#!/usr/bin/env python
import math

def angle_to_vector(angle):
    angle=angle*math.pi/180
    return [math.cos(angle), math.sin(angle)]


def get_line_feats(point1, point2):
    x1,y1 = point1
    x2,y2 = point2

    a = (y1-y2)/(x1-x2)
    b = y2 - a * x2
    return a,b



def segments_intersection(line1, line2):
    p1,p2 = line1
    p3,p4 = line2

    a1,b1 = get_line_feats(p1,p2)
    a2,b2 = get_line_feats(p3,p4)

    if a1==a2 :
        return None # parrallel lines
    
    x = (b2-b1)/(a1-a2)

    if min(p1[0], p2[0]) <= x <= max (p1[0], p2[0]) and min(p3[0], p4[0]) <= x <= max (p3[0], p4[0]) :
        y = a1 * x + b1
        return x,y
    else : 
        return None # intersect is outside segments



def distance(point1, point2):
    return math.hypot(point1[0] - point2[0], point1[1] - point2[1])