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You can use cv::projectpoints for this task:,%20InputArray%20rvec,%20InputArray%20tvec,%20InputArray%20cameraMatrix,%20InputArray%20distCoeffs,%20OutputArray%20imagePoints,%20OutputArray%20jacobian,%20double%20aspectRatio%29

The simplest way to use it is by passing the points in the coordinate frame of the camera and setting rvec and tvec to (0,0,0). Then just pass the intrinsic calibration and distortion and you get the projected points.