Unity: parallel vectors and cross product, how to compare vectors

Question

I read this post explaining a method to understand if the angle between 2 given vectors and the normal to the plane described by them, is clockwise or anticlockwise:

public static AngleDir GetAngleDirection(Vector3 beginDir, Vector3 endDir, Vector3 upDir)
{
    Vector3 cross = Vector3.Cross(beginDir, endDir);

    float dot = Vector3.Dot(cross, upDir);

    if (dot > 0.0f)
        return AngleDir.CLOCK;
    else if (dot < 0.0f)
        return AngleDir.ANTICLOCK;
    return AngleDir.PARALLEL;
}

After having used it a little bit, I think it's wrong. If I supply the same vector as input (beginDir equal to endDir), the cross product is zero, but the dot product is a little bit more than zero.

I think that to fix that I can simply check if the cross product is zero, means that the 2 vectors are parallel, but my code doesn't work.

I tried the following solution:

Vector3 cross = Vector3.Cross(beginDir, endDir);
if (cross == Vector.zero)
    return AngleDir.PARALLEL;

And it doesn't work because comparison between Vector.zero and cross is always different from zero (even if cross is actually [0.0f, 0.0f, 0.0f]).

I tried also this:

Vector3 cross = Vector3.Cross(beginDir, endDir);
if (cross.magnitude == 0.0f)
    return AngleDir.PARALLEL;

it also fails because magnitude is slightly more than zero.

So my question is: given 2 Vector3 in Unity, how to compare them?

I need the elegant equivalent version of this:

if (beginDir.x == endDir.x && beginDir.y == endDir.y && beginDir.z == endDir.z) 
    return true;

Answer 1

When working with floating point values it's usually not a good idea to use the comparison operator, as even slight inaccuracies will result in inequality. That's why a comparison of floats usually incorporates some sort of "epsilon".. a margin of error.

Example:

if(Math.abs(floatA - floatB) <= epsilon){
    // equal
}

Epsilon is the desired accuracy.. it's usually a really small number (1E-5 in C++ I believe).

So your check for equality could look like this:

if(Mathf.abs(cross.magnitude) <= Mathf.Epsilon){
    // equal
}