Although without checking it:

this.lastOrderVariant

sounds like it would give me the current formation

Certainly not, for it would prevent modders from overriding the value. (#6094)

I opted for this because when I tried to put in pi/2 as template value it didn't work. (And I like to think in degrees)
But sure, since this is probably not a value that is regularly touched I can also switch to radians and type it out.

If I understood @Freagarach correctly, they suggested to use it as a multiplier for pi, but that seemed like more complicated to understand.

Pi is not a valid entry in the template indeed. One can round off though (and one need not be very exact anyhow).

lol. that is one unintuitive named function.

yeah makes sense to make it global

I think because it is a magic value either way and I can't think of a benefit for having individual values for different formations

iirc actually not.

GetTargetPositions()

returns the current position if no target position is given, which means that

avgpos.angleTo(cmpFormationUnitAI.GetTargetPositions()[0]);

actually safely returns 0 in that case, while getTargetPosition always returns something non-zero, resulting in the unwanted behavoir that formations without a target always turn in the same direction, instead of the current one.

GetTargetPositions() returns [] with no orders present?

no : p

At least not in this context. See the output when I print out the numbers here (with no order given):

warn(uneval(cmpFormationUnitAI.GetTargetPositions()))
WARNING: [{x:598.5147399902344, y:800.5150451660156}]

warn(uneval(avgpos));
WARNING: ({x:598.5147399902344, y:800.5150451660156})

So the current state is certainly not the most elegant js, but it was the only way I found to get rid of the error.
Unfortunately @Freagarach 's suggestion with ? : doesn't work since it doesn't return undefined in all cases.

Mh no, you would need to take the modulo for both values individually
Not sure if this is more or less computing then the ||
sure, could also use that, but there should never be values outside the interval?

let a = 360;
let b = 80;

(Math.abs(a - b ) % 360;
// return: 280 

Math.abs((a % 360) - (b % 360));
// return: 80

Sure the value of d might change to 2Pi - d, but that is indifferent seeing the return value on the next line.

my thought was the using the modulo on both inputs would simplify the return to
return d < this.maxTurningAngle

That won't work in any case since if a_1=2\pi-eps and a_2=0, we will always be in the second case of the return value.

ah yes. true.

In that case it is only the question if the the extra calculation is worth the generalization.

switch x and y. it looks weird to me, because math.atan should take y as first argument, but I think in 0AD it's the opposite somehow.

return Math.atan(vector.x, vector.y);

still gives me something different (and a bit worse behavior wise) than

return Math.PI/2 - Math.atan2(vector.y, vector.x);

idk, that's where my math knowledge stops.