>>21004
Trigonometry is simply a way to find angles given two positions. The bullet patterns themselves generally don't use math, just simple timing and angles.
If you make an emitter move forward and constantly add an angle, it moves in a circle. If you have it send bullets towards the middle of that circle (own angle +90 or -90 depending on clockwise or counterclockwise) you get sort of a spiral. If the bullets move back after a certain distance, you get a different pattern. I think that may give results like your first picture, not 100% sure.
For the most part, the actual patterns are done with logic like that. Moving emitters, or just emitting bullets in sequence at angles. Trigonometry is used when you want to aim bullets at the player for instance, a variable location. For some patterns you might want to make an invisible emitter moving along some path, and shoot at that, but usually it's the player.
>>21007
>to convert points to angles
Do not think of it as points to angles, thing of it as distances to angles. My position is [1,3] and another object is at [4.7], the distance between us is 3 on the x scale and 4 on the y scale. atan2( 4,3 ) gives the angle I'd have to move in to move to that object.
>Fair warning: Too much of this can lead to weirdness.
A bigger problem is too much of it can lead to massive slowdown. Trigonometry functions are relatively slow for computers, so you don't want to do 5 million sin() computations per frame.