Pseudo code for Vector3d.VectorAngle please

I’m porting a code that is calling many functions from Rhino.Geometry to C++. Today I noticed I have no idea how to do VectorAngle() with my own code… It’s a bit embarrassing but if anybody could give me some insights, I’ll appreciate it very much. A pseudo-code is much more appreciated.


Hi @mikity_kogekoge,

This is from RhinoScript:

double ON_VectorAngle(ON_3dVector v0, ON_3fVector v1)
  double angle = ON_UNSET_VALUE;
  if (
    && v1.IsValid()
    && !v0.IsZero()
    && !v1.IsZero()
    double dot = RHINO_CLAMP(ON_DotProduct(v0, v1), -1.0, 1.0);
    angle = acos(dot);
  return angle;

– Dale

Thanks Dale!!

In my test, the acos(dot) sometimes returns Nan. Is that the reason you do RHINO_CLAMP? Isn’t it ensured that dot products always fit within -1.0-1.0?

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It might be very useful to to know that the vector dot product is very closely related to the trigonometric functions, namely the cosine:

\vec{u} \cdot \vec{v} = ||u||||v||\cos(\theta)

If \hat{u} and \hat{v} are normal vectors (unit vectors), their dot product is simply equal to \cos(\theta), since:

\begin{align} \vec{u} \cdot \vec{v} &= 1 \times 1 \times \cos(\theta)\\ \vec{u} \cdot \vec{v} &= \cos(\theta) \end{align}

You can thus get the vector angle by calculating the inverse cosine of their dot product.

\theta = \arccos(\vec{u} \cdot \vec{v})

@dale Is the clamping just a precaution? I’m asking because the dot product of two unit vectors should at least theoretically always be between -1 and 1.

that was what I was trying to say…

Ah, I must have misread. I’m still wondering why the dot product of two normal vectors can be NaN though?

Maybe slightly off from -1 or 1? Anyway added the clamp and it works now.

I’ve dug a little through the opennurbs project and I think it might rather be related to vector normalization.

Yes the normalization doesn’t ensure that the length is one there is a 2E-16 error.
The probability of occurrence of length > 1 is around 7%.

error (7.9 KB)

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Thanks for the demonstration, Laurent.

oh, really…

Floating point accuracy and math. Computers suck at it currently, even with simple arithmetic. There are many posts about the woes of working with floating points on this forum. Just summing it up in this screenshot.

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