I want projection matrix for radar for that I need velo_to_cam (radar_to_cam). I need only for one radar with corresponding image only. The given radar extrinsic with respect to lidar and lidar extrinsic with respect to the World. I am using this formula to calculate velo_to_cam
import numpy as np
from pyquaternion import Quaternion
# Radar transformation details
radar_translation = np.array([2.422, 0.8, 0.78])
radar_rotation_quaternion = Quaternion([0.7028982997921758, 0.0, 0.0, 0.7112903627557937])
radar_rotation_matrix = radar_rotation_quaternion.rotation_matrix
radar_transformation_matrix = np.eye(4)
radar_transformation_matrix[:3, :3] = radar_rotation_matrix
radar_transformation_matrix[:3, 3] = radar_translation
# Camera transformation details
camera_translation = np.array([1.5752559464, 0.500519383135, 1.50696032589])
camera_rotation_quaternion = Quaternion([0.6812088525125634, -0.6687507165046241, 0.2101702448905517, -0.21108161122114324])
camera_rotation_matrix = camera_rotation_quaternion.rotation_matrix
camera_transformation_matrix = np.eye(4)
camera_transformation_matrix[:3, :3] = camera_rotation_matrix
camera_transformation_matrix[:3, 3] = camera_translation
# Lidar transformation details
lidar_translation = np.array([0.985793, 0.0, 1.84019])
lidar_rotation_quaternion = Quaternion([0.706749235646644, -0.015300993788500868, 0.01739745181256607, -0.7070846669051719])
lidar_rotation_matrix = lidar_rotation_quaternion.rotation_matrix
lidar_transformation_matrix = np.eye(4)
lidar_transformation_matrix[:3, :3] = lidar_rotation_matrix
lidar_transformation_matrix[:3, 3] = lidar_translation
# Compute combined transformation
combined_transformation_matrix = (np.linalg.inv(camera_transformation_matrix)) @ (np.linalg.inv(lidar_transformation_matrix)) @ (np.linalg.inv(radar_transformation_matrix))
print("Combined Transformation Matrix (4x4):\n", combined_transformation_matrix)
Finally projection matrix is
projection = np.dot(cam_int, combined_transformation_matrix)