# typeface.py
# By Chris Proctor and _________

# Contains one function for each letter in the English alphabet. 
# Each function should draw its letter at a scale of `unit`, and then 
# return back to the same position and heading where it started. 

# Note: The `sqrt` function from math may be helpful--if you want to 
# move the turtle along the diagonal of a square with side length x, 
# the turtle should move a distance of sqrt(x)

from turtle import *
from math import sqrt
from math import atan
from math import degrees

def fly(dist):
    penup()
    forward(dist)
    pendown()


def diagonal(grids,unit):
    pendown()
    forward(grids*unit*sqrt(2))
    penup()

def  segment(grids,unit):
    pendown()
    forward(grids*unit)
    penup()

def no_pen(grids,unit):
    penup()
    forward(grids*unit)
    pendown()

def returnToHome(size):
    right(90)
    fly(size)
    right(180)

def draw_letter_a(unit):
    penup()
    forward(unit)
    pendown()
    forward(1.5 * unit)
    left(degrees(atan(2)))
    forward(sqrt(5) * 1.5 * unit)
    right(degrees(atan(2)))
    forward(unit)
    right(90)
    forward(3 * unit)
    left(90)
    forward(2 * unit)
    left(90)
    forward(8 * unit)
    left(90)
    forward(2 * unit)
    left(degrees(atan(2)))
    forward(sqrt(5) * 4 * unit)
    left(180 - degrees(atan(2)))
    penup()
    forward(3 * unit)
    left(90)
    forward(4 * unit)
    pendown()
    right(90)
    forward(1 * unit)
    left(90)
    forward(2 * unit)
    left(90 + degrees(atan(2)))
    forward(sqrt(5) * unit)
    penup()
    forward(sqrt(5) * 2 * unit)
    right(degrees(atan(2)))
    forward(2 * unit)
    right(180)
    pendown()

def draw_letter_b(unit):
    pass

def draw_letter_c(unit):
    no_pen(3,unit)

    segment(4,unit)
    left(90)
    segment(2,unit)
    left(90)
    segment(2,unit)
    right(45)
    diagonal(2,unit)
    right(90)
    diagonal(2,unit)
    right(45)
    segment(2,unit)
    left(90)
    segment(2,unit)
    left(90)
    segment(4,unit)
    left(45)
    diagonal(2,unit)
    left(45)
    segment(4,unit)
    left(45)
    diagonal(2,unit)

    right(135)
    no_pen(3,unit)
    left(180)

def draw_letter_d(unit):
    no_pen(1,unit)

    # the outline of the D
    segment(5,unit)
    left(45)
    diagonal(1,unit)
    left(45)
    segment(6,unit)
    left(45)
    diagonal(1,unit)
    left(45)
    segment(5,unit)
    left(90)
    segment(8,unit)

    left(90)
    no_pen(2,unit)
    left(90)
    no_pen(2,unit)

    # the inner part of the D
    segment(4,unit)
    right(90)
    segment(1,unit)
    right(45)
    diagonal(1,unit)
    right(45)
    segment(2,unit)
    right(45)
    diagonal(1,unit)
    right(45)
    segment(1,unit)

    no_pen(3,unit)
    left(90)
    no_pen(2,unit)
    left(90)
def draw_letter_e(unit):
    forward(unit * 0)
    left(90)
    forward(unit * 8)
    right(90)
    forward(unit * 7)
    right(90)
    forward(unit * 2)
    right(90)
    forward(unit * 5)
    left(90)
    forward(unit * 1)
    left(90)
    forward(unit * 5)
    right(90)
    forward(unit * 2)
    right(90)
    forward(unit * 5)
    left(90)
    forward(unit *1)
    left(90)
    forward(unit * 5)
    right(90)
    forward(unit * 2)
    right(90)
    forward(unit * 7)
    right(180)

def draw_letter_f(unit):
    #print(heading())
    #print(pos())
    circle(unit,90)  
    forward(6 * unit)
    circle(unit,90) 
    right(180)
    forward(7 * unit)
    right(90)
    forward(2 * unit)
    circle(-unit,-90) 
    left(180)
    forward(3 * unit)
    left(90)
    forward(2 * unit)
    left(90)
    forward(4 * unit)
    right(90)
    forward(2 * unit)
    circle(-unit,-90) 
    left(180)
    forward(3 * unit)
    left(90)
    forward(3 * unit)
    circle(unit,90)  
    left(180)
    forward(4 * unit)
    right(180)

