Smoking -- What's the point

BACKGROUND: Illinois recently passed an anti-smoking law that prohibits smoking within public buildings or 15 feet of the door to a public building.

At the courthouse today, I was walking along and I noticed a new sign painted on the door, “Smoking prohibited within 15 feet of this point.” For some reason, I started thinking which is always a bad thing when confronted with public notices. Back in the day, I took a geometry class and was actually not too bad at it which is why I have an issue with this sign. The door in question was a double door so call it a 6 foot by 8 foot rectangle.

Query: What exactly is the “point” from which I should measure to make sure I am in conformity with the notice?

See, that door is a geometric plane with an infinite number of points (and that’s not even allowing for the opening of the door which creates an infinite number of planes, each with an infinite number of points). When you label a plane with a sign referring to this point, suddenly your sign becomes meaningless. Which point exactly do you mean? Further, for any point you pick within the plane, I can find another point somewhere in space which is more than 15 feet from your point but still within 15 feet of a point in the door’s rectangle.

Why oh why didn’t whoever painted the sign simply say, “No smoking within 15 feet of the DOOR?”