finish first path

A/4/testplot.py

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+import matplotlib.pyplot as plt
+import numpy as np
+
+kPitch = 1.7
+kAlpha = kPitch / (2 * np.pi)
+kCriticalRadius = 4.5
+
+theta_max = (kCriticalRadius) / kAlpha + 2*2*np.pi
+kPlotingRadius = theta_max  * kAlpha
+
+kCriticalTheta =  2.86 / ((2/3)*kAlpha)
+# 生成角度数组
+theta = np.linspace(kCriticalTheta, theta_max, 1000)
+
+# 根据等距螺旋方程计算半径
+r1 = kAlpha * theta
+r2 = kAlpha * theta  # 半径保持正值
+
+# 为第二只螺旋添加相位偏移
+theta2 = theta + np.pi  # 角度偏移π
+
+# 创建图形
+plt.figure()
+ax = plt.subplot(projection='polar')  # 使用极坐标系
+
+# 绘制第一只螺旋
+ax.plot(theta, r1)
+
+# 绘制中心对称的另一只螺旋
+ax.plot(theta2, r2)
+
+# 绘制半径为4.5的圆
+circle_theta = np.linspace(0, 2 * np.pi, 1000)
+circle_r = np.full_like(circle_theta, kCriticalRadius)
+ax.plot(circle_theta, circle_r, linestyle='--')
+
+point_A_cartesian = (kAlpha*kCriticalTheta*np.cos(kCriticalTheta),kAlpha*kCriticalTheta*np.sin(kCriticalTheta))
+point_B_cartesian = (-kAlpha*kCriticalTheta*np.cos(kCriticalTheta),-kAlpha*kCriticalTheta*np.sin(kCriticalTheta))
+kPhi = np.arctan(kCriticalTheta)
+r = (1/3) * kAlpha * np.sqrt(1 + kCriticalTheta**2)
+dx, dy = point_A_cartesian[0] - point_B_cartesian[0], point_A_cartesian[1] - point_B_cartesian[1]
+angle = np.arctan2(dy, dx)
+dx, dy = np.cos(angle - (0.5*np.pi-kPhi)), np.sin(angle - (0.5*np.pi-kPhi))
+point_C1_cartesian = (point_A_cartesian[0] - 2*r*dx, point_A_cartesian[1] - 2*r*dy)
+point_C2_cartesian = (point_B_cartesian[0] + 1*r*dx, point_B_cartesian[1] + 1*r*dy)
+radius_of_C1 = 2*r
+radius_of_C2 = 1*r
+
+# 定义用于绘制圆的函数
+def draw_circle(ax, center, radius, num_points, beg_angle, span_angle):
+    t = np.linspace(beg_angle, beg_angle+span_angle, num_points)
+    x = center[0] + radius * np.cos(t)
+    y = center[1] + radius * np.sin(t)
+    r, theta = np.sqrt(x**2 + y**2), np.arctan2(y, x)
+    ax.plot(theta, r)
+
+# 绘制圆C1
+draw_circle(ax, point_C1_cartesian, radius_of_C1, 100, angle+0.5*np.pi-kPhi-np.pi, 2*kPhi)
+
+# 绘制圆C2
+draw_circle(ax, point_C2_cartesian, radius_of_C2, 100, angle+0.5*np.pi-kPhi, 2*kPhi)
+
+print(f"Total length={6*r*kPhi}")
+
+x_ticks = np.arange(-int(kPlotingRadius)-1, int(kPlotingRadius)+1, 1)
+y_ticks = np.arange(-int(kPlotingRadius)-1, int(kPlotingRadius)+1, 1)
+X, Y = np.meshgrid(x_ticks, y_ticks)
+X = X.flatten()
+Y = Y.flatten()
+
+# 将网格点转换为极坐标
+r_grid = np.sqrt(X**2 + Y**2)
+theta_grid = np.arctan2(Y, X)
+
+# 仅绘制半径不超过kPlotingRadius的点
+valid_points = r_grid <= kPlotingRadius
+ax.scatter(theta_grid[valid_points], r_grid[valid_points], color='red', s=10)  # 红色小点
+
+plt.title("The Moving Path")
+
+# 显示图像
+plt.show()