def draw_letter_g(unit):
    pass

def draw_letter_h(unit):
    for i in range(2):
        circle(unit,90)  
        forward(6 * unit)
        circle(unit,90) 
        right(180)
        forward(3.5 * unit)
        circle(-unit,-90)
        right(180)
        forward(1.5 * unit)
        circle(unit,90) 
        forward(1 * unit) 
        circle(unit,90)
        forward(1.5 * unit)
        circle(unit,90)
        right(180)
        forward(3.5 * unit)
        right(180)


def draw_letter_i(unit):
    fly(unit * 3.125)
    forward(unit * 1.75)
    left(90)
    forward(unit * 4)
    left(90)
    forward(unit * 0.875)
    right(90)
    fly(unit)
    right(90)
    circle(unit * .875)
    right(90)
    fly(unit)
    right(90)
    forward(unit * .875)
    left(90)
    forward(unit * 4)
    returnToHome(unit * 3.125)
def draw_letter_j(unit):
    # print(heading())
    # print(pos())
    left(90)
    penup()
    forward(8 * unit)
    right(90)
    forward(unit)
    pendown()
    forward(6 * unit)
    right(90)
    forward(6 * unit)
    circle(-2 * unit, 90)
    forward(2 * unit)
    circle(-2 * unit, 90)
    forward(unit)
    right(90)
    forward(2 * unit)
    right(90)
    forward(unit)
    circle(unit, 180)
    forward(4 * unit)
    left(90)
    forward(4 * unit)
    right(90)
    forward(2 * unit)
    penup()
    left(90)
    forward(unit)
    left(90)
    forward(8 * unit)
    left(90)

def draw_letter_k(unit):
    no_pen(1,unit)
    left(90)
    segment(8,unit)
    right(90)
    segment(2,unit)
    right(90)
    segment(2,unit)
    left(135)
    diagonal(2,unit)
    right(45)
    segment(2,unit)
    right(90)
    segment(1,unit)
    right(45)
    diagonal(3,unit)
    left(90)
    diagonal(3,unit)
    right(45)
    segment(1,unit)
    right(90)
    segment(2,unit)
    right(45)
    diagonal(2,unit)
    left(135)
    segment(2,unit)
    right(90)
    segment(2,unit)

    no_pen(1,unit)
    right(180)
def draw_letter_l(unit):
    left(90)
    forward(unit * 8)
    right(90)
    forward(unit * 2)
    right(90)
    forward(unit * 6)
    left(90)
    forward(unit * 6)
    right(90)
    forward(unit *2)
    right(90)
    forward(unit * 8)
    right(180)

def draw_letter_m(unit):
    pass

def draw_letter_n(unit):
    def draw_n_half(unit):
        forward(unit * 1.5)
        left(90)
        forward(unit * 3.5)
        right(164.054604)
        forward(unit * sqrt(13.25))
        left(74.054604)
        forward(unit * 1.5)
        left(90)
        forward(unit *8)

    fly(unit * 2)
    draw_n_half(unit)  
    left(90)  
    draw_n_half(unit)
    returnToHome(unit * 2)

def draw_letter_o(unit):
    left (90)
    forward (unit * 8)
    right(90)
    forward (unit * 4)
    right (90)
    forward (unit * 8)
    right (90)
    forward (unit * 4)
    penup ()
    right (90)
    forward (unit * 1)
    right (90)
    forward (unit * 1)
    pendown ()
    forward (unit * 2)
    left (90)
    forward (unit * 6)
    left (90)
    forward (unit * 2)
    left (90)
    forward (unit * 6)
    penup ()
    forward (unit * 1)
    right (90)
    forward (unit * 1)
    right (180)

def draw_letter_p(unit):
    circle(unit,90)  
    forward(6 * unit)
    circle(unit,90) 
    right(180)
    forward(5 * unit)
    circle(-2*unit,180)
    forward(2 * unit)
    left(90)
    forward(3 * unit)
    circle(unit,90)  
    left(180)
    forward(4 * unit)
    right(180)
    penup()
    forward(3 * unit)
    left(90)
    forward(7 * unit)
    right(90)
    pendown()
    forward(unit)
    circle(-unit,180)
    forward(unit)
    right(90)
    forward(2 * unit)
    penup()
    left(90)
    forward(3 * unit)
    left(90)
    forward(7 * unit)
    left(90)




