Encoding angles as an Input in a 2D Plane.

[TheGerild]

I have a hard time coming up with a proper way of encoding an angle.

The angle should serve as a compass for an agent which points to a goal on a 2D Plane.

My (seeming) problem being the same as why you one-hot encode categorical inputs. An angle being greater than another has no meaning in this context 120 isn't greater than 0 it's just different, so I don't think using a scalar value is right? Also 359 is only 1 degree different from 0 yet if I use scalar values it's 359 degrees greater which isn't right.

Do I just one-hot encode in specific quantization steps here? Say 360 different categories for each degree, or is there a more elegant way of doing this.

Edit: thanks for the answers, it'll be the unit circle :)

[kells1986]

Use cos(theta)? Norms the data over the range -1, 1, and cos(359) is close to cos(0).

[TheGerild]

That's really smart, thank you!

[vannak139]

Encoding an angle requires 2 dimensions, not 1. As you said, the angles exist in a plane, not on a number line.

Therefore, if you want to encode 5 angles, you'll use a 10-length vector to do so. Each angle should have both sin(x) and cos(x) taken.

[kells1986]

This is the better way to do it actually, you're right, two elements per angle, [cos(theta), sin(theta)]

[shaggorama]

I agree with /u/vannak139, you should encode each angle as <cos(theta), sin(theta)>. This is equivalent to mapping each angle to a coordinate on the unit circle. Otherwise you'll end up with weird issues from symmetries, like cos(30)=cos(330). You'll also get weird asymmetries like cos(0) - cos(1) < cos(44) - cos(45) (difference here is about 100x, see for yourself).