Direction of an object with elliptical movement?

[Myp]

I'm pretty sure there must be some post out there where the answer I need is, but I can't find it.
I need to know the direction of the object with the elliptical movement of the "Clickteam Movement Controller" object, to give it the rotation.
I've been trying to find the formula, but this one is having a hard time.


Thanks in advance.


PS: It has to be the elliptical motion of that object, it can't be any other alternative.

[Myp]

After doing tests I was able to find something approximate, although it looks acceptable up to x/y between 1/4 and 4, if it moves away from that, the margin of error becomes very large and the error begins to be very noticeable.

Attachment 30992

β - is the angle to which the object should be rotated
α - is the current angle taken from the clickteam movement controller object
offs - is the offset
x - is the amplitud X
y - is the amplitud Y
? - is "k", it stayed that way from previous tests

For now I'm going to use this formula, but if someone share the real formula I would be very grateful.


ps: Since it is relevant, I share this other formula, it is for the same thing but for the angle of the sinusoidal movement.

Attachment 30993

β - is the angle between the starting point and the arrival point
α - is the current angle taken from the clickteam movement controller object
a - is the amplitude
f - is the angular speed (I called it "f" because it fits "frequency" better)
π - 3.1416 is enough
v - is the speed

Although I also tried it out by trial and error, it worked fine in every case I tried it, so I'm assuming it's the exact formula.

[aenever]

Attachments aren't working

[Myp]

Oh sorry, I didn't notice.
I don't quite understand this, so I'm going to upload the images to a random server and share the links.

Attachment 1 https://i.ibb.co/KhBfVPR/imagen-2022-01-19-044946.png
β - is the angle to which the object should be rotated
α - is the current angle taken from the clickteam movement controller object
offs - is the offset
x - is the amplitud X
y - is the amplitud Y
(I took the opportunity to replace "?")


https://i.ibb.co/TH6q0DF/imagen-2022-01-19-045544.png
β - is the angle between the starting point and the arrival point
α - is the current angle taken from the clickteam movement controller object
a - is the amplitude
f - is the angular speed (I called it "f" because it fits "frequency" better)
π - 3.1416 is enough
v - is the speed


I take this opportunity to repeat that if someone knows the real formula for the direction in elliptical motion, I would appreciate it if you share it.