A camera with focal length f = 1000 pixels and principal point c = (320, 240) is calibrated to have intrinsic matrix K = [[1000, 0, 320], [0, 1000, 240], [0, 0, 1]]. A 3D point at world position P_w = (0.1, 0.05, 1.0) m (1 meter in front of the camera) projects onto the image at:
AImage pixel (420, 290)
BImage pixel (220, 190)
CImage pixel (320, 240) (the principal point)
DInsufficient information; need the extrinsic pose of the camera
This pipeline combines camera geometry, kinematics, and planning. Each step requires accurate calibration and computation. Errors in camera calibration propagate to errors in perceived 3D positions, degrading grasp success. This is why robots in manufacturing are carefully calibrated with hand-eye calibration (determining T_camera_to_base) as a critical setup step.