Tolerance

[JAvanth]

Hello everyone!

I have question about Equal Vector and Tolerance.
Tolerance - what is it? I know from UE tips what tolerance is “…a specified error…”, but what does it really mean? How can I calculate it by manual?
I don’t understand why I have different results (if I correct copy/paste log):

Equal vectors is True
X=0.000 Y=1.000 Z=0.000
X=0.293 Y=0.858 Z=0.421

Equal vectors is False
X=0.000 Y=1.000 Z=0.000
X=-0.411 Y=0.359 Z=0.838

Tolerance in both cases is 0.7.

I can not find info in manual? If you can find info, please send link me.

Thanks in advance.

[archimonde1111]

Hi, not sure how much you know about the floats so I’ll start from the basics.

Because of how float variables are stored in computer memory there is a really high chance that 2 float variables declared as 0.7 won’t actually be 0.7000(…) but for example 0.70001 and 0.6999, and that makes default comparison operator unreliable (to say the least). To make that bearable ;D people got an idea that they will check the range instead of 1 value comparison. For example if the variable is somewhere between 6.9f and 7.1f and you’re using 0.7f as base, that would make it a tolerance of 0.1

Having that in mind the vector is just a struct with 3 float so the same rules apply. Here is the code the vector’s Equals() method use:

FORCEINLINE bool TVector<T>::Equals(const TVector<T>& V, T Tolerance) const
{
    return FMath::Abs(X-V.X) <= Tolerance && FMath::Abs(Y-V.Y) <= Tolerance && FMath::Abs(Z-V.Z) <= Tolerance;
}

As you can see it takes absolute of the difference between the vector you’re calling method on and the checking(?) vector, then checks whether that value is <= your tolerance.

Oh and going back to your example, the one when the method returns false, the difference between Z values is higher than 0.7 that’s why this returns false.

Hope that helps you : )

EDIT: Updated my float explanation.

[JAvanth]

Hi again.

I know a little about floats.

Do I right understend?

Case True:
0.000-0.293<=0.7 && 1.000-0.858<=0.7 && 0.000-0.421<=0.7
-0.293<=0.7 (True) && 0.142<=0.7 (True) && -0.421<=0.7 (True) - Result - True

Case False:
0.000-(-0.411)<=0.7 && 1.000-0.359<=0.7 && 0.000-0.838<=0.7
0.411<=0.7 (True) && 0.641<=0.7 (True) && -0.838<=0.7 (True) - Result - True, UE Result - False

It seems I have done mistake. Where have I done it? This moment confuse me.

[JAvanth]

I forgot Abs().
Abs(-0.838) is 0.838. And it isn’t <= 0.7.

Thanks for explanation.

[archimonde1111]

You’re welcome. Glad I was able to help : D