How can I check if a point is below a line or not ?

Solution 1:

You could try using a cross product -- http://en.wikipedia.org/wiki/Cross_product.

v1 = (x2-x1, y2-y1)   # Vector 1
v2 = (x2-xA, y2-yA)   # Vector 2
xp = v1[0]*v2[1] - v1[1]*v2[0]  # Cross product
if xp > 0:
    print('on one side')
elif xp < 0:
    print('on the other')
else:
    print('on the same line!')

You'd need to calibrate what each side is. If you want it to be "below" or "above" you need to ensure the points on the line are sorted horizontally.

I haven't tested this.

Edit I initially put in the dot product formula. :o

Edit 2 D'oh, I was putting the coordinates into a set instead of a tuple. Using namedtuple('point', 'x y') for the vectors is nice if you're running a reasonably modern version of Python.

Luckily I found Calculating a 2D Vector's Cross Product.

Solution 2:

You could try using a cross product, but the trick is how to choose the point to form a vector, here I choose the closest point from points, assume I got pointA(you can fairly loop points to calculate to distance from loop point to Line):

v1 = {x2-x1, y2-y1}   # Vector 1
v2 = {xA-x1, yA-y1}   # Vector 2
cross_product = v1.x*v2.y - v1.y*v2.x
if cross_product > 0:
    print 'pointA is on the counter-clockwise side of line'
elif cross_product < 0:
    print 'pointA is on the clockwise side of line'
else:
    print 'pointA is exactly on the line'