Aaginor - 6 months ago 27

C# Question

I have a set of points. I want to separate them into 2 distinct sets. To do this, I choose two points (*a* and *b*) and draw an imaginary line between them. Now I want to have all points that are left from this line in one set and those that are right from this line in the other set.

How can I tell for any given point *z* whether it is in the left or in the right set? I tried to calculate the angle between *a-z-b* – angles smaller than 180 are on the right hand side, greater than 180 on the left hand side – but because of the definition of ArcCos, the calculated angles are always smaller than 180°. Is there a formula to calculate angles greater than 180° (or any other formula to chose right or left side)?

Answer

Use the sign of the determinant of vectors `(AB,AM)`

, where `M(X,Y)`

is the query point:

```
position = sign((Bx - Ax) * (Y - Ay) - (By - Ay) * (X - Ax))
```

It is `0`

on the line, and `+1`

on one side, `-1`

on the other side.