Why doesn't c4d.Vector.GetAngle throw an error for the null vector?

HerrMay

Hi guys,

TL;DR
Shouldn't c4d.Vector.GetAngle throw a e.g. ZeroDivisionError when invoked on a identity vector, that is a c4d.Vector(0, 0, 0) instead of return 90°?

For anyone who's interested:
I'm currently trying to teach myself linear algebra and therefore trying to wrap my head around vectors, its properties, methods and dependencies.

To get a better understanding I wrote my own Vector class, did research and implemented the common methods as well as the properties that define a vector.

While I'm doing this I constantly compare my vector class and the outcome of any calculation with the native c4d.Vector to test if my calculations/assumptions hold true.

When using c4d.Vector.GetAngle with a identity vector, c4d.Vector(0, 0, 0) the method returns 90°. Maybe this is a stupid question but shouldn't it raise an exception that the vector has no direction as well as no length and therefore by definition no angle?

Cheers,
Sebastian

ferdinand

Hello Herr May,

Thank you for reaching out to us. I am not quite sure why you think it should do that.

The angle between two vectors u and v is defined as:

theta(u, v) = arccosine(~u * ~v)

I.e., the arccosine of the dot product of the two normalized vectors. This is due to the so called circle functions, specifically this identity:

Under the hood, GetAngle does exactly what I declared above (just in a bit more efficient manner, as calculating the normalized vector is much more expensive than this little trick):

As you can see, the correct solution to the arccosine of the dot product of the null vector with itself is 0.5 π, i.e., the value you got :

You could now argue if that is a sensible result for a method that is called 'GetAngle' and if it should throw an error on getting an input vector or being called on a vector with the length zero. But you have also to keep in mind that the C++ backend is used by people who will know the identity pi_half = arccosine(~(0, 0, 0) * ~(0, 0, 0)) and might want to make use of it.

Cheers,
Ferdinand