projectPoints functionality question

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So if I understand you correctly, I just need to rotate and translate the axis using rvecs and tvecs, and that should be what I need.

The problem is, I use solvePnP to get the rotation and translation for a face. And I draw an axis on the face and use projectPoints to draw it on the image plane. I want to find the world coordinates of the axis after its rotated. What I did was find the rotation matrix using Rodrigues, and do rotation_matrix*axis_point + tvec. And then used projectPoints to project the result of that onto the image plane (passing identity matrix and zero matrix for rotation, tvec respectively). But the result of that was different than what I got from just using projectPoints normally. Why is that?

It should be the same result:

  cv::Mat K = (cv::Mat_<double>(3,3) <<
      700, 0, 320,
      0, 700, 240,
      0, 0, 1);

  double theta = 24.0 * M_PI / 180.0;
  cv::Mat rvec = (cv::Mat_<double>(3,1) <<
      0.4, 0.2, 0.8944) * theta;
  cv::Mat R;
  cv::Rodrigues(rvec, R);    

  cv::Mat tvec = (cv::Mat_<double>(3,1) <<
        0.5, 0.38, 1.4);    

  cv::Mat mat_point_x = (cv::Mat_<double>(3,1) <<
      1, 0, 0);

  std::vector<cv::Point3f> object_points;
  cv::Point3f object_point_x(1, 0, 0);
  object_points.push_back(object_point_x);
  std::vector<cv::Point2f> image_points;

Code:

cv::projectPoints(object_points, rvec, tvec, K, cv::noArray(), image_points);

  std::cout << "image_point_x=" << image_points.front() << std::endl;

  cv::Mat cam_image_point_x = R * mat_point_x + tvec;
  cv::Point3f cam_image_point_x2(
      cam_image_point_x.at<double>(0), cam_image_point_x.at<double>(1), cam_image_point_x.at<double>(2));
  object_points.clear();
  object_points.push_back(cam_image_point_x2);

  image_points.clear();
  cv::projectPoints(object_points, cv::Mat::eye(3, 3, CV_64F), cv::Mat::zeros(3,1,CV_64F), K, cv::noArray(), image_points);
  std::cout << "image_point_x_2=" << image_points.front() << std::endl;

Got it, thanks!