OK. Effectively these become zones of control, a mechanism I use a lot in grid based games, and funnily enough, also appear in the 1956 British Army Tactical Wargame.
Indeed I think the first opportunity fire rule I’m aware of, in the SPI boardgame “Combat Command” back in 1972, implemented it by means of ZOCs — units could be attacked when leaving a ZOC, as many times as they did so. SPI’s “Raid” (1977) gave MGs arcs of fire that were effectively zones of control extending over seceral hexes range, but limited in angle. Victory Games’ “Panzer Command” (1984) had ZOCs extending three hexes from the unit, but made opportunity fire dependent on passing a troop quality
Something that grid-based games do naturally is to regulate the number of opportunity fire attack occurrences to one per hex moved. In miniatures games one might want to rule that an opportunity fire attack is possible once for every so many metres moved, but I have yet to see such a provision in any set of miniatures rules I have read.
All the best,