PMAE 7 : regular star polygon

Python Matplotlib Animation Example7

regular star polygon

The Python code presented utilizes matplotlib to dynamically visualize a regular star polygon, employing mathematical principles to compute its coordinates. The getdata function calculates these coordinates based on the number of vertices (n) and a parameter (k) determining the star's density. Trigonometric functions are employed for computation. The update function dynamically updates the plot with generated coordinates as the animation progresses, controlled by the drawfig function for timing and theta calculation. Through the FuncAnimation class, the animation smoothly portrays the rotation of the star polygon, showcasing its geometric properties. This code exemplifies Python's capacity for mathematical visualization, facilitating both exploration and representation of complex geometric concepts in an interactive manner.

 

 

The Python code skillfully animates a regular star polygon by first leveraging a function called getdata to accurately compute the vertices of the star based on the desired number of points and a scaling factor. It then harnesses the power of Matplotlib for visualization, creating a clean and well-defined figure. The animation is achieved through a time-dependent loop that continuously updates the plot with a calculated portion of the star's points, masterfully generating the illusion of smooth rotation. This code showcases a deep understanding of both geometric principles and Python's plotting and animation tools, resulting in an informative and visually engaging experience.

Python source code   

import time import matplotlib.pyplot as plt import matplotlib.animation as animation from math import cos, sin, tan, pi fig = plt.figure(figsize=(3,3), facecolor="#FFFFFF") ax = plt.axes([0.0, 0.0, 1.0, 1.0]) ax.set_xlim([-1.2, 1.2]) ax.set_ylim([-1.2, 1.2]) ax.axis("off") def getdata(n, k): nth = 3000 dth = 2*pi/(nth-1) sth = 2*pi/n xs, ys = [], [] for ith in range(nth): theta = ith*dth rth = int(theta/sth)*sth x1 = cos(sth/2) y1 = tan(sth/2-(theta-rth))*x1 x2 = cos(sth/2*k) y2 = y1*(tan(sth/2*k)*x2)/(tan(sth/2)*x1) x3 = x2*cos(rth*k) + y2*sin(rth*k) y3 = -x2*sin(rth*k) + y2*cos(rth*k) xs.append(x3) ys.append(y3) xs.append(xs[0]) ys.append(ys[0]) return xs, ys pl = ax.plot([], [], color="#0000FF")[0] xs, ys = getdata(5, 2) def update(theta): ith = int(theta/(2*pi/(len(xs)-1))) pl.set_data(xs[0:ith+1], ys[0:ith+1]) def drawfig(i): P = 5.0 t = time.time() theta = t/P*2.0*pi%(2.0*pi) update(theta) ani = animation.FuncAnimation(fig, drawfig, interval=40) plt.show()

 ■ Import Necessary Libraries:

   • `time` for time-based operations
   • `matplotlib.pyplot` for creating visualizations
   • `matplotlib.animation` for animating the plot
   • `math` for mathematical functions

■  Figure Setup:
   • Create a figure with a white background and square dimensions.
   • Define axes with limits ranging from -1.2 to 1.2 for both x and y.
   • Turn off axis labels and ticks for visual clarity.

■  Polygon Data Generation (`getdata` Function):
   • Takes two parameters: the number of points (`n`) and a scaling factor (`k`).
   • Calculates the x and y coordinates of the star polygon's vertices using trigonometric functions and rotations.
   • Returns lists of x and y coordinates for the polygon.

■  Initial Plot Creation:
   • Create an empty plot with blue color for later updates.

■  Polygon Data Calculation:
   • Call `getdata` to generate coordinates for a 5-pointed star with scale factor 2.

■  Animation Loop (`drawfig` Function):
   • Calculate a time-dependent angle `theta`.
   • Call `update` to update the plot with a portion of the polygon based on `theta`.

■  Plot Update (`update` Function):
   • Determine how much of the polygon to display based on `theta`.
   • Set the plot's data to the calculated portion of coordinates.

■  Animation Initialization:
   • Create an animation using `matplotlib.animation.FuncAnimation`.
   • Call `drawfig` repeatedly for animation, with a 40-millisecond interval.

■  Show the Animation:
   • Display the animated plot using `plt.show()`.