The problem is that Factorio is a tile based game and everything is not practically moving exactly as math would make you expect to, based on rounding and whatnot.
Exactly!
The problem of rounding errors existed always, but it is not observable in the game for angles which are multiple of 45 ...

Yeah you can set a line towards a goal, but what if you predicted the orientation wrong initially? It's quite an odd angle there requiring arctan()
Ok, if for some reason arctg() usage looks unclear, another approach can be taken.
These half-diagonal lines have pretty simple equations: y = k*x + b ...

what if you predicted the orientation wrong initially?

How could it be predicted incorrectly?
There are only 16 correct orientations, and we know for sure which one of them was selected by the car driver.
While the car driver is changing car orientation manually, the mod stops modifying the ...

I have fixed the problem, see my patch on github. But again, it's hard-to-understand code.

The idea is following: at the moment when car orientation get snapped, we remember the trajectory (the "ray") which the car must follow in the future.
The ray is just 3 numbers: start_x, start_y and ...

Indeed, in "Sandbox" mode, after driving forward for 10 km I found myself 10 m away from imaginary half-diagonal railway.

-- 0.07386350632 measured from train wagon orientation, still off very tiny bit
local rail_est = 0.07405 -- Best estimate so far 0.07405
local lockAxis = {
rail_est, 0.25-rail_est, 0.25+rail_est, 0.5-rail_est,
0.5+rail_est, 0.75-rail_est, 0.75+rail_est, 1.0-rail_est }
As it seems 1:2 is ...

But i never considered this mod to actually use more than 8 rail directions, the extra angles between were just for immersion. I set it to 8 in mod settings myself.

Ok, you are using only 8 directions when playing the game.
Nevertheless the most popular user choice is 16, not 8.
So thank you for ...

Thanks for the most useful Factorio mod! (BTW, it is not a joke)
I like to drive a car along rails, and it was not a problem in Factorio 1.x due to this nice mod!
But in Factorio 2.0 there are 16 rail directions instead of 8, and they are not placed at equal angles anymore.
So, by setting snap ...