So assuming you’re in a car, your “optimal car” route involves two right turns (into and out of the driveways), three left turns, and three straights. If you instead went due north and then due east, that would be two left turns (driveways), one right turn, and three straights. Isn’t that a strictly better route?
(Also, isn’t turning right usually easier than going straight? I often make a right turn when going straight would have been prohibited (due to a red light), but I almost never go straight when turning right would have been prohibited (due to a pedestrian or bicycle to my right whose path I would have crossed).)
If you instead went due north and then due east, that would be two left turns (driveways), one right turn, and three straights. Isn’t that a strictly better route?
I assumed turning left into/out of a driveway (i.e. “crossing the street when not on a crossroad”) is impossible or at least hard (slow). This is often the case in a dense city. If we’re not in a dense city then Taxicab assumption is an error as well.
Ah, that makes sense. But then doesn’t the route direction depend on where the starting and ending points are located, still? With your picture, if the starting point is on the north or east side of the block and the ending point is on the south or west side (as they are), a counterclockwise route works better. If the starting point is on the south or west side and the ending point is on the north or east side, a clockwise route seems to be better. And if there’s one of each, you’ll end up with a figure-eight route.
So assuming you’re in a car, your “optimal car” route involves two right turns (into and out of the driveways), three left turns, and three straights. If you instead went due north and then due east, that would be two left turns (driveways), one right turn, and three straights. Isn’t that a strictly better route?
(Also, isn’t turning right usually easier than going straight? I often make a right turn when going straight would have been prohibited (due to a red light), but I almost never go straight when turning right would have been prohibited (due to a pedestrian or bicycle to my right whose path I would have crossed).)
I assumed turning left into/out of a driveway (i.e. “crossing the street when not on a crossroad”) is impossible or at least hard (slow). This is often the case in a dense city. If we’re not in a dense city then Taxicab assumption is an error as well.
Ah, that makes sense. But then doesn’t the route direction depend on where the starting and ending points are located, still? With your picture, if the starting point is on the north or east side of the block and the ending point is on the south or west side (as they are), a counterclockwise route works better. If the starting point is on the south or west side and the ending point is on the north or east side, a clockwise route seems to be better. And if there’s one of each, you’ll end up with a figure-eight route.