# typeface.py
# By Chris Proctor and Tristan Gaeta

# 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 (pos, teleport, goto)

class Point(tuple):
    "Class for doing element-wise arithmetic on tuples"
    def __add__(self, other):
        return Point((x + y for x, y in zip(self, other)))
    
    def __sub__(self, other):
        return Point((x - y for x, y in zip(self, other)))
    
    def __rmul__(self, other):
        return Point((other * x for x in self))
    
    def __truediv__(self, other):
        return Point((x / other for x in self))
    
def bezier(t, *points: tuple[float, ...]) -> Point:
    "Recursive definition of a Bezier curve"
    assert(len(points) > 0)
    if len(points) == 1:
        return Point(points[0])
    return (1-t) * bezier(t, *points[0:-1]) + t * bezier(t, *points[1:])

def draw_bezier(unit, segments, *points: tuple[float, ...]):
    "Draws bezier and returns turtle to initial position"
    segments = int(unit * (segments / 40)) 
    origin = pos()
    points = tuple(origin + unit * Point(x) for x in points)
    
    teleport(*points[0])
    for i in range(0, segments + 1):
        bz = bezier(i / segments, *points)
        goto(bz)
        
    teleport(*origin)
    

def draw_letter_a(unit):
    pass

def draw_letter_b(unit):
    pass

def draw_letter_c(unit):
    draw_bezier(unit, 160,
                (7, 7),
                (0.5, 11.88),
                (0.5, -3.88),
                (7, 1))

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):
    pass

def draw_letter_k(unit):
    pass

def draw_letter_l(unit):
    draw_bezier(unit, 100, 
                (1, 8), 
                (5.27, -6.66), 
                (-5.94, 4.27), 
                (7, 0))

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):
    pass

def draw_letter_r(unit):
    pass

def draw_letter_s(unit):
    pass

def draw_letter_t(unit):
    pass

def draw_letter_u(unit):
    draw_bezier(unit, 100,
                (1, 8),
                (0, -2.5),
                (8, -2.5),
                (7, 8))

def draw_letter_v(unit):
    draw_bezier(unit, 80,
                (1, 8),
                (4, -0.33),
                (3.44, -4.33),
                (7, 8))

def draw_letter_w(unit):
    pass

def draw_letter_x(unit):
    pass

def draw_letter_y(unit):
    pass

def draw_letter_z(unit):
    pass