Python编程使用matplotlib绘制动态圆锥曲线示例
目录
- 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
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
代码为:
# 这三个包在后面的程序中不再复述 import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation a,b,c = 5,3,4 fig = 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°\n lenL = %.1f, lenR = %.1f\n lenL+lenR = %.1f''' xs,ys = [], [] def animate(i): if(i==0): xs.clear() ys.clear() theta = i*0.04 x = 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_text ani = 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
设 a = 4 , b = 3 , c = 5 则代码如下
a,b,c = 4,3,5 fig = 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\n lenL = %.1f, lenR = %.1f\n lenL-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_text frames = np.arange(-3,3,0.05) ani = animation.FuncAnimation(fig, animate, frames, interval=5, blit=True) ani.save("hyperbola.gif") plt.show()
抛物线
import numpy as np import matplotlib.pyplot as plt import matplotlib.animation as animation a,b,c = 4,3,5 p = 1 fig = 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\n lenL = %.1f, lenF = %.1f\n lenL-lenF = %.1f''' xs,ys = [],[] def animate(y): if(y==-3): xs.clear() ys.clear() x = y**2/p/2 xs.append(x) ys.append(y) line.set_data([-p,x,p/2], [y,y,0]) trace.set_data(xs,ys) lenL = x+p/2 lenF = np.sqrt((x-p/2)**2+y**2) theta_text.set_text(textTemplate % (y, lenL, lenF, lenL-lenF)) return line, trace, theta_text frames = np.arange(-3,3,0.1) ani = animation.FuncAnimation(fig, animate, frames, interval=5, blit=True) ani.save("parabola.gif") plt.show()
极坐标方程
圆锥曲线在极坐标系下有相同的表达式,即
在matplotlib
中,极坐标图像需要通过projection='polar'
来标识,其代码为
p = 2 fig = 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_text frames = np.arange(-2,2,0.1) ani = animation.FuncAnimation(fig, animate, frames, interval=100, blit=True) ani.save("polar.gif") plt.show()
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