from math import sqrt
from tkinter import *
def mdp(E):
    D=[]
    x1=E[0][0]
    x2=E[-1][0]
    y1=E[0][1]
    y2=E[-1][1]
    for i in E:
        dist=abs((y2-y1)*i[0]-(x2-x1)*i[1]+x2*y1-y2*x1)/\
             (sqrt((y2-y1)**2+(x2-x1)**2))
        D.append((dist,i[0],i[1],E.index(i)))
    D.sort(reverse=1)
    return D[0]

def new_line(N):
    for i in range (len(N)-1):
        canvas.create_line(N[i][0], N[i][1], N[i+1][0], N[i+1][1], width=5, fill='red')

def click(click_event):
    global prev
    try:
        canvas.create_line(prev.x, prev.y, click_event.x, click_event.y, width=2, fill='green')
        S.append((click_event.x,click_event.y))
    except:
        prev = click_event
        S.append((click_event.x,click_event.y))
        return
    prev = click_event

def action(K):
    if len(K)<=2:
        print('end',K)
        return
    else:
        mdpoint = mdp(K)           #макс удаленная точка вида [дистанция, х,у, индекс в списке К]
        print(mdpoint[0])
        if mdpoint[0]<=epsilon:
            for i in range(len(K)-2,0,-1):
                print('remove point',S.remove(K[i]))
            return
        else:
            print('recurs')
            K1=K[0:mdpoint[3]+1]
            K2=K[mdpoint[3]:]
            print(K1)
            print(K2)
            action(K1)
            action(K2)
            return

def oper():
    global epsilon
    epsilon = int(eps.get())
    action(S)
    new_line(S)

S=[]
epsilon=0

master = Tk()
canvas = Canvas(master, width=600, height=300,bg='white')
canvas.pack(padx=20, pady=20)
canvas.bind('<Button-1>', click)
but1=Button(master,text='show',command=oper);but1.pack()
eps=Entry(master,width=5);eps.pack()

mainloop()