Calculating the angle (of the line) between two points on a wrapping plane?

I'd use this approach: Use the target as the center of your coordinate system (and wrap the missile's coordinates properly), then calculate the angle. So, pseudo-code should be this (EDIT2: Corrected code, a similar problem also led to the problems in your tests).

Just to make the obvious suggestion: shouldn't it be Math. Atan2(ay-by,ax-bx)? Apologies if that was just a typo in your post, but I can certainly see that causing bizarre behaviour in your missiles.

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