[Python] How to get the projection matrix of Orbbec Gemini 2XL RGB camera and align it with a...

I’m using an Orbbec Gemini 2XL RGB-D camera and a 3D LiDAR. The camera is positioned 8 cm above and 1 cm behind the LiDAR’s center.

1. 
   The SDK datasheet gives a formula to compute the camera’s projection matrix from intrinsics. Is this the standard approach, or is there a better way?
   
   
2. 
   How do I build the extrinsic transformation matrix between the LiDAR and camera using this physical offset?
   
   
3. 
   Assuming no rotation, can I model it as a simple translation?
   
   
4. 
   How do I correctly transform LiDAR points to the camera frame and project them onto the RGB image?
   

Thanks for any help!

I tried calculating matrices but can’t get projection right

P0: 596.8097 0.0000 640.0000 0.0000 0.0000 593.0244 400.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 1.0000 Tr_lidar_to_cam: 1.00 0.00 0.00 0.00 0.00 0.00 1.00 -0.08 0.00 0.00 1.00 0.00 0.00 0.00 0.00 1.00

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