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Fragment of a discussion from Talk:Polylunar
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This is a very belated comment of mine, but I'll note that Polylunar's "Guaranteed Hit Targeting" is a good bit more sophisticated than those distance-based approximations. It runs two iterative simulations of the enemy bot's movement. One for the case of maximally clockwise-around-self movement, and one for maximally counterclockwise-around-self movement, and performs precise intersection calculations to determine the range of angles where a shot will intersect the robot. Then, there is a check for whether these two ranges of angles intersect with eachother. If so, aiming within that overlap is considered a "guaranteed hit", and so Polylunar will aim in the center of that overlap when such overlap exists.

I think it's technically not quite a perfect guarantee due to some unusual scenarios the simulated paths may not account for, but it's quite close. One of the main corner cases is how, while the simulation accounts for walls, the simulated enemy does not have wall avoidance. This detail likely doesn't affect things too much for Polylunar since the distance you have to be at for guaranteed hits to even be possible, doesn't give an opponent much time to actually collide with a wall anyway, let alone avoid a wall in a fashion that gives a narrower escape angle range.

Rednaxela (talk)10:54, 15 June 2021