#circle_division.py

import math
import random
from itertools import combinations
from ezgraphics import GraphicsWindow

size = int(input("Enter size of 'rosette': "))
radius = size / 2
num_points = int(input("Enter number of points: "))
is_randomness = True if input("Add some randomness? (y or n): ").lower()=='y' else False

margin = 20
win = GraphicsWindow(size+margin,size+margin)
canvas = win.canvas()
#canvas.setBackground("yellow")
canvas.setColor("red")

points = []
for p in range(num_points):
    if is_randomness:
        alpha = 2*math.pi/num_points * p + random.random()
    else:
        alpha = 2*math.pi/num_points * p    #regular polygon
    sin_p = math.sin(alpha)
    cos_p = math.cos(alpha)
    points.append((cos_p*radius+radius+margin/2,sin_p*radius+radius+margin/2)) 


   
for from_pt in range(num_points):
    for to_pt in range(from_pt+1,num_points):
        canvas.drawLine(points[from_pt][0], points[from_pt][1],\
                        points[to_pt][0],   points[to_pt][1])


canvas.setColor("blue")
canvas.setFill()
canvas.drawOval(margin/2,margin/2,size,size)


def num_combos(n,k):
    if k>n:
        return 0
    return int(math.factorial(n) / (math.factorial(n-k) * math.factorial(k)))

num_quad_points = num_combos(num_points,4)
print("#4-combinations=#intersections:",num_quad_points)

#intersection point of two line (segments) defined by two points each
#def intersection_point(x1,y1, x2,y2,  x3,y3, x4,y4):
#    m1 = (y2-y1) / (x2-x1)
#    m2 = (y3-y4) / (x3-x4)
#    b1 = -m1*x1 + y1
#    b2 = -m2*x3 + y3
def intersection_point(p1,p2, p3,p4):
    m1 = (p2[1]-p1[1]) / (p2[0]-p1[0])
    if m1 > 1000:
        m1 = 1000
    m2 = (p3[1]-p4[1]) / (p3[0]-p4[0])
    if m2 > 1000:
        m2 = 1000
    b1 = -m1*p1[0] + p1[1]
    b2 = -m2*p3[0] + p3[1]
    xi = (b1-b2) / (m2-m1)
    yi = m2*xi + b2
    return xi,yi

canvas.setColor("green")

combos =  combinations(range(num_points),4)
# Print the obtained combinations
for comb in list(combos):
    print (comb)
    i,j,k,l = comb
    
    xi,yi = intersection_point(points[i],points[k], points[j],points[l])
    canvas.drawOval(xi-1,yi-1,3,3)

win.showStatus()
num_regions = 1 + num_points*(num_points-1)//2 + num_quad_points
win.setStatus("#points on circle: n="+str(num_points)+"  #intersections: nC4="+str(num_quad_points)+\
              "  #regions: nC0+nC2+nC4="+str(num_regions))

print("Go look at the graphics window")

for i in range(1,11):
    iChoose2 =  i*(i-1)//2
    iChoose4 = num_combos(i,4)
    print(i,":",1,iChoose2,iChoose4,"=",1+iChoose2+iChoose4)

    
#win.wait()