import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from IPython.display import HTML

fig, ax = plt.subplots()

def update(num):
    if len(round_circles) > 0:
        round_circles.pop().remove()
        epicycloids.pop().remove()
        points.pop().remove()

    round_circle, = plt.plot(x_move[num]+xm, y_move[num]+ym, 'b-', lw=2)
    epicycloid, = plt.plot(x[:num+1] ,y[:num+1], 'g-', lw=2)
    point, = plt.plot(x[num], y[num], 'ko', markersize=4)

    round_circles.append(round_circle)
    epicycloids.append(epicycloid)
    points.append(point)

    theta_str = r'$\theta=$'
    ax.set_title(theta_str + str(theta[num]/np.pi)[:4] + str(r' $\pi$'))

ax.grid()
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_aspect('equal')

#plot data

theta = np.linspace(0, 4*np.pi,200)
phi= np.linspace(0,2*np.pi,100)

rc=5
rm=2

x = (rc+rm)*np.cos(theta)-rm*np.cos(theta*((rc+rm)/rm))
y = (rc+rm)*np.sin(theta)-rm*np.sin(theta*((rc+rm)/rm))
epicycloids=[]
points=[]

xm = rm*np.cos(phi)
ym = rm*np.sin(phi)
round_circles =[]

xc = rc*np.cos(phi)
yc = rc*np.sin(phi)
plt.plot(xc, yc, 'k-', lw=2)#center_circle

x_move = (rc+rm)*np.cos(theta)
y_move = (rc+rm)*np.sin(theta)

ani = animation.FuncAnimation(fig, update, 200, interval=100)
HTML(ani.to_html5_video())
#dpi=100
#ani.save('episaikuroid.mp4', writer="ffmpeg",dpi=dpi)