So if a flag is 3 up and 4 to the right of another, then the distance is 5 not 7, Pythagorean theorem. The distance is also Euclidean meaning it's a straight distance from one to the other. As long as you choose the same spot on each flag, then it doesn't matter for calculating distance since it's all relative to the flag. Technically code-wise, it's the spot just above the top center of the flag. Distances are calculated based on the location of NPC flags. NPCs form a town when there are at least 3 within 240 tiles of each other. NPCs are neighbors when they are within 50 tiles of each other. If an NPC is too far from their home, their home is destroyed, or their home is in the Crimson, Corruption, or Dungeon, then they gain a maximized penalty of 50%. She also loves all the NPCs, all the NPCs like her, and she has no biome preferences. The Princess NPC is very unique, if she doesn't have any neighbors, then she gains maximized penalty of 50%. Love and Hate provide a 10% bonus and penalty. Like and Dislike provide a 5% bonus and penalty. NPCs receive a 5% penalty for having more than 3 neighbors. In order to not lose this bonus, you have to make sure that non neighbors are at least 50 blocks away. NPCs receive a 5% bonus for having only 1 neighbor (within 50 tiles), and having no more than 3 other NPCs (not counting the one neighbor) in their town (within 240 tiles). Bonuses and penalties will be labeled as their effective values. When they are neighbors with both NPCs, then they get a 25% bonus.
The only exception to this is when people love more than one NPC which only the Party Girl and Princess do. However since the system rounds to the nearest 5, it becomes effectively additive and orderly. Happiness bonuses and penalties are multiplicative and at odd values. I didn't want to bloat the image with text so I am leaving this comment to cover some of the happiness mechanics. This is meant to be a quick reference and starter guide.
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