import numpy as np
import matplotlib.pyplot as plt
from numpy.polynomial.polynomial import Polynomial

points = [
  (0,1),
  (0.01,1.03),
  (0.02,1.03),
  (0.03,1.06),
  (0.04,1.18),
  (0.05,1.38),
  (0.06,1.63),
  (0.07,2.09),
  (0.08,2.69),
  (0.09,3.54),
  (0.1,4.79),
  (0.11,6.41),
  (0.12,8.9),
  (0.13,12.06),
  (0.14,16.36),
  (0.15,22.1),
  (0.16,29.48),
  (0.17,39.05),
  (0.18,50.99),
  (0.19,65.32),
  (0.2,81.79),
  (0.21,99.78),
  (0.22,117.72),
  (0.23,134.26),
  (0.24,146.9),
  (0.25,153.68)]
x = np.array([point[0] for point in points])
y = np.array([point[1] for point in points])

spl = Polynomial.fit(x, y, 16) # highest order without ringing
roots_arr = [0,0.10]
for n in range(1,5):
  dspl = spl.deriv(n)
  roots = dspl.roots()
  for r in roots:
    if isinstance(r,complex):
      if abs(r.imag) > 0.001:
        continue
      r = r.real
    if not (0.11 < r < 0.25):
      continue
    r = round(r, 2)
    if r == 0.24:
      continue
    roots_arr.append(r)
roots = np.array(roots_arr)

x_fine = np.linspace(0, 0.25, 1000)
y_fine = spl(x_fine)

# check fit
if False:
  y_spl_err = spl(x)-y
  plt.plot(x,y_spl_err,'.')
  plt.show()
  plt.plot(x_fine,y_fine,'-',x,y,'.')
  plt.show()

roots_y = spl(roots)
plt.plot(x_fine,y_fine,'-',roots,roots_y,'o')
plt.grid(False)
plt.axis('off')
for i in range(len(roots)):
    plt.annotate(f'{roots_y[i]:.0f}x @ {roots[i]:.2f}%', (roots[i], roots_y[i]), textcoords="offset points", xytext=(0,10), ha='right')
plt.savefig('BAC_driving_risk.svg')
plt.show()