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demo_19.py
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import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from matplotlib.widgets import Slider, Button
interval = 50 # ms, time between animation frames
fig, ax = plt.subplots(figsize=(6,6))
plt.subplots_adjust(left=0.15, bottom=0.35)
ax.set_aspect('equal')
plt.xlim(-1.6*40,1.7*2*40)
plt.ylim(-1.6*40,1.7*40)
#plt.grid()
t = np.linspace(0, 2*np.pi, 2000)
t1 = np.linspace(90*np.pi/180.0, 270*np.pi/180.0, 2000)
t2 = np.linspace(-90*np.pi/180.0, 90*np.pi/180.0, 2000)
delta = 1
m1, = ax.plot([0], [0],'k-')
m2, = ax.plot([0], [0],'k-')
def draw_circle(n1,D):
RD=D/2
n = (n1) * 2 +1
rm = (RD/(n))
# draw arc1
x1 = (RD+rm)*np.cos(t1)
y1 = (RD+rm)*np.sin(t1)
m1.set_data(x1,y1)
x2 = D - 2*rm + (RD+rm)*np.cos(t2)
y2 = (RD+rm)*np.sin(t2)
m2.set_data(x2,y2)
##hypocycloidA:
num_hypocycloidA = 50
hypocycloidA = [ax.plot([0],[0],'r-')[0] for n in range(num_hypocycloidA)]
num_hypocycloidA1 = 50
hypocycloidA1 = [ax.plot([0],[0],'r-')[0] for n in range(num_hypocycloidA1)]
def hypocycloidA_init():
for eh in hypocycloidA:
eh.set_data([0], [0])
for eh in hypocycloidA1:
eh.set_data([0], [0])
def update_hypocycloidA(n1,D,phis):
RD=D/2
n = (n1) * 2 +1
rc = (n-1)*(RD/(n))
rm = (RD/(n))
t1 = np.linspace(0, 2*np.pi/(n-1), 2000)
t2 = np.linspace(-2*np.pi/(n-1), 0, 2000)
for i in range(int((n-1)/2)):
xa = (rc+rm)*np.cos(t1)-rm*np.cos((rc+rm)/rm*t1)
ya = (rc+rm)*np.sin(t1)-rm*np.sin((rc+rm)/rm*t1)
x = (xa )*np.cos(-phis/((n-1)/2) -np.pi/(n-1) - (4*i)*np.pi/(n-1))-(ya )*np.sin(-phis/((n-1)/2) -np.pi/(n-1) - (4*i)*np.pi/(n-1))
y = (xa )*np.sin(-phis/((n-1)/2) -np.pi/(n-1) - (4*i)*np.pi/(n-1))+(ya )*np.cos(-phis/((n-1)/2) -np.pi/(n-1) - (4*i)*np.pi/(n-1))
hypocycloidA[i].set_data(x,y)
xa1 = (rc-rm)*np.cos(t2)+rm*np.cos((rc-rm)/rm*t2)
ya1 = (rc-rm)*np.sin(t2)-rm*np.sin((rc-rm)/rm*t2)
x1 = (xa1 )*np.cos(-phis/((n-1)/2) -np.pi/(n-1) + (4*i)*np.pi/(n-1))-(ya1 )*np.sin(-phis/((n-1)/2) -np.pi/(n-1) + (4*i)*np.pi/(n-1))
y1 = (xa1 )*np.sin(-phis/((n-1)/2) -np.pi/(n-1) + (4*i)*np.pi/(n-1))+(ya1 )*np.cos(-phis/((n-1)/2) -np.pi/(n-1) + (4*i)*np.pi/(n-1))
hypocycloidA1[i].set_data(x1,y1)
##hypocycloidB:
num_hypocycloidB = 50
hypocycloidB = [ax.plot([0],[0],'b-')[0] for n in range(num_hypocycloidB)]
num_hypocycloidB1 = 50
hypocycloidB1 = [ax.plot([0],[0],'b-')[0] for n in range(num_hypocycloidB1)]
def hypocycloidB_init():
for eh in hypocycloidB:
eh.set_data([0], [0])
for eh in hypocycloidB1:
eh.set_data([0], [0])
def update_hypocycloidB(n1,D, phis):
RD=D/2
n = (n1) * 2 +1
rc = (n-1)*(RD/(n))
rm = (RD/(n))
t1 = np.linspace(0, 2*np.pi/(n-1), 2000)
