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 在这里插入图片描述 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 1 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 在这里插入图片描述 在这里插入图片描述 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 在这里插入图片描述 Python客栈送红包、纸质书 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() 在这里插入图片描述 抛物线 在这里插入图片描述 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() 在这里插入图片描述 极坐标方程 圆锥曲线在极坐标系下有相同的表达式，即 在这里插入图片描述 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() 在这里插入图片描述 https://studygolang.com/tag/%E5%8D%8E%E7%BA%B3%E5%85%AC%E5%8F%B8%E5%BC%80%E6%88%B718313230473