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Im dealing in vertices. I want to check which hemisphere a point is in compared to a 3d angle of a vertice.
I want to make sure the point is on the oposite side of the face.

What are you trying to accomplish?

You want to make sure two points are on opposite sides of a triangle right? I think you can just do this with dot product and cross product.

You have P1 P2 and P3 defining the triangle, and you have a point A. Consider P1 the origin, so now we have a triangle defined by (0,0,0), P2-P1 and P3-P1, with point A-P1.

The cross product will get a vector perpendicular to the surface of the triangle, that is: (P2-P1)x(P3-P1). To find where A-P1 lies along this line, take the dot product:
((P2-P1)x(P3-P1)).(A-P1)
To find out where another point B lies along this line, calculate the dot product again:
((P2-P1)x(P3-P1)).(B-P1)
If these two values have opposite signs, they lie on different sides of the triangle.


For two vectors, the dot product is defined by:

(Ax,Ay,Az).(Bx,By,Bz)=Ax*Bx+Ay*By+Az*Bz (a scalar value)

and cross product:
(Ax,Ay,Az)x(Bx,By,Bz)=(AyBz-ByAz,AzBx-BzAx,AxBy-BxAy) (a vector value)