在Python Funcanimation中进行褪色的踪迹

Question

我有以下代码，该代码使用第四阶runge kutta来求解双子摆的运动方程。我试图使用Funcanimation来动画两个摆的位置。我尝试删除每个坐标列表的0个元素，然后每10个新元素被绘制。我认为这会产生褪色的跟踪效果。相反，它只是绘制了一分。 （注意X1和Y1是第一个摆的坐标，而X2和Y2是第二个耦合摆的坐标）我觉得自己已经使事情变得复杂了。当我删除时，如果我％10 == 1：循环循环代码良好，但不会删除任何以前的点。我觉得这应该很容易做到，但是我找不到任何直截了当的示例，并且文档并不非常有用。

简而言之，我有4个坐标列表来描述两个对象的位置。我想对这两个对象的当前位置进行动画，而不是任何以前的位置。

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.animation as animation
from matplotlib.animation import FuncAnimation 
from itertools import count
from IPython import display

h=.001
t=0
l1=1
l2=1
m1=1
m2=1
theta1= 0
theta2 = np.pi/2
thetadot1=0
thetadot2=0
g=9.8
x1=[]
y1=[]
x2=[]
y2=[]
E=[]
T=[]
Theta_dot1=[]
Theta_dot2=[]
kinetic_energy=[]
potential_energy=[]



    
while(t<4):

    KE = .5*m1*((thetadot1*l1*np.cos(theta1))**2+(thetadot1*l1*np.sin(theta1))**2) + .5*m2*((thetadot1*l1*np.cos(theta1)+thetadot2*l2*np.cos(theta2))**2+(thetadot1*l1*np.sin(theta1)+thetadot2*l2*np.sin(theta2))**2)
    PE = (m1*g*(l1-l1*np.cos(theta1))+m2*g*(l1+l2-l1*np.cos(theta1)-l2*np.cos(theta2))) 
    E.append(KE+PE)
    kinetic_energy.append(KE)
    potential_energy.append(PE)
    Theta_dot1.append(thetadot1)
    Theta_dot2.append(thetadot2)
        
    T.append(t)
    x1.append(l1*np.sin(theta1))
    y1.append(-l1*np.cos(theta1))
    x2.append(l1*np.sin(theta1)+l2*np.sin(theta2))
    y2.append(-l1*np.cos(theta1)-l2*np.cos(theta2))

    P1 = (-g*(2*m1+m2)*np.sin(theta1)-m2*g*np.sin(theta1-2*theta2)-2*np.sin(theta1-theta2)*m2*(l2*thetadot2**2+l1*thetadot1**2*(np.cos(theta1-theta2))))/(l1*(2*m1+m2*(1-np.cos(2*(theta1-theta2)))))
    L1 = (2*np.sin(theta1-theta2)*(l1*thetadot1**2*(m1+m2)+np.cos(theta1)*g*(m1+m2)+l2*m2*thetadot2**2*np.cos(theta1-theta2)) )/(l2*(2*m1+m2*(1-np.cos(2*(theta1-theta2)))))
    G1 = thetadot1
    H1 = thetadot2
    
    

    thetadot1_1     = thetadot1     + (h/2)*P1
    thetadot2_1     = thetadot2     + (h/2)*L1
    theta1_1        = theta1        + (h/2)*G1
    theta2_1        = theta2        + (h/2)*H1
 
    
    
    P2 = (-g*(2*m1+m2)*np.sin(theta1_1)-m2*g*np.sin(theta1_1-2*theta2_1)-2*np.sin(theta1_1-theta2_1)*m2*(l2*thetadot2_1**2+l1*thetadot1_1**2*(np.cos(theta1_1-theta2_1))))/(l1*(2*m1+m2*(1-np.cos(2*(theta1_1-theta2_1)))))
    L2 = (2*np.sin(theta1_1-theta2_1)*(l1*thetadot1_1**2*(m1+m2)+np.cos(theta1_1)*g*(m1+m2)+l2*m2*thetadot2_1**2*np.cos(theta1_1-theta2_1)) )/(l2*(2*m1+m2*(1-np.cos(2*(theta1_1-theta2_1)))))
    G2 = thetadot1_1
    H2 = thetadot2_1
    
    thetadot1_2     = thetadot1_1     + (h/2)*P2
    thetadot2_2     = thetadot2_1     + (h/2)*L2
    theta1_2        = theta1_1        + (h/2)*G2
    theta2_2        = theta2_1        + (h/2)*H2
    
    P3 =  (-g*(2*m1+m2)*np.sin(theta1_2)-m2*g*np.sin(theta1_2-2*theta2_2)-2*np.sin(theta1_2-theta2_2)*m2*(l2*thetadot2_2**2+l1*thetadot1_2**2*(np.cos(theta1_2-theta2_2))))/(l1*(2*m1+m2*(1-np.cos(2*(theta1_2-theta2_2)))))
    L3 = (2*np.sin(theta1_2-theta2_2)*(l1*thetadot1_2**2*(m1+m2)+np.cos(theta1_2)*g*(m1+m2)+l2*m2*thetadot2_2**2*np.cos(theta1_2-theta2_2)) )/(l2*(2*m1+m2*(1-np.cos(2*(theta1_2-theta2_2)))))
    G3 = thetadot1_2
    H3 = thetadot2_2
    
    thetadot1_3     = thetadot1_2     + (h/2)*P3
    thetadot2_3     = thetadot2_2     + (h/2)*L3
    theta1_3        = theta1_2        + (h/2)*G3
    theta2_3        = theta2_2        + (h/2)*H3
    