def draw_letter_q(unit):
    penup()
    forward(3 * unit)
    pendown()
    forward(2 * unit)
    left(45)
    forward(sqrt(2) * unit / 2)
    penup()
    forward(sqrt(2) * unit / 2)
    pendown()
    forward(2 * sqrt(2) * unit)
    left(45)
    for i in range(3):
        forward(2 * unit)
        left(45)
        forward(3 * sqrt(2) * unit)
        left(45)
    penup()
    forward(unit)
    left(90)
    forward(unit)
    right(45)
    for i in range(2):
        pendown()
        forward(sqrt(2) * unit)
        penup()
        forward(sqrt(2) * unit)
        pendown()
        forward(sqrt(2) * unit)
        left(90)
    for i in range(2):
        forward(3 * sqrt(2) * unit)
        left(90)
    forward(sqrt(2) * unit)
    left(45)
    forward(4 * unit)
    right(135)
    penup()
    forward(sqrt(2) * unit)
    right(45)
    pendown()
    forward(2 * unit)
    penup()
    forward(2 * unit)
    pendown()
    left(45)
    forward(sqrt(2) * unit)
    right(135)
    forward(unit)
    right(45)
    forward(sqrt(2) * unit / 2)
    penup()
    left(90)
    forward(sqrt(2) * unit / 2)
    right(45)
    forward(5 * unit)
    right(180)

def draw_letter_r(unit):
    fly(unit * 2)
    forward(unit * 1.5)
    left(90)
    forward(unit * 3.5)
    right(135)
    forward(unit * sqrt(2))
    right(45)
    forward(unit * 2.5)
    left(90)
    forward(unit * 1.5)
    left(90)
    forward(unit * 2.5)
    left(45)
    forward(unit * sqrt(2))
    right(90)
    forward(unit * sqrt(2))
    left(45)
    forward(unit * 2.5)
    left(45)
    forward(unit * sqrt(2))
    left(45)
    forward(unit * 3)
    left(135)
    fly(unit * 1.5 * sqrt(2))
    right(45)
    forward(unit * 1.5)
    left(90)
    forward(unit * .5)
    left(45)
    forward(unit * sqrt(2) * .5)
    left(45)
    forward(unit * .5)
    left(45)
    forward(unit* sqrt(2)*.5)
    left(45)
    forward(unit * .5)
    right(45)
    fly(unit * 1.5 * sqrt(2))
    left(135)
    forward(unit * 8)
    returnToHome(unit * 2)

def draw_letter_s(unit):
    pass

def draw_letter_t(unit):
    penup()
    forward(unit * 3)
    pendown()
    left(90)
    forward (unit * 7)
    left (90)
    forward (unit * 2)
    right (90)
    forward (unit * 1)
    right (90)
    forward (unit * 5)
    right (90)
    forward (unit * 1)
    right (90)
    forward (unit * 2)
    left (90)
    forward (unit * 7)
    right (90)
    forward (unit * 1)
    penup ()
    forward (unit * 3)
    left (180)

    
    

def draw_letter_u(unit):
    
    left (90)
    forward (unit * 8)
    right(90)
    forward (unit * 1)
    right (90)
    forward (unit * 7)
    left (90)
    forward (unit * 2)
    left (90)
    forward (unit * 7)
    right (90)
    forward (unit * 1)
    right (90)
    forward (unit * 8)
    right (90)
    forward (unit * 4)
    right (180)

def draw_letter_v(unit):
    pass

def draw_letter_w(unit):
    pass

def draw_letter_x(unit):
    pass

def draw_letter_y(unit):
    pass

def draw_letter_z(unit):
    penup()
    forward(3 * unit)
    left(90)
    forward(4 * unit)
    right(degrees(atan(2 / 3)))
    pendown()
    for i in range(2):
        forward(sqrt(13) * unit)
        left(90 + degrees(atan(2 / 3)))
        forward(4 * unit)
        right(90)
        forward(unit)
        right(90)
        forward(6 * unit)
        right(90)
        forward(unit)
        right(degrees(atan(2 / 3)))
        forward(sqrt(13) * unit)
    penup()
    right(90 - degrees(atan(2 / 3)))
    forward(unit / 2.0)
    left(90 - degrees(atan(2/3)))
    pendown()
    for i in range(2):
        forward(sqrt(13) * unit)
        right(90 - degrees(atan(2 / 3)))
        forward(unit)
        right(90 + degrees(atan(2 / 3)))
        forward(sqrt(13) * unit)
    left(90 + degrees(atan(2 / 3)))
    penup()
    forward(3.5 * unit)
    left(90)
    forward(4 * unit)
    left(90)