Python编程使用matplotlib绘制动态圆锥曲线示例 Python编程使用matplotlib绘制动态

椭圆
双曲线
抛物线
极坐标方程

作为让高中生心脏骤停的四个字，对于高考之后的人来说可谓刻骨铭心，所以定义不再赘述，直接撸图，其标准方程分别为

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在Python中，绘制动图需要用到matplotlib中的animation包，其调用方法以及接下来要用到的参数为

ani = animation.FuncAnimation(fig, func, frames, interval)

其中fig为绘图窗口，func为绘图函数，其返回值为图像，frames为迭代参数，如果为整型的话，其迭代参数则为range(frames)。

椭圆为了绘图方便，椭圆的参数方程为

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代码为：

# 这三个包在后面的程序中不再复述import numpy as npimport matplotlib.pyplot as pltimport matplotlib.animation as animationa,b,c = 5,3,4fig = plt.figure(figsize=(12,9))ax = fig.add_subplot(autoscale_on=False, xlim=(-a,a),ylim=(-b,b))ax.grid()line, = ax.plot([],[],'o-',lw=2)trace, = ax.plot([],[],'-', lw=1)theta_text = ax.text(0.02,0.85,'',transform=ax.transAxes)textTemplate = '''theta = %.1f°\nlenL = %.1f, lenR = %.1f\nlenL+lenR = %.1f'''xs,ys = [], []def animate(i):if(i==0):xs.clear()ys.clear()theta = i*0.04x = a*np.cos(theta)y = b*np.sin(theta)xs.append(x)ys.append(y)line.set_data([-c,x,c], [0,y,0])trace.set_data(xs,ys)lenL = np.sqrt((x+c)**2+y**2)lenR = np.sqrt((x-c)**2+y**2)theta_text.set_text(textTemplate % (180*theta/np.pi, lenL, lenR, lenL+lenR))return line, trace, theta_textani = animation.FuncAnimation(fig, animate, 157, interval=5, blit=True)ani.save("ellipse.gif")plt.show()

双曲线双曲线的参数方程为

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设 a = 4 , b = 3 , c = 5 则代码如下

a,b,c = 4,3,5fig = plt.figure(figsize=(12,9))ax = fig.add_subplot(autoscale_on=False, xlim=(-c,16),ylim=(-12,12))ax.grid()line, = ax.plot([],[],'o-',lw=2)trace, = ax.plot([],[],'-', lw=1)theta_text = ax.text(0.01,0.85,'',transform=ax.transAxes)textTemplate = '''t = %.1f\nlenL = %.1f, lenR = %.1f\nlenL-lenR = %.1f'''xs,ys = [],[]def animate(t):if(t==-3):xs.clear()ys.clear()x = a*np.cosh(t)y = b*np.sinh(t)xs.append(x)ys.append(y)line.set_data([-c,x,c], [0,y,0])trace.set_data(xs,ys)lenL = np.sqrt((x+c)**2+y**2)lenR = np.sqrt((x-c)**2+y**2)theta_text.set_text(textTemplate % (t, lenL, lenL, lenL-lenR))return line, trace, theta_textframes = np.arange(-3,3,0.05)ani = animation.FuncAnimation(fig, animate, frames, interval=5, blit=True)ani.save("hyperbola.gif")plt.show()

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抛物线

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import numpy as npimport matplotlib.pyplot as pltimport matplotlib.animation as animationa,b,c = 4,3,5p = 1fig = plt.figure(figsize=(12,9))ax = fig.add_subplot(autoscale_on=False, xlim=(-0.6,4.5),ylim=(-3,3))ax.grid()ax.plot([-p/2,-p/2],[-5,5],'-',lw=2)line, = ax.plot([],[],'o-',lw=2)trace, = ax.plot([],[],'-', lw=1)theta_text = ax.text(0.05,0.85,'',transform=ax.transAxes)textTemplate = '''y = %.1f\nlenL = %.1f, lenF = %.1f\nlenL-lenF = %.1f'''xs,ys = [],[]def animate(y):if(y==-3):xs.clear()ys.clear()x = y**2/p/2xs.append(x)ys.append(y)line.set_data([-p,x,p/2], [y,y,0])trace.set_data(xs,ys)lenL = x+p/2lenF = np.sqrt((x-p/2)**2+y**2)theta_text.set_text(textTemplate % (y, lenL, lenF, lenL-lenF))return line, trace, theta_textframes = np.arange(-3,3,0.1)ani = animation.FuncAnimation(fig, animate, frames, interval=5, blit=True)ani.save("parabola.gif")plt.show()

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极坐标方程圆锥曲线在极坐标系下有相同的表达式，即

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在matplotlib中，极坐标图像需要通过projection='polar'来标识，其代码为

p = 2fig = plt.figure(figsize=(12,9))ax = fig.add_subplot(autoscale_on=False, projection='polar')ax.set_rlim(0,8)trace, = ax.plot([],[],'-', lw=1)theta_text = ax.text(0.05,0.95,'',transform=ax.transAxes)textTemplate = 'e = %.1f\n'theta = np.arange(-3.1,3.2,0.1)def animate(e):rho = p/(1-e*np.cos(theta))trace.set_data(theta,rho)theta_text.set_text(textTemplate % e)return trace, theta_textframes = np.arange(-2,2,0.1)ani = animation.FuncAnimation(fig, animate, frames, interval=100, blit=True)ani.save("polar.gif")plt.show()