import matplotlib.pyplot as plt
import numpy as np
from scipy.spatial import ConvexHull

#a = [0, 1, 1j, 0.7+0.8j]
#a = [0, 1, 2, 3, 4]
#a = [0, 1] * 3
#a = [0, 1, .5+.5j*3**.5] * 30
a = [0, 1, 2] * 30

p = np.array([1])


for i, ai in enumerate(a):
    p = np.polyint(p)
    p = np.polysub(p, np.polyval(p, ai))

    r = np.roots(p)
    plt.plot(np.real(r), np.imag(r), 'o', label=str(ai))
    print('p', p, 'r', r)

    if i == 0:
        continue
    elif i == 1:
        plt.fill(np.real(r), np.imag(r), edgecolor="#000000", alpha=0.5)
    else:
        if i < 5 or i % 20 != 0: continue
        points = np.reshape(np.concatenate([np.real(r), np.imag(r)]),
                            (len(r), 2), order='F')
        hull = ConvexHull(points)
        print('vert', hull.vertices)
        plt.fill(points[hull.vertices, 0], points[hull.vertices, 1],
                 alpha=0.3)

#plt.legend()
plt.show()