def crossing(p1: Point, p2: Point, p3: Point, p4: Point):
line1, seg1 = Line(p1, p2), Segment(p1, p2)
line2, seg2 = Line(p3, p4), Segment(p3, p4)
intersect = line1.intersection(line2)
if intersect:
seg1 = Segment(p1, p2)
seg2 = Segment(p3, p4)
pi = intersect[0]
return seg1.contains(pi) and seg2.contains(pi)
def is_projection_between_two_points(p, p1, p2) :
#return (p1.x - p.x)*(p2.x - p.x) <= 0 and (p1.y - p.y) * (p2.y - p.y) <= 0
seg = Segment(p1, p2)
return seg.contains(p)
