#! /usr/bin/env python

from typing import Final
from math import pi, cos
import turtle

amplitude: tuple[float, float] = (1, 1)
# frequent
omega: tuple[float, float] = (-1, -2)
# phase
phi: tuple[float, float] = (pi/2, 3*pi/4)

# Diskretisieren
N: Final[int] = 360
step = (2*pi) / N
T = [k * step for k in range(N)]
points = [(
        amplitude[0] * cos(omega[0]*t + phi[0]),
        amplitude[1] * cos(omega[1]*t + phi[1])
    ) for t in T
]

# Plot with turtle
(canvaswidth, canvasheight) = turtle.screensize()
point_size = 3
# scale up
x_factor = (canvaswidth / 2) / amplitude[0]
y_factor = (canvasheight / 2) / amplitude[1]
print(x_factor, y_factor)
# as fast as possible
turtle.speed(0)
turtle.pendown()
for p in points:
    x = x_factor * p[0]
    y = y_factor * p[1]
    turtle.teleport(x, y)
    turtle.dot(point_size)

turtle.done()