import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
import mpmath as mp
import json
import sys

def visualize_spiral(node_list):
    plt.figure(figsize=(12, 12))
    
    # 绘制灰色螺旋线
    theta = np.linspace(0, node_list[0]["theta"], 1000)
    x = [Theta2Dot(t)[0] for t in theta]
    y = [Theta2Dot(t)[1] for t in theta]
    plt.plot(x, y, color='gray', linewidth=0.5)

    # 绘制节点和连接线
    for i in range(len(node_list) - 1):
        x1, y1 = node_list[i]["node"]
        x2, y2 = node_list[i+1]["node"]
        
        # 绘制红色节点
        plt.plot(x1, y1, 'ro', markersize=3)
        
        # 绘制蓝色连接线
        plt.plot([x1, x2], [y1, y2], 'b-', linewidth=0.5)
        
        # 计算并绘制长方形
        dx = x2 - x1
        dy = y2 - y1
        length = np.sqrt(dx**2 + dy**2)
        angle = np.arctan2(dy, dx)
        
        rect_length = length + 0.55  # 0.275 * 2
        rect_width = 0.3
        
        rect_x = x1 - 0.275 * np.cos(angle)
        rect_y = y1 - 0.275 * np.sin(angle)
        
        rect = Rectangle((rect_x, rect_y), rect_length, rect_width,
                         angle=angle*180/np.pi, fill=False, edgecolor='g')
        plt.gca().add_patch(rect)

    plt.axis('equal')
    plt.title(f"Spiral visualization at time={time_point}")
    plt.show()

content=json.load(sys.stdin)
visualize_spiral(content)