    
    P4 = (-g*(2*m1+m2)*np.sin(theta1_3)-m2*g*np.sin(theta1_3-2*theta2_3)-2*np.sin(theta1_3-theta2_3)*m2*(l2*thetadot2_3**2+l1*thetadot1_3**2*(np.cos(theta1_3-theta2_3))))/(l1*(2*m1+m2*(1-np.cos(2*(theta1_3-theta2_3)))))
    L4 = (2*np.sin(theta1_3-theta2_3)*(l1*thetadot1_3**2*(m1+m2)+np.cos(theta1_3)*g*(m1+m2)+l2*m2*thetadot2_3**2*np.cos(theta1_3-theta2_3)) )/(l2*(2*m1+m2*(1-np.cos(2*(theta1_3-theta2_3))))) 
    G4 = thetadot1_3
    H4 = thetadot2_3
    
    
    
 
    thetadot1   = thetadot1  + (h/6.0) * (P1+(2.*P2)+(2.0*P3) + P4)
    thetadot2   = thetadot2  + (h/6.0) * (L1+(2.*L2)+(2.0*L3) + L4)
    theta1      = theta1     + (h/6.0) * (G1+(2.*G2)+(2.0*G3) + G4)
    theta2      = theta2     + (h/6.0) * (H1+(2.*H2)+(2.0*H3) + H4)
    t=t+h 
 
    





fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize = (15,5))
axes.set_ylim(-2.5, 2.5)
axes.set_xlim(-2.5, 2.5)
plt.style.use("ggplot")


x_1,y_1,x_2,y_2 = [], [], [], []
def animate(i):
    
    
    
    if i % 10 ==1:     #this is the stuff that is not working
        x_1.remove(0) 
        y_1.remove(0)
        x_2.remove(0)
        y_2.remove(0)
   
    x_1.append(x1[i*10])
    y_1.append(y1[i*10])
    x_2.append(x2[i*10])
    y_2.append(y2[i*10])
    

    
    axes.plot(x_1,y_1,'.', color="red")
    axes.plot(x_2,y_2,'.', color="gray", linewidth=0.5)
    
    
    
anim = FuncAnimation(fig, animate, interval=.1)

Answer 1

如果您想要褪色线，则必须处理linecollection的额外复杂性，这很难主化。

import matplotlib.colors as colors
from matplotlib.collections import LineCollection
from matplotlib.lines import Line2D

n_points_to_render = 500
# opacity of the segments
alphas = np.linspace(0, 1, n_points_to_render)

# create "solid" color maps with a varying opacity
red = colors.to_rgb("red") + (0.0,)
redfade = colors.LinearSegmentedColormap.from_list('my', [red, "red"])
green = colors.to_rgb("green") + (0.0,)
greenfade = colors.LinearSegmentedColormap.from_list('my', [green, "green"])

def get_segments(i):
    # LineCollection requires segments
    _x1 = x1[i:i+n_points_to_render]
    _y1 = y1[i:i+n_points_to_render]
    _x2 = x2[i:i+n_points_to_render]
    _y2 = y2[i:i+n_points_to_render]
    points1 = np.vstack((_x1, _y1)).T.reshape(-1, 1, 2)
    segments1 = np.hstack((points1[:-1], points1[1:]))
    points2 = np.vstack((_x2, _y2)).T.reshape(-1, 1, 2)
    segments2 = np.hstack((points2[:-1], points2[1:]))
    return segments1, segments2

fig, ax = plt.subplots(nrows = 1, ncols = 1)
ax.set_ylim(-2.5, 2.5)
ax.set_xlim(-2.5, 2.5)
plt.style.use("ggplot")

# create and add two LineCollections
segments1, segments2 = get_segments(0)
lc1 = LineCollection(segments1, array=alphas, cmap=redfade, lw=2)
lc2 = LineCollection(segments2, array=alphas, cmap=greenfade, lw=2)
line1 = ax.add_collection(lc1)
line2 = ax.add_collection(lc2)

def animate(i):
    segments1, segments2 = get_segments(i)
    line1.set_segments(segments1)
    line2.set_segments(segments2)

# create a legend as LineCollection doesn't have any by default
l1_legend = Line2D([0, 1], [0, 1], color="r", linewidth=2)
l2_legend = Line2D([0, 1], [0, 1], color="g", linewidth=2)
ax.legend([l1_legend, l2_legend], ['Line 1', 'Line 2'])

anim = FuncAnimation(fig, animate, frames=len(x1) - n_points_to_render, interval=30)
plt.show()