How do you find the singed angles between two vectors in three.js?

Question

I have 2 vectors A, B. Using A.angleTo(B), I know the mangitude of the angle between them.

How do I find the sign of this angle? Maybe we need to use some reference vector for this?

Answer 1

I'll suggest you to use a reference plane, personally i didn't need the sign of the angle returned from .angleTo() method so i suggest you to read this two posts:

Signed angle between two 3D vectors with same origin within the same plane

How to calculate the angle between 2 vectors in a plane

Answer 2

Angle sign is arbitrary in 3D, so I'm assuming you mean in 2D? In which case this solution worked for me:

import {Plane, Vector3} from 'three';

export function getNormal(u: Vector3, v: Vector3): Vector3 {
    return new Plane().setFromCoplanarPoints(new Vector3(), u, v).normal;
}

export function signedAngleTo(u: Vector3, v: Vector3): number {
    // Get the signed angle between u and v, in the range [-pi, pi]
    const angle = u.angleTo(v);
    const normal = getNormal(u, v);
    return normal.z * angle;
}