autointerseccao.py

import numpy as np
import math
import matplotlib.pyplot as plt

min = 0
max = 2*math.pi
precision = 3

def x(t):
  return round(12*math.cos(t) - 6*math.cos(6*t), precision)

def y(t):
  return round(12*math.sin(t) - 6*math.sin(6*t), precision)

pontos = []
autointerseccao = []

for t in np.arange(min, max, 1/10**precision):
  ponto = (x(t), y(t), t)

  for p in pontos[:-5]:
    if math.isclose(p[0], ponto[0], abs_tol=(1/10**precision)*20) and math.isclose(p[1], ponto[1], abs_tol=(1/10**precision)*20):
      autointerseccao.append((p[2], t))

  pontos.append(ponto)

[(0.874, 1.6400000000000001),
 (2.13, 2.896),
 (3.387, 4.1530000000000005),
 (4.644, 5.41),
 (0.383, 5.9)]