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I want to implement diffraction of waves by edges. I have a wedge with 2 faces o-face and n-face. I have the tangent and normal of each face.

Assume the angle between the 2 faces is alpha where alpha is the outer angle (> 180).

I have an incident vector, passing through the edge though the outer angle (alpha)

I want the angle between the incident vector and the o-face in the same direction as alpha (i.e. without crossing n-face).

In the normal circumstances, I would thus use the dot product and get the cosine of the angle between them.

But the problem is that in some cases the angle is greater than 180 and in other it is not. How can I determine this? The dot product only gets angles [0, 180].

Thanks in advance