How to tell wether a point is right or left of a line

Question

Hi folks,

I have a set of points. I want to separate them into 2 distinct sets. To do this, I chose 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.

My question is: How can I tell for any given point z wheter 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 angels are always smaller than 180°. Is there a formula to calculate angels greater than 180° (or any other formula to chose right or left side)?

Thanks in advance, Frank

Answer 1

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.

Answer 2

Using the equation of the line ab, get the x-coordinate on the line at the same y-coordinate as the point to be sorted.

• If point's x > line's x, the point is to the right of the line.
• If point's x < line's x, the point is to the left of the line.
• If point's x == line's x, the point is on the line.