Multiplication Curves

#!/usr/bin/python3

'''
multiplication curves

inspired by:
http://superdecade.blogspot.co.uk/2017/12/advent-calendar-for-geeks-21.html
https://youtu.be/qhbuKbxJsk8

James Edmundson 12/2017
james-edmundson.com
'''

import turtle  as t
import math
import time
import datetime
import random
import sys

numberOfPoints=300  #number of points
radiusOfCircle=400   #radius of circle

def polToCart(radiusOfCircle,theta):                   #function to convert a polar coordinate to a
    coord=[]
    coord.append(radiusOfCircle*math.cos(math.radians(theta)))    #cartesian coordinate that turtle can follow
    coord.append(radiusOfCircle*math.sin(math.radians(theta)))
    return coord    #returns the coordinate in cartesian form

def loopMult(numberOfPoints,d,radiusOfCircle,multupto):
    for i in range(multupto):
        specific(numberOfPoints,d,radiusOfCircle,i) #draws each multiplication curve up to the value specified
        time.sleep(0.7)
        t.clear()

def specific(numberOfPoints,d,radiusOfCircle,specificMultiple):
    t.tracer(0,0)               #for speeding up turtle graphics
    for i in range(numberOfPoints):          #for each point on the circumference of the cirle
        point=(specificMultiple*i)%numberOfPoints                  #determins which point the line should go to
        t.goto(polToCart(radiusOfCircle,i*d))  #goes to the next point
        t.pd()
        t.goto(polToCart(radiusOfCircle,point*d))  #goes to the new point
        t.pu()
    t.update() #updates turtle window, so all lines are drawn

def screenCap():
    ts = t.getscreen()
    ts.getcanvas().postscript(file="{}.eps".format(datetime.datetime.now().strftime("%Y-%m-%d%H:%M"))) # saves the turtle screen as the date and time.eps

def init(radiusOfCircle): #changing turtle settings ready for drawing
    t.bgcolor("Black")  #changing the background colour to black
    t.color("Red")      #turtle pen colour to red
    t.ht()              #hiding the turtle character itself
    t.penup()           #pen up
    t.goto(polToCart(radiusOfCircle, 0)) #going to the first point on the circle
    t.pd()              #pen down

def main(numberOfPoints=numberOfPoints, radiusOfCircle=radiusOfCircle): #defaults to global variables, but can be set as otherwise
    menuOption = input("> ")
    if menuOption == "s": #specific curve drawn
        try:
            multiple = int(input("multiple: ")) #getting the multiple
            init(radiusOfCircle)                #making turtle pretty
            specific(numberOfPoints, 360/numberOfPoints, radiusOfCircle, multiple) #drawing the specific curve
        except ValueError:  #if the user's naughty
            print("Multiple needs to be an int!")
    elif menuOption == "l": #drawing many curves in a loop
        try:
            upto = int(input("Loop up to: "))
            init(radiusOfCircle)
            loopMult(numberOfPoints, 360/numberOfPoints, radiusOfCircle, upto)
        except ValueError:
            print("Multiple needs to be an int!")
    elif menuOption == "c": #clears turtle screen
        t.clear()
    elif menuOption == "p": #takes a screen grab of the turtle window
        screenCap()
    elif menuOption == "h" or menuOption == "help": #prints help commands
        print("s for specific pattern\nl for looping multiples\nc to clear turtle\np to take a picture\nh for this help\nq to quit")
    elif menuOption == "q": #quit
        sys.exit()
    else:
        print("NOT RECOGNISED")

if __name__ == '__main__':
    while True:
        main()