import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D import matplotlib.animation as animation

duration = 5 total_frames = duration * 24 frame_interval = 1000 / 24

x = np.linspace(-2, 2, 100) y = np.linspace(-2, 2, 100) x, y = np.meshgrid(x, y) z_surface = x**2 - y**2

1. Function to update the plot for animation

def update(num, ax, fig):

   ax.clear()
   h = np.linspace(-1, 1, total_frames)[num]

   # Plot the surface
   ax.plot_surface(x, y, z_surface, color='blue', alpha=0.7)

   # Plot the plane
   ax.plot_surface(x, y, np.full_like(z_surface, h), color='green', alpha=0.5)

   # Calculate and plot intersections
   intersection_y = np.linspace(-2, 2, 100)
   intersection_x1 = np.sqrt(intersection_y**2 + h)
   intersection_x2 = -np.sqrt(intersection_y**2 + h)
   ax.plot(intersection_x1, intersection_y, h, color='red')
   ax.plot(intersection_x2, intersection_y, h, color='red')

   # Remove the x, y, z axes and grid
   ax.set_axis_off()

1. Create figure and axis

fig = plt.figure(figsize=(10, 10)) ax = fig.add_subplot(111, projection='3d')

ani = animation.FuncAnimation(fig, update, frames=total_frames, fargs=(ax, fig), interval=frame_interval)

from matplotlib.animation import FFMpegWriter writer = FFMpegWriter(fps=24, codec='libvpx', extra_args=['-vcodec', 'vp9']) ani.save('dupin_indicatrix.webm', writer=writer)