from turtle import Turtle
from numpy import cos, sin, pi

t = Turtle()
t.speed(100_000)


def jump2next(pt: tuple):
    t.penup()
    t.goto(pt)
    t.pendown()


def pol2dec(r: float, phi: float) -> tuple:
    x = r * cos(phi)
    y = r * sin(phi)
    return x, y


def draw_circle(radius: int, x0: int=0, y0: int=0) ->None:
    vertex_num = 10 + 5 * radius // 10
    x, y = pol2dec(radius, 0)
    jump2next((x0 + x, y0 + y))
    for vn in range(vertex_num + 1):
        angle = vn * 2 * pi / vertex_num
        x, y = pol2dec(radius, angle)
        t.goto((x0 + x,y0 + y))


def draw_flower(num_petal = 5, size=200, x0=0, y0=0):
    base_angle = 0
    max_petal = num_petal
    angle_inc = 2 * pi / max_petal
    flower_radius = size
    petal_radius = int(flower_radius * sin(angle_inc / 2))
    for petal_n in range(max_petal):
        angle = base_angle + petal_n * angle_inc
        x, y = pol2dec(flower_radius, angle)
        draw_circle(petal_radius, x0+x, y0+y)

draw_flower(5)
draw_flower(7, 150, 300, 300)
draw_flower(5, 10, -300, -300)