Find which side of a line is my point

Hello ,

I'm looking for a simple way to know where C or D are in relation to the line AB

I already computed their distance to line AB but it is absolute so I don't know in which direction they are.

Would someone have a solution for this ? Ideally to obtain a negative distance for point C and positive one for point D

I tried computing coeff d=(x−x1)(y2−y1)−(y−y1)(x2−x1) but it's not working well

Thanks a lot

Answer 1

[Bora Eryilmaz]

You can use the sign of the z-term of the cross product of the vectors defining the line and the points of interest:

vAB = [3 2 0]; % Vector from A to B, or anywhere along the line
vC = [5 2 0]; % From origin to C
vD = [2 4 0]; % From origin to D

X = cross(vAB, vC);
sign(X(3)) % Below the line when negative

ans = -1

Y = cross(vAB, vD);
sign(Y(3)) % Above the line when positive

ans = 1

[Clementine Bodin]

But how to I get vAB from xa ya and xb yb ?

Also I don't have the point of intersection between the line and point C or D ( just the distance)

[Bora Eryilmaz]

vAb = [xb-xa, yb-ya, 0]
vC = [xc, yc, 0]

You don't need the point of intersection. You need the coordinates of C and D.

[Clementine Bodin]

Ok got it it seems to work now !! thank you so much