12.3.10.1.13. 1D func animation

This example demonstrates how matplotlib can be used to create animated movie and export these in the mp4 movie format. It is shown here with some random generated 2d images, which ware plotted via matplotlib. By using the figure handle the animation is created. So you can plot your matplot figures in your own way and used some similar syntax to create an animation.

First of all you must install the matplotlib package, e.g. from https://pypi.org/project/matplotlib/

Then you must install the ffmpeg codec. A detailed description can be found on: http://blog.gregzaal.com/how-to-install-ffmpeg-on-windows/

The build version of the ffmpeg codec can be downloaded here: http://ffmpeg.zeranoe.com/builds/

Download and unzip the builds files to your harddrive. Typically the folder is like: C:Program filesffmpeg

The bin folder of ffmpeg must be added to the path variables of your system: C:Program filesffmpegbin

Finally start the command prompt and run the command: C:Program filesffmpegbinffmpeg.exe -codecs

or easier: ffmpeg -codecs

import numpy as np

Import namespaces

import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

Function to generate parametric plot

def parametric_plot(T, e):
    t = np.linspace(0, T, 1000)
    x = np.cos(-t)
    y = np.cos(-t + e)

    plt.plot(x, y, color="b")

    plt.xlim(-1.1, 1.1)
    plt.ylim(-1.1, 1.1)
    plt.gca().set_aspect("equal", adjustable="box")
    plt.title(f"T = {T:.2f}, e = {e:.2f}")

Function to calculate ellipse parameters

def calculate_ellipse_params(T, e):
    t = np.linspace(0, T, 1000)
    x = np.cos(-t)
    y = np.cos(-t + e)

    # Calculate width and height
    width = np.max(x) - np.min(x)
    height = np.max(y) - np.min(y)

    # Calculate covariance matrix
    covariance_matrix = np.cov(x, y)

    # Calculate eigenvalues and eigenvectors
    eigenvalues, eigenvectors = np.linalg.eig(covariance_matrix)

    # Get angle of rotation (angle of major axis with respect to x-axis)
    major_axis_index = np.argmax(eigenvalues)
    major_axis_vector = eigenvectors[:, major_axis_index]
    angle_rad = np.arctan2(major_axis_vector[1], major_axis_vector[0])
    angle_deg = np.degrees(angle_rad)

    return width, height, angle_deg

Calculate ellipse parameters for a full oscillation

T_full = 2 * np.pi
e_full = 45
width, height, angle_deg = calculate_ellipse_params(T_full, e_full)

# Create figure and plot ellipse
fig, ax = plt.subplots()


# Setting up the animation
def update(frame):
    ax.clear()
    parametric_plot(frame, e)


e = 45
ani = FuncAnimation(
    fig, update, frames=np.linspace(0.01, T_full, 100), repeat=True, interval=50
)

plt.show()

Once Loop Reflect