it is toothed belts! Guess the software does 2d trig to find its position, if you know (x,y) and (x', y') the starting points, then count the length of each of the belts by counting teeth through the gears -- you'd come to the point the spray paint is at? Just then say "pfft" and its done!
It might be one way? (well it would be one of 2 possible locations - but Hector don't fly!)