Guaranteed Hit?

I use asin(botWidth / (distance - 18)) which takes bot width and the square shape of the bot into account(Isn't it better than botWidth / distance) but I am pretty sure that everybody else uses the formula which calculates the exact width.

asin(botWdith / (distance - 18)) is incorrect because when distance = 18 it gives NaN instead of PI.

if you assume a bot is a circle then asin(botWidth / distance) is correct; if you assume a bot is a square then atan(botWidth / (distance - 18)) is correct as long as absolute bearing from source to target is 0, 90, 180 or 270 degrees.

however, a moving bot is neither a circle nor a square, that’s why precise intersection is used.

Anyway, botWidth / distance is fine as long as distance is far, and the result is almost the same as the asin/atan version.

It gives a NaN but a distance less than 36 is impossible in robocode. botWidth / distance is always incorrect, asin(botWidth / distance) is always incorrect too but it less incorrect however, asin(botWidth / (distance - 18) is correct in four cases and gives higher results than all other imprecise formulas which always results in closer results to the precise one.

a distance less than 36 is impossible in robocode, but a correct formula should give correct result in this case. So I prefer the atan approach.

asin approach is incorrect by geometry as well.

however trigs are always expensive, so using 18 / distance is acceptable since it gives similar result.

Wrong. Infinity means nothing in radians. Valid values are 0~2pi or -pi~pi or so.

An angle should never be infinty radians.

If it means nothing can't we assume that the traditional formula is completely wrong since with a bullet velocity of 0, it will return positive infinity.

Bullet velocity = 0 is another geometrical situation. But in this case, distance < 36 should still fit in to your image. Or, it must be wrong.l