How does traveling on the right imply a counter-clockwise route? Given two equal-length ways of getting from one place to another, I’ll probably prefer the one that involves fewer left turns, or more right turns. If the road is circular, and both places are outside the road, I’ll want to go counterclockwise, but if both places are inside, I’ll want to go clockwise.
I was assuming travelling diagonally in Taxicab geometry and considered 4 potential starting points and 4 potential destinations (on every side of the src/dst block) and also that crossing a two-way street was forbidden or at least difficult when not on a crossroad.
I still don’t understand, then. Isn’t it easier to travel clockwise around city blocks than counterclockwise? Maybe you could give an example of a trip where going counterclockwise is easier?
Isn’t it easier to travel clockwise around city blocks than counterclockwise?
It is! But that only makes it easier to travel counterclockwise between blocks.
Maybe you could give an example of a trip where going counterclockwise is easier?
Sure, catch: routes
Pedestrian would go clockwise in this case and I suppose for a pedestrian the cases are split 50⁄50. A car is better off counterclockwise in most cases though.
Actually my original model was insufficient—I didn’t thought it matters how src/dst blocks are located relatively to each other. I initially missed that pedestrian lights layout is different than that of a car and I didn’t list all assumptions, e.g. for a car “go straight” > “turn right” > “turn left” > “turn around” and for pedestrian it depends on which side of the road you are. And all that while we’re only in Taxicab!
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.
How does traveling on the right imply a counter-clockwise route? Given two equal-length ways of getting from one place to another, I’ll probably prefer the one that involves fewer left turns, or more right turns. If the road is circular, and both places are outside the road, I’ll want to go counterclockwise, but if both places are inside, I’ll want to go clockwise.
I was assuming travelling diagonally in Taxicab geometry and considered 4 potential starting points and 4 potential destinations (on every side of the src/dst block) and also that crossing a two-way street was forbidden or at least difficult when not on a crossroad.
I still don’t understand, then. Isn’t it easier to travel clockwise around city blocks than counterclockwise? Maybe you could give an example of a trip where going counterclockwise is easier?
It is! But that only makes it easier to travel counterclockwise between blocks.
Sure, catch: routes Pedestrian would go clockwise in this case and I suppose for a pedestrian the cases are split 50⁄50. A car is better off counterclockwise in most cases though.
Actually my original model was insufficient—I didn’t thought it matters how src/dst blocks are located relatively to each other. I initially missed that pedestrian lights layout is different than that of a car and I didn’t list all assumptions, e.g. for a car “go straight” > “turn right” > “turn left” > “turn around” and for pedestrian it depends on which side of the road you are. And all that while we’re only in Taxicab!
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.