# Epicicloid

Mar 27th, 2023
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1. import numpy as np
2. import matplotlib.pyplot as plt
3. import matplotlib.animation as animation
4.
5. R1 = 8
6. R2 = 8
7.
8. def circle(a, b, r):
9.     T = 100
10.     x, y = [0]*T, [0]*T
11.     for i,theta in enumerate(np.linspace(0,2*np.pi,T)):
12.         x[i] = a + r*np.cos(theta)
13.         y[i] = b + r*np.sin(theta)
14.     return x, y
15.
16.
17. def gen():
18.     for theta in np.linspace(0,15*np.pi,500):
19.         k = R1/R2
20.         a = R2 * (k + 1)*(np.cos(theta) - np.cos((k + 1) * theta )/ (k + 1))
21.         b = R2 * (k + 1)*(np.sin(theta) - np.sin((k + 1) * theta )/ (k + 1))
22.         yield a, b, (R1+R2) * np.cos(theta), (R1+R2) * np.sin(theta)
23.
24. fig = plt.figure(figsize=(6, 3))
26. ax.set_ylim(-20, 20)
27. ax.set_xlim(-20, 20)
28. ax.set_xlabel('x')
29. ax.set_ylabel('y')
30. ax.set_aspect('equal')
31. #ax.grid()
32. time_text = ax.text(0.05, 0.8, '', transform=ax.transAxes)
33.
34. cardiod, = ax.plot([], [], 'r-', lw=2)
35. line, = ax.plot([], [], 'y-', lw=2)
36. circle_line, = ax.plot([], [], 'g', lw=2)
37. circle_static, = ax.plot([], [], 'g', lw=2)
38. point, = ax.plot([], [], 'bo', ms=4)
39.
40. xx, yy = [], []
41.
42. def func(data):
43.     x, y, Rx, Ry = data
44.     xx.append(x)
45.     yy.append(y)
46.     cx, cy = circle(Rx, Ry, R2)
47.     c1_x, c1_y = circle(0, 0, R1)
48.
49.     cardiod.set_data(xx, yy)
50.     line.set_data((x, Rx), (y, Ry))
51.     circle_line.set_data(cx, cy)
52.     circle_static.set_data(c1_x, c1_y)
53.     point.set_data(x, y)
54.
55. ani = animation.FuncAnimation(fig, func, gen, blit=False, interval=50)
56. plt.show()
57. # fn = 'cacloid_FuncAnimation'
58. # #ani.save('%s.mp4'%(fn), writer='ffmpeg', fps=1000/50)
59. # xx, yy = [], []
60. # ani.save('%s.gif'%(fn), writer='imagemagick', fps=1000/50)
61.