Aaginor Aaginor - 2 months ago 7
C# Question

How to tell whether a point is to the right or left side of a line

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.

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