I am old. My high school maths is a long way in my past and I am struggling to devise an algorithm that will produce a 2D 'flying through space' effect like [the old Windows screen saver](https://www.youtube.com/watch?v=SiSXDEIu3GI). It has—

* stars generated close to the screen centre, which move outwards at increasing speed, and
* on a key press, a hyperspace effect is generated with the stars turning to lines stretching to the edge of the screen.

I've figured out that I can use arctan and x,y offsets from screen centre to identify a direction, but given that the trig functions work in a 90 degree field. My old brain is struggling to pull it all together.

How can I create this effect?