'''function to allow visualization of Monte Carlo method for approximating pi'''
import random
import math
import cTurtle

# This is the function that draws the visualization
def showMontePi(numDarts):
    drawingT = cTurtle.Turtle()

    # define the coordinate system for the turtle
    drawingT.setWorldCoordinates(-2,-2,2,2)

    # draw the crossbars that situate the graph
    drawingT.up()
    drawingT.goto(-1,0)
    drawingT.down()
    drawingT.goto(1,0)
    
    drawingT.up()
    drawingT.goto(0,1)
    drawingT.down()
    drawingT.goto(0,-1)

    # initialize the circle counter to 0
    circle = 0
    drawingT.up()

    # throw as many darts as the user asked for in the input parameter
    for i in range(numDarts):
        # randomly determine where the dart goes
        x = random.random()
        y = random.random()

        # calculate the distance of x,y from the center
        d = math.sqrt(x**2 + y**2)

        # move the turtle to the x,y point
        drawingT.goto(x,y)

        # if d is <= 1, then we are inside circle, so draw blue
        if d <= 1:
            circle = circle + 1
            drawingT.color("blue")
        # otherwise draw red
        else:
            drawingT.color("red")

        # actually draw the dot at the x,y location with the right color
        drawingT.dot()

    # estimate for pi is the percentage inside the circle, times 4 because
    # we are only working with 1/4 of the full unit circle
    pi = circle/numDarts * 4

    return pi