# 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 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):
    pass

def draw_letter_d(unit):
    pass

def draw_letter_e(unit):
    pass

def draw_letter_f(unit):
    pass

def draw_letter_g(unit):
    pass

def draw_letter_h(unit):
    pass

def draw_letter_i(unit):
    pass

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):
    pass

def draw_letter_l(unit):
    pass

def draw_letter_m(unit):
    pass

def draw_letter_n(unit):
    pass

def draw_letter_o(unit):
    pass

def draw_letter_p(unit):
    pass

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):
    pass

def draw_letter_s(unit):
    pass

def draw_letter_t(unit):
    pass

def draw_letter_u(unit):
    pass

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)