sheets.py

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

sheet_length = 4
l_values = []
packing_factors = []

def get_height(L):
    return np.sqrt(4 - (L/2)**2)

def plot_frame(L):
    plt.clf()
    
    ax1 = plt.subplot(211)
    ax2 = plt.subplot(212)
    
    ax1.set_facecolor('#f0f0f0')
    
    height = get_height(L)
    max_height = get_height(2.01)
    
    # Bottom circles
    for i in range(-1, sheet_length * 2):
        bot_circle = plt.Circle((i * L, 0), 1, fill=True, color='royalblue')
        bot_circle_edge = plt.Circle((i * L, 0), 1, fill=False, color='navy', linewidth=1.5, alpha=0.8)
        ax1.add_artist(bot_circle)
        ax1.add_artist(bot_circle_edge)

    # Top circles
    for i in range(sheet_length * 2):
        top_circle = plt.Circle((i * L - L/2, height), 1, fill=True, color='indianred')
        top_circle_edge = plt.Circle((i * L - L/2, height), 1, fill=False, color='darkred', linewidth=1.5, alpha=0.8)
        ax1.add_artist(top_circle)
        ax1.add_artist(top_circle_edge)

    # Bottom rectangle
    bot_rect = plt.Rectangle((-100, 0), 300, -100, fill=True, color='royalblue')
    ax1.add_artist(bot_rect)
    
    # Top rectangle
    top_rect = plt.Rectangle((-100, height), 300, 100, fill=True, color='indianred')
    ax1.add_artist(top_rect)

    packing_factor = L * height - np.pi * 1**2
    
    l_values.append(L)
    packing_factors.append(packing_factor)

    max_width = 3.45 * sheet_length - 3.45/2
    ax1.set_xlim(-1, max_width)
    ax1.set_ylim(-0.1, max_height + 0.1)
    ax1.set_aspect('equal', adjustable='box')
    ax1.grid(True, linestyle='--', alpha=0.3)
    ax1.set_title(f'Packing Factor: {packing_factor:.3f}\nL = {L:.3f}', 
                  pad=20, fontsize=10)

    ax2.clear()
    ax2.plot(l_values, packing_factors, 'b-', label='Packing Factor')
    ax2.set_xlim(2.01, 3.45)
    ax2.set_ylim(0, max(packing_factors) * 1.1 if packing_factors else 5)
    ax2.set_xlabel('L Value')
    ax2.set_ylabel('Packing Factor')
    ax2.grid(True, linestyle='--', alpha=0.3)
    ax2.set_title('Packing Factor vs L', pad=20, fontsize=10)
    
    plt.tight_layout()
    
    return packing_factor

fig = plt.figure(figsize=(12, 7), dpi=60)

def animate(frame):
    L = 2.01 + frame * (3.45 - 2.01) / 79
    plot_frame(L)

anim = FuncAnimation(fig, animate, frames=80, interval=100)
writer = animation.PillowWriter(fps=8)
anim.save('packing_animation.gif', writer=writer)

plt.close()