将拉伸变形环形点云还原为原始圆形的变换方法求助

有一组由激光轮廓仪采集的环形点云（如图所示），当前呈现拉伸变形状态，仅已知该点云的XYZ坐标，希望将其变换还原为原始圆形。尝试了以下两种方法均未成功：

方法1 #

x_min = 0
x_max = 360
D = 1
        
x_coordinates = xyz[:, 1]
y_coordinates = xyz[:, 0]
z_coordinates = xyz[:, 2]
theta = (x_coordinates - x_min)/(x_max - x_min)*2*np.radians(180)
gamma = D - y_coordinates
x_round = gamma * np.cos(theta)
y_round = gamma * np.sin(theta)
z_round = z_coordinates
        
assert x_round.ndim == 1 and y_round.ndim == 1 and z_round.ndim == 1, "Arrays must be 1-dimensional"
points = np.stack((x_round, y_round, z_round), axis=-1)  # Stack arrays along a new axis to get Nx3
        
pcd = o3d.geometry.PointCloud()
pcd.points = o3d.utility.Vector3dVector(points)
o3d.visualization.draw_geometries([pcd], window_name="Original Shape")

方法2 #

def cart2sph(x, y, z):
   xy = np.sqrt(x**2 + y**2) # sqrt(x² + y²)
   x_2 = x**2
   y_2 = y**2
   z_2 = z**2
   r = np.sqrt(x_2 + y_2 + z_2) # r = sqrt(x² + y² + z²)
   theta = np.arctan2(y, x) 
   phi = np.arctan2(xy, z) 
   return r, theta, phi

内容的提问来源于stack exchange，提问作者José Alejandro Donate