t2 = np.linspace(-2*np.pi/(n-1), 0, 2000)
for i in range(int((n-1)/2)):
xa = (rc+rm)*np.cos(t1)-rm*np.cos((rc+rm)/rm*t1)
ya = (rc+rm)*np.sin(t1)-rm*np.sin((rc+rm)/rm*t1)
xa1 = (rc-rm)*np.cos(t2)+rm*np.cos((rc-rm)/rm*t2)
ya1 = (rc-rm)*np.sin(t2)-rm*np.sin((rc-rm)/rm*t2)
if (n1)%2 != 1:
x = (xa )*np.cos(phis/((n-1)/2) +np.pi/(n-1) - (4*i)*np.pi/(n-1))-(ya )*np.sin(phis/((n-1)/2) +np.pi/(n-1) - (4*i)*np.pi/(n-1)) + D - 2*rm
y = (xa )*np.sin(phis/((n-1)/2) +np.pi/(n-1) - (4*i)*np.pi/(n-1))+(ya )*np.cos(phis/((n-1)/2) +np.pi/(n-1) - (4*i)*np.pi/(n-1))
hypocycloidB[i].set_data(x,y)
x1 = (xa1 )*np.cos(phis/((n-1)/2) +np.pi/(n-1) + (4*i)*np.pi/(n-1))-(ya1 )*np.sin(phis/((n-1)/2) +np.pi/(n-1) + (4*i)*np.pi/(n-1)) + D - 2*rm
y1 = (xa1 )*np.sin(phis/((n-1)/2) +np.pi/(n-1) + (4*i)*np.pi/(n-1))+(ya1 )*np.cos(phis/((n-1)/2) +np.pi/(n-1) + (4*i)*np.pi/(n-1))
hypocycloidB1[i].set_data(x1,y1)
if (n1)%2 == 1:
x = (xa )*np.cos(phis/((n-1)/2) +3*np.pi/(n-1) - (4*i)*np.pi/(n-1))-(ya )*np.sin(phis/((n-1)/2) +3*np.pi/(n-1) - (4*i)*np.pi/(n-1)) + D - 2*rm
y = (xa )*np.sin(phis/((n-1)/2) +3*np.pi/(n-1) - (4*i)*np.pi/(n-1))+(ya )*np.cos(phis/((n-1)/2) +3*np.pi/(n-1) - (4*i)*np.pi/(n-1))
hypocycloidB[i].set_data(x,y)
x1 = (xa1 )*np.cos(phis/((n-1)/2) +3*np.pi/(n-1) + (4*i)*np.pi/(n-1))-(ya1 )*np.sin(phis/((n-1)/2) +3*np.pi/(n-1) + (4*i)*np.pi/(n-1)) + D - 2*rm
y1 = (xa1 )*np.sin(phis/((n-1)/2) +3*np.pi/(n-1) + (4*i)*np.pi/(n-1))+(ya1 )*np.cos(phis/((n-1)/2) +3*np.pi/(n-1) + (4*i)*np.pi/(n-1))
hypocycloidB1[i].set_data(x1,y1)
axcolor = 'lightgoldenrodyellow'
ax_fm = plt.axes([0.25, 0.08, 0.5, 0.015], facecolor=axcolor)
ax_N = plt.axes([0.25, 0.06, 0.5, 0.015], facecolor=axcolor)
ax_D = plt.axes([0.25, 0.04, 0.5, 0.015], facecolor=axcolor)
sli_fm = Slider(ax_fm, 'fm', 10, 100, valinit=50, valstep=delta)
sli_N = Slider(ax_N, 'N', 2, 50, valinit=2, valstep=delta)
sli_D = Slider(ax_D, 'D', 5, 100, valinit=80,valstep=delta)
def update(val):
sN = sli_N.val
sD = sli_D.val
ax.set_xlim(-1.6*0.5*sD,1.7*sD)
ax.set_ylim(-1.6*0.5*sD,1.7*0.5*sD)
sli_fm.on_changed(update)
sli_N.on_changed(update)
sli_D.on_changed(update)
resetax = plt.axes([0.85, 0.01, 0.1, 0.04])
button = Button(resetax, 'Reset', color=axcolor, hovercolor='0.975')
def reset(event):
sli_fm.reset()
sli_N.reset()
sli_D.reset()
button.on_clicked(reset)
def animate(frame):
sfm = sli_fm.val
sN = sli_N.val
sD = sli_D.val
frame = frame+1
phi = 2*np.pi*frame/sfm
draw_circle(sN,sD)
hypocycloidA_init()
update_hypocycloidA(sN,sD, phi)
hypocycloidB_init()
update_hypocycloidB(sN,sD, phi)
fig.canvas.draw_idle()
ani = animation.FuncAnimation(fig, animate,frames=sli_fm.val*(sli_N.val-1), interval=interval)
dpi=100
plt.show()